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.

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.

Replicator equations, maximal cliques, and graph isomorphism.

PubMed

Pelillo, M

1999-11-15

We present a new energy-minimization framework for the graph isomorphism problem that is based on an equivalent maximum clique formulation. The approach is centered around a fundamental result proved by Motzkin and Straus in the mid-1960s, and recently expanded in various ways, which allows us to formulate the maximum clique problem in terms of a standard quadratic program. The attractive feature of this formulation is that a clear one-to-one correspondence exists between the solutions of the quadratic program and those in the original, combinatorial problem. To solve the program we use the so-called replicator equations--a class of straightforward continuous- and discrete-time dynamical systems developed in various branches of theoretical biology. We show how, despite their inherent inability to escape from local solutions, they nevertheless provide experimental results that are competitive with those obtained using more elaborate mean-field annealing heuristics.

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)

Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach

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

Pham, Huyên, E-mail: pham@math.univ-paris-diderot.fr; Wei, Xiaoli, E-mail: tyswxl@gmail.com

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.

A Comparison of Approaches for Solving Hard Graph-Theoretic Problems

DTIC Science & Technology

2015-04-29

can be converted to a quadratic unconstrained binary optimization ( QUBO ) problem that uses 0/1-valued variables, and so they are often used...Frontiers in Physics, 2:5 (12 Feb 2014). [7] “Programming with QUBOs ,” (instructional document) D-Wave: The Quantum Computing Company, 2013. [8

Quantum optimization for training support vector machines.

PubMed

Anguita, Davide; Ridella, Sandro; Rivieccio, Fabio; Zunino, Rodolfo

2003-01-01

Refined concepts, such as Rademacher estimates of model complexity and nonlinear criteria for weighting empirical classification errors, represent recent and promising approaches to characterize the generalization ability of Support Vector Machines (SVMs). The advantages of those techniques lie in both improving the SVM representation ability and yielding tighter generalization bounds. On the other hand, they often make Quadratic-Programming algorithms no longer applicable, and SVM training cannot benefit from efficient, specialized optimization techniques. The paper considers the application of Quantum Computing to solve the problem of effective SVM training, especially in the case of digital implementations. The presented research compares the behavioral aspects of conventional and enhanced SVMs; experiments in both a synthetic and real-world problems support the theoretical analysis. At the same time, the related differences between Quadratic-Programming and Quantum-based optimization techniques are considered.

Estimation of positive semidefinite correlation matrices by using convex quadratic semidefinite programming.

PubMed

Fushiki, Tadayoshi

2009-07-01

The correlation matrix is a fundamental statistic that is used in many fields. For example, GroupLens, a collaborative filtering system, uses the correlation between users for predictive purposes. Since the correlation is a natural similarity measure between users, the correlation matrix may be used in the Gram matrix in kernel methods. However, the estimated correlation matrix sometimes has a serious defect: although the correlation matrix is originally positive semidefinite, the estimated one may not be positive semidefinite when not all ratings are observed. To obtain a positive semidefinite correlation matrix, the nearest correlation matrix problem has recently been studied in the fields of numerical analysis and optimization. However, statistical properties are not explicitly used in such studies. To obtain a positive semidefinite correlation matrix, we assume the approximate model. By using the model, an estimate is obtained as the optimal point of an optimization problem formulated with information on the variances of the estimated correlation coefficients. The problem is solved by a convex quadratic semidefinite program. A penalized likelihood approach is also examined. The MovieLens data set is used to test our approach.

Conic Sampling: An Efficient Method for Solving Linear and Quadratic Programming by Randomly Linking Constraints within the Interior

PubMed Central

Serang, Oliver

2012-01-01

Linear programming (LP) problems are commonly used in analysis and resource allocation, frequently surfacing as approximations to more difficult problems. Existing approaches to LP have been dominated by a small group of methods, and randomized algorithms have not enjoyed popularity in practice. This paper introduces a novel randomized method of solving LP problems by moving along the facets and within the interior of the polytope along rays randomly sampled from the polyhedral cones defined by the bounding constraints. This conic sampling method is then applied to randomly sampled LPs, and its runtime performance is shown to compare favorably to the simplex and primal affine-scaling algorithms, especially on polytopes with certain characteristics. The conic sampling method is then adapted and applied to solve a certain quadratic program, which compute a projection onto a polytope; the proposed method is shown to outperform the proprietary software Mathematica on large, sparse QP problems constructed from mass spectometry-based proteomics. PMID:22952741

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.

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…

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

Zamzam, Ahmed, S.; Zhaoy, Changhong; Dall'Anesey, Emiliano

This paper examines the AC Optimal Power Flow (OPF) problem for multiphase distribution networks featuring renewable energy resources (RESs). We start by outlining a power flow model for radial multiphase systems that accommodates wye-connected and delta-connected RESs and non-controllable energy assets. We then formalize an AC OPF problem that accounts for both types of connections. Similar to various AC OPF renditions, the resultant problem is a non convex quadratically-constrained quadratic program. However, the so-called Feasible Point Pursuit-Successive Convex Approximation algorithm is leveraged to obtain a feasible and yet locally-optimal solution. The merits of the proposed solution approach are demonstrated usingmore » two unbalanced multiphase distribution feeders with both wye and delta connections.« less

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…

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…

Design of reinforced areas of concrete column using quadratic polynomials

NASA Astrophysics Data System (ADS)

Arif Gunadi, Tjiang; Parung, Herman; Rachman Djamaluddin, Abd; Arwin Amiruddin, A.

2017-11-01

Designing of reinforced concrete columns mostly carried out by a simple planning method which uses column interaction diagram. However, the application of this method is limited because it valids only for certain compressive strenght of the concrete and yield strength of the reinforcement. Thus, a more applicable method is still in need. Another method is the use of quadratic polynomials as a basis for the approach in designing reinforced concrete columns, where the ratio of neutral lines to the effective height of a cross section (ξ) if associated with ξ in the same cross-section with different reinforcement ratios is assumed to form a quadratic polynomial. This is identical to the basic principle used in the Simpson rule for numerical integral using quadratic polynomials and had a sufficiently accurate level of accuracy. The basis of this approach to be used both the normal force equilibrium and the moment equilibrium. The abscissa of the intersection of the two curves is the ratio that had been mentioned, since it fulfill both of the equilibrium. The application of this method is relatively more complicated than the existing method but provided with tables and graphs (N vs ξN ) and (M vs ξM ) so that its used could be simplified. The uniqueness of these tables are only distinguished based on the compresssive strength of the concrete, so in application it could be combined with various yield strenght of the reinforcement available in the market. This method could be solved by using programming languages such as Fortran.

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.

Item Pool Construction Using Mixed Integer Quadratic Programming (MIQP). GMAC® Research Report RR-14-01

ERIC Educational Resources Information Center

Han, Kyung T.; Rudner, Lawrence M.

2014-01-01

This study uses mixed integer quadratic programming (MIQP) to construct multiple highly equivalent item pools simultaneously, and compares the results from mixed integer programming (MIP). Three different MIP/MIQP models were implemented and evaluated using real CAT item pool data with 23 different content areas and a goal of equal information…

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)

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…

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…

The reduced space Sequential Quadratic Programming (SQP) method for calculating the worst resonance response of nonlinear systems

NASA Astrophysics Data System (ADS)

Liao, Haitao; Wu, Wenwang; Fang, Daining

2018-07-01

A coupled approach combining the reduced space Sequential Quadratic Programming (SQP) method with the harmonic balance condensation technique for finding the worst resonance response is developed. The nonlinear equality constraints of the optimization problem are imposed on the condensed harmonic balance equations. Making use of the null space decomposition technique, the original optimization formulation in the full space is mathematically simplified, and solved in the reduced space by means of the reduced SQP method. The transformation matrix that maps the full space to the null space of the constrained optimization problem is constructed via the coordinate basis scheme. The removal of the nonlinear equality constraints is accomplished, resulting in a simple optimization problem subject to bound constraints. Moreover, second order correction technique is introduced to overcome Maratos effect. The combination application of the reduced SQP method and condensation technique permits a large reduction of the computational cost. Finally, the effectiveness and applicability of the proposed methodology is demonstrated by two numerical examples.

A Factorization Approach to the Linear Regulator Quadratic Cost Problem

NASA Technical Reports Server (NTRS)

Milman, M. H.

1985-01-01

A factorization approach to the linear regulator quadratic cost problem is developed. This approach makes some new connections between optimal control, factorization, Riccati equations and certain Wiener-Hopf operator equations. Applications of the theory to systems describable by evolution equations in Hilbert space and differential delay equations in Euclidean space are presented.

Hyperspectral and multispectral data fusion based on linear-quadratic nonnegative matrix factorization

NASA Astrophysics Data System (ADS)

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

2017-04-01

This paper proposes three multisharpening approaches to enhance the spatial resolution of urban hyperspectral remote sensing images. These approaches, related to linear-quadratic spectral unmixing techniques, use a linear-quadratic nonnegative matrix factorization (NMF) multiplicative algorithm. These methods begin by unmixing the observable high-spectral/low-spatial resolution hyperspectral and high-spatial/low-spectral resolution multispectral images. The obtained high-spectral/high-spatial resolution features are then recombined, according to the linear-quadratic mixing model, to obtain an unobservable multisharpened high-spectral/high-spatial resolution hyperspectral image. In the first designed approach, hyperspectral and multispectral variables are independently optimized, once they have been coherently initialized. These variables are alternately updated in the second designed approach. In the third approach, the considered hyperspectral and multispectral variables are jointly updated. Experiments, using synthetic and real data, are conducted to assess the efficiency, in spatial and spectral domains, of the designed approaches and of linear NMF-based approaches from the literature. Experimental results show that the designed methods globally yield very satisfactory spectral and spatial fidelities for the multisharpened hyperspectral data. They also prove that these methods significantly outperform the used literature approaches.

Optimal Link Removal for Epidemic Mitigation: A Two-Way Partitioning Approach

PubMed Central

Enns, Eva A.; Mounzer, Jeffrey J.; Brandeau, Margaret L.

2011-01-01

The structure of the contact network through which a disease spreads may influence the optimal use of resources for epidemic control. In this work, we explore how to minimize the spread of infection via quarantining with limited resources. In particular, we examine which links should be removed from the contact network, given a constraint on the number of removable links, such that the number of nodes which are no longer at risk for infection is maximized. We show how this problem can be posed as a non-convex quadratically constrained quadratic program (QCQP), and we use this formulation to derive a link removal algorithm. The performance of our QCQP-based algorithm is validated on small Erdős-Renyi and small-world random graphs, and then tested on larger, more realistic networks, including a real-world network of injection drug use. We show that our approach achieves near optimal performance and out-perform so ther intuitive link removal algorithms, such as removing links in order of edge centrality. PMID:22115862

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 numerical approach to solve Thomas-Fermi model of an atom using bio-inspired heuristics integrated with sequential quadratic programming.

PubMed

Raja, Muhammad Asif Zahoor; Zameer, Aneela; Khan, Aziz Ullah; Wazwaz, Abdul Majid

2016-01-01

In this study, a novel bio-inspired computing approach is developed to analyze the dynamics of nonlinear singular Thomas-Fermi equation (TFE) arising in potential and charge density models of an atom by exploiting the strength of finite difference scheme (FDS) for discretization and optimization through genetic algorithms (GAs) hybrid with sequential quadratic programming. The FDS procedures are used to transform the TFE differential equations into a system of nonlinear equations. A fitness function is constructed based on the residual error of constituent equations in the mean square sense and is formulated as the minimization problem. Optimization of parameters for the system is carried out with GAs, used as a tool for viable global search integrated with SQP algorithm for rapid refinement of the results. The design scheme is applied to solve TFE for five different scenarios by taking various step sizes and different input intervals. Comparison of the proposed results with the state of the art numerical and analytical solutions reveals that the worth of our scheme in terms of accuracy and convergence. The reliability and effectiveness of the proposed scheme are validated through consistently getting optimal values of statistical performance indices calculated for a sufficiently large number of independent runs to establish its significance.

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

ERIC Educational Resources Information Center

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

2012-01-01

Two Monte Carlo simulations were performed to compare methods for estimating and testing hypotheses of quadratic effects in latent variable regression models. The methods considered in the current study were (a) a 2-stage moderated regression approach using latent variable scores, (b) an unconstrained product indicator approach, (c) a latent…

A Comparison of Trajectory Optimization Methods for the Impulsive Minimum Fuel Rendezvous Problem

NASA Technical Reports Server (NTRS)

Hughes, Steven P.; Mailhe, Laurie M.; Guzman, Jose J.

2002-01-01

In this paper we present a comparison of optimization approaches to the minimum fuel rendezvous problem. Both indirect and direct methods are compared for a variety of test cases. The indirect approach is based on primer vector theory. The direct approaches are implemented numerically and include Sequential Quadratic Programming (SQP), Quasi-Newton, Simplex, Genetic Algorithms, and Simulated Annealing. Each method is applied to a variety of test cases including, circular to circular coplanar orbits, LEO to GEO, and orbit phasing in highly elliptic orbits. We also compare different constrained optimization routines on complex orbit rendezvous problems with complicated, highly nonlinear constraints.

Exploring quantum computing application to satellite data assimilation

NASA Astrophysics Data System (ADS)

Cheung, S.; Zhang, S. Q.

2015-12-01

This is an exploring work on potential application of quantum computing to a scientific data optimization problem. On classical computational platforms, the physical domain of a satellite data assimilation problem is represented by a discrete variable transform, and classical minimization algorithms are employed to find optimal solution of the analysis cost function. The computation becomes intensive and time-consuming when the problem involves large number of variables and data. The new quantum computer opens a very different approach both in conceptual programming and in hardware architecture for solving optimization problem. In order to explore if we can utilize the quantum computing machine architecture, we formulate a satellite data assimilation experimental case in the form of quadratic programming optimization problem. We find a transformation of the problem to map it into Quadratic Unconstrained Binary Optimization (QUBO) framework. Binary Wavelet Transform (BWT) will be applied to the data assimilation variables for its invertible decomposition and all calculations in BWT are performed by Boolean operations. The transformed problem will be experimented as to solve for a solution of QUBO instances defined on Chimera graphs of the quantum computer.

A path following algorithm for the graph matching problem.

PubMed

Zaslavskiy, Mikhail; Bach, Francis; Vert, Jean-Philippe

2009-12-01

We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We, therefore, construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore, perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four data sets: simulated graphs, QAPLib, retina vessel images, and handwritten Chinese characters. In all cases, the results are competitive with the state of the art.

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

A linear quadratic regulator approach to the stabilization of uncertain linear systems

NASA Technical Reports Server (NTRS)

Shieh, L. S.; Sunkel, J. W.; Wang, Y. J.

1990-01-01

This paper presents a linear quadratic regulator approach to the stabilization of uncertain linear systems. The uncertain systems under consideration are described by state equations with the presence of time-varying unknown-but-bounded uncertainty matrices. The method is based on linear quadratic regulator (LQR) theory and Liapunov stability theory. The robust stabilizing control law for a given uncertain system can be easily constructed from the symmetric positive-definite solution of the associated augmented Riccati equation. The proposed approach can be applied to matched and/or mismatched systems with uncertainty matrices in which only their matrix norms are bounded by some prescribed values and/or their entries are bounded by some prescribed constraint sets. Several numerical examples are presented to illustrate the results.

Evaluating the effects of real power losses in optimal power flow based storage integration

DOE PAGES

Castillo, Anya; Gayme, Dennice

2017-03-27

This study proposes a DC optimal power flow (DCOPF) with losses formulation (the `-DCOPF+S problem) and uses it to investigate the role of real power losses in OPF based grid-scale storage integration. We derive the `- DCOPF+S problem by augmenting a standard DCOPF with storage (DCOPF+S) problem to include quadratic real power loss approximations. This procedure leads to a multi-period nonconvex quadratically constrained quadratic program, which we prove can be solved to optimality using either a semidefinite or second order cone relaxation. Our approach has some important benefits over existing models. It is more computationally tractable than ACOPF with storagemore » (ACOPF+S) formulations and the provably exact convex relaxations guarantee that an optimal solution can be attained for a feasible problem. Adding loss approximations to a DCOPF+S model leads to a more accurate representation of locational marginal prices, which have been shown to be critical to determining optimal storage dispatch and siting in prior ACOPF+S based studies. Case studies demonstrate the improved accuracy of the `-DCOPF+S model over a DCOPF+S model and the computational advantages over an ACOPF+S formulation.« less

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

Expected value based fuzzy programming approach to solve integrated supplier selection and inventory control problem with fuzzy demand

NASA Astrophysics Data System (ADS)

Sutrisno; Widowati; Sunarsih; Kartono

2018-01-01

In this paper, a mathematical model in quadratic programming with fuzzy parameter is proposed to determine the optimal strategy for integrated inventory control and supplier selection problem with fuzzy demand. To solve the corresponding optimization problem, we use the expected value based fuzzy programming. Numerical examples are performed to evaluate the model. From the results, the optimal amount of each product that have to be purchased from each supplier for each time period and the optimal amount of each product that have to be stored in the inventory for each time period were determined with minimum total cost and the inventory level was sufficiently closed to the reference level.

Reduction of shock induced noise in imperfectly expanded supersonic jets using convex optimization

NASA Astrophysics Data System (ADS)

Adhikari, Sam

2007-11-01

Imperfectly expanded jets generate screech noise. The imbalance between the backpressure and the exit pressure of the imperfectly expanded jets produce shock cells and expansion or compression waves from the nozzle. The instability waves and the shock cells interact to generate the screech sound. The mathematical model consists of cylindrical coordinate based full Navier-Stokes equations and large-eddy-simulation turbulence modeling. Analytical and computational analysis of the three-dimensional helical effects provide a model that relates several parameters with shock cell patterns, screech frequency and distribution of shock generation locations. Convex optimization techniques minimize the shock cell patterns and the instability waves. The objective functions are (convex) quadratic and the constraint functions are affine. In the quadratic optimization programs, minimization of the quadratic functions over a set of polyhedrons provides the optimal result. Various industry standard methods like regression analysis, distance between polyhedra, bounding variance, Markowitz optimization, and second order cone programming is used for Quadratic Optimization.

Advanced Nonlinear Latent Variable Modeling: Distribution Analytic LMS and QML Estimators of Interaction and Quadratic Effects

ERIC Educational Resources Information Center

Kelava, Augustin; Werner, Christina S.; Schermelleh-Engel, Karin; Moosbrugger, Helfried; Zapf, Dieter; Ma, Yue; Cham, Heining; Aiken, Leona S.; West, Stephen G.

2011-01-01

Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x[superscript 2] [subscript 1], x[subscript 1]x[subscript 4]) to serve as indicators of each nonlinear latent construct. These approaches require the use of…

Modelling biochemical reaction systems by stochastic differential equations with reflection.

PubMed

Niu, Yuanling; Burrage, Kevin; Chen, Luonan

2016-05-07

In this paper, we gave a new framework for modelling and simulating biochemical reaction systems by stochastic differential equations with reflection not in a heuristic way but in a mathematical way. The model is computationally efficient compared with the discrete-state Markov chain approach, and it ensures that both analytic and numerical solutions remain in a biologically plausible region. Specifically, our model mathematically ensures that species numbers lie in the domain D, which is a physical constraint for biochemical reactions, in contrast to the previous models. The domain D is actually obtained according to the structure of the corresponding chemical Langevin equations, i.e., the boundary is inherent in the biochemical reaction system. A variant of projection method was employed to solve the reflected stochastic differential equation model, and it includes three simple steps, i.e., Euler-Maruyama method was applied to the equations first, and then check whether or not the point lies within the domain D, and if not perform an orthogonal projection. It is found that the projection onto the closure D¯ is the solution to a convex quadratic programming problem. Thus, existing methods for the convex quadratic programming problem can be employed for the orthogonal projection map. Numerical tests on several important problems in biological systems confirmed the efficiency and accuracy of this approach. Copyright © 2016 Elsevier Ltd. All rights reserved.

PIFCGT: A PIF autopilot design program for general aviation aircraft

NASA Technical Reports Server (NTRS)

Broussard, J. R.

1983-01-01

This report documents the PIFCGT computer program. In FORTRAN, PIFCGT is a computer design aid for determing Proportional-Integral-Filter (PIF) control laws for aircraft autopilots implemented with a Command Generator Tracker (CGT). The program uses Linear-Quadratic-Regulator synthesis algorithms to determine feedback gains, and includes software to solve the feedforward matrix equation which is useful in determining the command generator tracker feedforward gains. The program accepts aerodynamic stability derivatives and computes the corresponding aerodynamic linear model. The nine autopilot modes that can be designed include four maneuver modes (ROLL SEL, PITCH SEL, HDG SEL, ALT SEL), four final approach models (APR GS, APR LOCI, APR LOCR, APR LOCP), and a BETA HOLD mode. The program has been compiled and executed on a CDC computer.

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

NASA Technical Reports Server (NTRS)

Thompson, P. M.

1980-01-01

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 to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalue and the directional derivatives of closed loop eigenvectors. An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, 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. An algorithm is presented that can be used to select a feedback gain matrix for the linear state feedback problem which produces a specified asymptotic eigenstructure. Another algorithm is given to compute the asymptotic eigenstructure properties inherent in a given set of quadratic weights. Finally, it is shown that optimal root loci for nongeneric problems can be approximated by generic ones in the nonasymptotic region.

Homotopy approach to optimal, linear quadratic, fixed architecture compensation

NASA Technical Reports Server (NTRS)

Mercadal, Mathieu

1991-01-01

Optimal linear quadratic Gaussian compensators with constrained architecture are a sensible way to generate good multivariable feedback systems meeting strict implementation requirements. The optimality conditions obtained from the constrained linear quadratic Gaussian are a set of highly coupled matrix equations that cannot be solved algebraically except when the compensator is centralized and full order. An alternative to the use of general parameter optimization methods for solving the problem is to use homotopy. The benefit of the method is that it uses the solution to a simplified problem as a starting point and the final solution is then obtained by solving a simple differential equation. This paper investigates the convergence properties and the limitation of such an approach and sheds some light on the nature and the number of solutions of the constrained linear quadratic Gaussian problem. It also demonstrates the usefulness of homotopy on an example of an optimal decentralized compensator.

Automation of reverse engineering process in aircraft modeling and related optimization problems

NASA Technical Reports Server (NTRS)

Li, W.; Swetits, J.

1994-01-01

During the year of 1994, the engineering problems in aircraft modeling were studied. The initial concern was to obtain a surface model with desirable geometric characteristics. Much of the effort during the first half of the year was to find an efficient way of solving a computationally difficult optimization model. Since the smoothing technique in the proposal 'Surface Modeling and Optimization Studies of Aerodynamic Configurations' requires solutions of a sequence of large-scale quadratic programming problems, it is important to design algorithms that can solve each quadratic program in a few interactions. This research led to three papers by Dr. W. Li, which were submitted to SIAM Journal on Optimization and Mathematical Programming. Two of these papers have been accepted for publication. Even though significant progress has been made during this phase of research and computation times was reduced from 30 min. to 2 min. for a sample problem, it was not good enough for on-line processing of digitized data points. After discussion with Dr. Robert E. Smith Jr., it was decided not to enforce shape constraints in order in order to simplify the model. As a consequence, P. Dierckx's nonparametric spline fitting approach was adopted, where one has only one control parameter for the fitting process - the error tolerance. At the same time the surface modeling software developed by Imageware was tested. Research indicated a substantially improved fitting of digitalized data points can be achieved if a proper parameterization of the spline surface is chosen. A winning strategy is to incorporate Dierckx's surface fitting with a natural parameterization for aircraft parts. The report consists of 4 chapters. Chapter 1 provides an overview of reverse engineering related to aircraft modeling and some preliminary findings of the effort in the second half of the year. Chapters 2-4 are the research results by Dr. W. Li on penalty functions and conjugate gradient methods for quadratic programming problems.

Optimization by nonhierarchical asynchronous decomposition

NASA Technical Reports Server (NTRS)

Shankar, Jayashree; Ribbens, Calvin J.; Haftka, Raphael T.; Watson, Layne T.

1992-01-01

Large scale optimization problems are tractable only if they are somehow decomposed. Hierarchical decompositions are inappropriate for some types of problems and do not parallelize well. Sobieszczanski-Sobieski has proposed a nonhierarchical decomposition strategy for nonlinear constrained optimization that is naturally parallel. Despite some successes on engineering problems, the algorithm as originally proposed fails on simple two dimensional quadratic programs. The algorithm is carefully analyzed for quadratic programs, and a number of modifications are suggested to improve its robustness.

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.

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.

Mixed Integer Programming and Heuristic Scheduling for Space Communication Networks

NASA Technical Reports Server (NTRS)

Cheung, Kar-Ming; Lee, Charles H.

2012-01-01

We developed framework and the mathematical formulation for optimizing communication network using mixed integer programming. The design yields a system that is much smaller, in search space size, when compared to the earlier approach. Our constrained network optimization takes into account the dynamics of link performance within the network along with mission and operation requirements. A unique penalty function is introduced to transform the mixed integer programming into the more manageable problem of searching in a continuous space. The constrained optimization problem was proposed to solve in two stages: first using the heuristic Particle Swarming Optimization algorithm to get a good initial starting point, and then feeding the result into the Sequential Quadratic Programming algorithm to achieve the final optimal schedule. We demonstrate the above planning and scheduling methodology with a scenario of 20 spacecraft and 3 ground stations of a Deep Space Network site. Our approach and framework have been simple and flexible so that problems with larger number of constraints and network can be easily adapted and solved.

Robust Finite-Dimensional LQG (Linear Quadric Gaussian)-Based Controllers for a Class of Distributed Parameter Systems.

DTIC Science & Technology

1988-06-01

abilities when I lost confidence. Without her help I would not have completed the program. Next, I wish to thank Dr. Peter Maybeck, my research ...being not only a resource for my research . but also for being a friend who listened when I needed a shoulder to cry on. Finally, I wish to give thanks...considered in this research are assumed to be linear quadratic Gaussian (LQG) based controllers. This research first uses a direct approach to

A Unified Approach to Teaching Quadratic and Cubic Equations.

ERIC Educational Resources Information Center

Ward, A. J. B.

2003-01-01

Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)

Learning quadratic receptive fields from neural responses to natural stimuli.

PubMed

Rajan, Kanaka; Marre, Olivier; Tkačik, Gašper

2013-07-01

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

One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations

NASA Astrophysics Data System (ADS)

Gomez, Humberto; Lopez-Arcos, Cristhiam; Talavera, Pedro

2017-10-01

In this paper we reconsider the Cachazo-He-Yuan construction (CHY) of the so called scattering amplitudes at one-loop, in order to obtain quadratic propagators. In theories with colour ordering the key ingredient is the redefinition of the Parke-Taylor factors. After classifying all the possible one-loop CHY-integrands we conjecture a new one-loop amplitude for the massless Bi-adjoint Φ3 theory. The prescription directly reproduces the quadratic propagators of the traditional Feynman approach.

A Generalization of the Karush-Kuhn-Tucker Theorem for Approximate Solutions of Mathematical Programming Problems Based on Quadratic Approximation

NASA Astrophysics Data System (ADS)

Voloshinov, V. V.

2018-03-01

In computations related to mathematical programming problems, one often has to consider approximate, rather than exact, solutions satisfying the constraints of the problem and the optimality criterion with a certain error. For determining stopping rules for iterative procedures, in the stability analysis of solutions with respect to errors in the initial data, etc., a justified characteristic of such solutions that is independent of the numerical method used to obtain them is needed. A necessary δ-optimality condition in the smooth mathematical programming problem that generalizes the Karush-Kuhn-Tucker theorem for the case of approximate solutions is obtained. The Lagrange multipliers corresponding to the approximate solution are determined by solving an approximating quadratic programming problem.

Unravelling Student Challenges with Quadratics: A Cognitive Approach

ERIC Educational Resources Information Center

Kotsopoulos, Donna

2007-01-01

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

Controller design approach based on linear programming.

PubMed

Tanaka, Ryo; Shibasaki, Hiroki; Ogawa, Hiromitsu; Murakami, Takahiro; Ishida, Yoshihisa

2013-11-01

This study explains and demonstrates the design method for a control system with a load disturbance observer. Observer gains are determined by linear programming (LP) in terms of the Routh-Hurwitz stability criterion and the final-value theorem. In addition, the control model has a feedback structure, and feedback gains are determined to be the linear quadratic regulator. The simulation results confirmed that compared with the conventional method, the output estimated by our proposed method converges to a reference input faster when a load disturbance is added to a control system. In addition, we also confirmed the effectiveness of the proposed method by performing an experiment with a DC motor. © 2013 ISA. Published by ISA. All rights reserved.

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.

A neural network approach to job-shop scheduling.

PubMed

Zhou, D N; Cherkassky, V; Baldwin, T R; Olson, D E

1991-01-01

A novel analog computational network is presented for solving NP-complete constraint satisfaction problems, i.e. job-shop scheduling. In contrast to most neural approaches to combinatorial optimization based on quadratic energy cost function, the authors propose to use linear cost functions. As a result, the network complexity (number of neurons and the number of resistive interconnections) grows only linearly with problem size, and large-scale implementations become possible. The proposed approach is related to the linear programming network described by D.W. Tank and J.J. Hopfield (1985), which also uses a linear cost function for a simple optimization problem. It is shown how to map a difficult constraint-satisfaction problem onto a simple neural net in which the number of neural processors equals the number of subjobs (operations) and the number of interconnections grows linearly with the total number of operations. Simulations show that the authors' approach produces better solutions than existing neural approaches to job-shop scheduling, i.e. the traveling salesman problem-type Hopfield approach and integer linear programming approach of J.P.S. Foo and Y. Takefuji (1988), in terms of the quality of the solution and the network complexity.

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…

Efficient dual approach to distance metric learning.

PubMed

Shen, Chunhua; Kim, Junae; Liu, Fayao; Wang, Lei; van den Hengel, Anton

2014-02-01

Distance metric learning is of fundamental interest in machine learning because the employed distance metric can significantly affect the performance of many learning methods. Quadratic Mahalanobis metric learning is a popular approach to the problem, but typically requires solving a semidefinite programming (SDP) problem, which is computationally expensive. The worst case complexity of solving an SDP problem involving a matrix variable of size D×D with O(D) linear constraints is about O(D(6.5)) using interior-point methods, where D is the dimension of the input data. Thus, the interior-point methods only practically solve problems exhibiting less than a few thousand variables. Because the number of variables is D(D+1)/2, this implies a limit upon the size of problem that can practically be solved around a few hundred dimensions. The complexity of the popular quadratic Mahalanobis metric learning approach thus limits the size of problem to which metric learning can be applied. Here, we propose a significantly more efficient and scalable approach to the metric learning problem based on the Lagrange dual formulation of the problem. The proposed formulation is much simpler to implement, and therefore allows much larger Mahalanobis metric learning problems to be solved. The time complexity of the proposed method is roughly O(D(3)), which is significantly lower than that of the SDP approach. Experiments on a variety of data sets demonstrate that the proposed method achieves an accuracy comparable with the state of the art, but is applicable to significantly larger problems. We also show that the proposed method can be applied to solve more general Frobenius norm regularized SDP problems approximately.

Memetic computing through bio-inspired heuristics integration with sequential quadratic programming for nonlinear systems arising in different physical models.

PubMed

Raja, Muhammad Asif Zahoor; Kiani, Adiqa Kausar; Shehzad, Azam; Zameer, Aneela

2016-01-01

In this study, bio-inspired computing is exploited for solving system of nonlinear equations using variants of genetic algorithms (GAs) as a tool for global search method hybrid with sequential quadratic programming (SQP) for efficient local search. The fitness function is constructed by defining the error function for systems of nonlinear equations in mean square sense. The design parameters of mathematical models are trained by exploiting the competency of GAs and refinement are carried out by viable SQP algorithm. Twelve versions of the memetic approach GA-SQP are designed by taking a different set of reproduction routines in the optimization process. Performance of proposed variants is evaluated on six numerical problems comprising of system of nonlinear equations arising in the interval arithmetic benchmark model, kinematics, neurophysiology, combustion and chemical equilibrium. Comparative studies of the proposed results in terms of accuracy, convergence and complexity are performed with the help of statistical performance indices to establish the worth of the schemes. Accuracy and convergence of the memetic computing GA-SQP is found better in each case of the simulation study and effectiveness of the scheme is further established through results of statistics based on different performance indices for accuracy and complexity.

Conservation of Mass and Preservation of Positivity with Ensemble-Type Kalman Filter Algorithms

NASA Technical Reports Server (NTRS)

Janjic, Tijana; Mclaughlin, Dennis; Cohn, Stephen E.; Verlaan, Martin

2014-01-01

This paper considers the incorporation of constraints to enforce physically based conservation laws in the ensemble Kalman filter. In particular, constraints are used to ensure that the ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. In certain situations filtering algorithms such as the ensemble Kalman filter (EnKF) and ensemble transform Kalman filter (ETKF) yield updated ensembles that conserve mass but are negative, even though the actual states must be nonnegative. In such situations if negative values are set to zero, or a log transform is introduced, the total mass will not be conserved. In this study, mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate non-negativity constraints. Simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. In two examples, an update that includes a non-negativity constraint is able to properly describe the transport of a sharp feature (e.g., a triangle or cone). A number of implementation questions still need to be addressed, particularly the need to develop a computationally efficient quadratic programming update for large ensemble.

Sequential Quadratic Programming Algorithms for Optimization

DTIC Science & Technology

1989-08-01

quadratic program- ma ng (SQ(2l ) aIiatain.seenis to be relgarded aIs tie( buest choice for the solution of smiall. dlense problema (see S tour L)toS...For the step along d, note that a < nOing + 3 szH + i3.ninA A a K f~Iz,;nd and from Id1 _< ,,, we must have that for some /3 , np , 11P11 < dn"p. 5.2...Nevertheless, many of these problems are considered hard to solve. Moreover, for some of these problems the assumptions made in Chapter 2 to establish the

Electromagnetic tracking system with reduced distortion using quadratic excitation.

PubMed

Bien, Tomasz; Li, Mengfei; Salah, Zein; Rose, Georg

2014-03-01

Electromagnetic tracking systems, frequently used in minimally invasive surgery, are affected by conductive distorters. The influence of conductive distorters on electromagnetic tracking system accuracy can be reduced through magnetic field modifications. This approach was developed and tested. The voltage induced directly by the emitting coil in the sensing coil without additional influence by the conductive distorter depends on the first derivative of the voltage on the emitting coil. The voltage which is induced indirectly by the emitting coil across the conductive distorter in the sensing coil, however, depends on the second derivative of the voltage on the emitting coil. The electromagnetic tracking system takes advantage of this difference by supplying the emitting coil with a quadratic excitation voltage. The method is adaptive relative to the amount of distortion cause by the conductive distorters. This approach is evaluated with an experimental setup of the electromagnetic tracking system. In vitro testing showed that the maximal error decreased from 10.9 to 3.8 mm when the quadratic voltage was used to excite the emitting coil instead of the sinusoidal voltage. Furthermore, the root mean square error in the proximity of the aluminum disk used as a conductive distorter was reduced from 3.5 to 1.6 mm when the electromagnetic tracking system used the quadratic instead of sinusoidal excitation. Electromagnetic tracking with quadratic excitation is immune to the effects of a conductive distorter, especially compared with sinusoidal excitation of the emitting coil. Quadratic excitation of electromagnetic tracking for computer-assisted surgery is promising for clinical applications.

Robust Weak Chimeras in Oscillator Networks with Delayed Linear and Quadratic Interactions

NASA Astrophysics Data System (ADS)

Bick, Christian; Sebek, Michael; Kiss, István Z.

2017-10-01

We present an approach to generate chimera dynamics (localized frequency synchrony) in oscillator networks with two populations of (at least) two elements using a general method based on a delayed interaction with linear and quadratic terms. The coupling design yields robust chimeras through a phase-model-based design of the delay and the ratio of linear and quadratic components of the interactions. We demonstrate the method in the Brusselator model and experiments with electrochemical oscillators. The technique opens the way to directly bridge chimera dynamics in phase models and real-world oscillator networks.

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.

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.

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.

Developing an Understanding of Quadratics through the Use of Concrete Manipulatives: A Case Study Analysis of the Metacognitive Development of a High School Student with Learning Disabilities

ERIC Educational Resources Information Center

Strickland, Tricia K.

2014-01-01

This case study analyzed the impact of a concrete manipulative program on the understanding of quadratic expressions for a high school student with a learning disability. The manipulatives were utilized as part of the Concrete-Representational-Abstract Integration (CRA-I) intervention in which participants engaged in tasks requiring them to…

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.

The Benefit of Interleaved Mathematics Practice Is Not Limited to Superficially Similar Kinds of Problems

ERIC Educational Resources Information Center

Rohrer, Doug; Dedrick, Robert F.; Burgess, Kaleena

2014-01-01

Most mathematics assignments consist of a group of problems requiring the same strategy. For example, a lesson on the quadratic formula is typically followed by a block of problems requiring students to use the quadratic formula, which means that students know the appropriate strategy before they read each problem. In an alternative approach,…

A Bayesian Model for the Estimation of Latent Interaction and Quadratic Effects When Latent Variables Are Non-Normally Distributed

ERIC Educational Resources Information Center

Kelava, Augustin; Nagengast, Benjamin

2012-01-01

Structural equation models with interaction and quadratic effects have become a standard tool for testing nonlinear hypotheses in the social sciences. Most of the current approaches assume normally distributed latent predictor variables. In this article, we present a Bayesian model for the estimation of latent nonlinear effects when the latent…

A model predictive speed tracking control approach for autonomous ground vehicles

NASA Astrophysics Data System (ADS)

Zhu, Min; Chen, Huiyan; Xiong, Guangming

2017-03-01

This paper presents a novel speed tracking control approach based on a model predictive control (MPC) framework for autonomous ground vehicles. A switching algorithm without calibration is proposed to determine the drive or brake control. Combined with a simple inverse longitudinal vehicle model and adaptive regulation of MPC, this algorithm can make use of the engine brake torque for various driving conditions and avoid high frequency oscillations automatically. A simplified quadratic program (QP) solving algorithm is used to reduce the computational time, and the approach has been applied in a 16-bit microcontroller. The performance of the proposed approach is evaluated via simulations and vehicle tests, which were carried out in a range of speed-profile tracking tasks. With a well-designed system structure, high-precision speed control is achieved. The system can robustly model uncertainty and external disturbances, and yields a faster response with less overshoot than a PI controller.

Path Following in the Exact Penalty Method of Convex Programming.

PubMed

Zhou, Hua; Lange, Kenneth

2015-07-01

Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value.

Path Following in the Exact Penalty Method of Convex Programming

PubMed Central

Zhou, Hua; Lange, Kenneth

2015-01-01

Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value. PMID:26366044

Pseudodynamic systems approach based on a quadratic approximation of update equations for diffuse optical tomography.

PubMed

Biswas, Samir Kumar; Kanhirodan, Rajan; Vasu, Ram Mohan; Roy, Debasish

2011-08-01

We explore a pseudodynamic form of the quadratic parameter update equation for diffuse optical tomographic reconstruction from noisy data. A few explicit and implicit strategies for obtaining the parameter updates via a semianalytical integration of the pseudodynamic equations are proposed. Despite the ill-posedness of the inverse problem associated with diffuse optical tomography, adoption of the quadratic update scheme combined with the pseudotime integration appears not only to yield higher convergence, but also a muted sensitivity to the regularization parameters, which include the pseudotime step size for integration. These observations are validated through reconstructions with both numerically generated and experimentally acquired data.

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.

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.

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.

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.

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.

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.

Neural network for solving convex quadratic bilevel programming problems.

PubMed

He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie

2014-03-01

In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network. Copyright © 2013 Elsevier Ltd. All rights reserved.

DE and NLP Based QPLS Algorithm

NASA Astrophysics Data System (ADS)

Yu, Xiaodong; Huang, Dexian; Wang, Xiong; Liu, Bo

As a novel evolutionary computing technique, Differential Evolution (DE) has been considered to be an effective optimization method for complex optimization problems, and achieved many successful applications in engineering. In this paper, a new algorithm of Quadratic Partial Least Squares (QPLS) based on Nonlinear Programming (NLP) is presented. And DE is used to solve the NLP so as to calculate the optimal input weights and the parameters of inner relationship. The simulation results based on the soft measurement of diesel oil solidifying point on a real crude distillation unit demonstrate that the superiority of the proposed algorithm to linear PLS and QPLS which is based on Sequential Quadratic Programming (SQP) in terms of fitting accuracy and computational costs.

Some Comments on the Use of de Moivre's Theorem to Solve Quadratic Equations with Real or Complex Coefficients

ERIC Educational Resources Information Center

Bardell, Nicholas S.

2014-01-01

This paper describes how a simple application of de Moivre's theorem may be used to not only find the roots of a quadratic equation with real or generally complex coefficients but also to pinpoint their location in the Argand plane. This approach is much simpler than the comprehensive analysis presented by Bardell (2012, 2014), but it does not…

Two Reconfigurable Flight-Control Design Methods: Robust Servomechanism and Control Allocation

NASA Technical Reports Server (NTRS)

Burken, John J.; Lu, Ping; Wu, Zheng-Lu; Bahm, Cathy

2001-01-01

Two methods for control system reconfiguration have been investigated. The first method is a robust servomechanism control approach (optimal tracking problem) that is a generalization of the classical proportional-plus-integral control to multiple input-multiple output systems. The second method is a control-allocation approach based on a quadratic programming formulation. A globally convergent fixed-point iteration algorithm has been developed to make onboard implementation of this method feasible. These methods have been applied to reconfigurable entry flight control design for the X-33 vehicle. Examples presented demonstrate simultaneous tracking of angle-of-attack and roll angle commands during failures of the fight body flap actuator. Although simulations demonstrate success of the first method in most cases, the control-allocation method appears to provide uniformly better performance in all cases.

Reconfigurable Flight Control Designs With Application to the X-33 Vehicle

NASA Technical Reports Server (NTRS)

Burken, John J.; Lu, Ping; Wu, Zhenglu

1999-01-01

Two methods for control system reconfiguration have been investigated. The first method is a robust servomechanism control approach (optimal tracking problem) that is a generalization of the classical proportional-plus-integral control to multiple input-multiple output systems. The second method is a control-allocation approach based on a quadratic programming formulation. A globally convergent fixed-point iteration algorithm has been developed to make onboard implementation of this method feasible. These methods have been applied to reconfigurable entry flight control design for the X-33 vehicle. Examples presented demonstrate simultaneous tracking of angle-of-attack and roll angle commands during failures of the right body flap actuator. Although simulations demonstrate success of the first method in most cases, the control-allocation method appears to provide uniformly better performance in all cases.

A Comparison of Trajectory Optimization Methods for the Impulsive Minimum Fuel Rendezvous Problem

NASA Technical Reports Server (NTRS)

Hughes, Steven P.; Mailhe, Laurie M.; Guzman, Jose J.

2003-01-01

In this paper we present, a comparison of trajectory optimization approaches for the minimum fuel rendezvous problem. Both indirect and direct methods are compared for a variety of test cases. The indirect approach is based on primer vector theory. The direct approaches are implemented numerically and include Sequential Quadratic Programming (SQP). Quasi- Newton and Nelder-Meade Simplex. Several cost function parameterizations are considered for the direct approach. We choose one direct approach that appears to be the most flexible. Both the direct and indirect methods are applied to a variety of test cases which are chosen to demonstrate the performance of each method in different flight regimes. The first test case is a simple circular-to-circular coplanar rendezvous. The second test case is an elliptic-to-elliptic line of apsides rotation. The final test case is an orbit phasing maneuver sequence in a highly elliptic orbit. For each test case we present a comparison of the performance of all methods we consider in this paper.

Taylor O(h³) Discretization of ZNN Models for Dynamic Equality-Constrained Quadratic Programming With Application to Manipulators.

PubMed

Liao, Bolin; Zhang, Yunong; Jin, Long

2016-02-01

In this paper, a new Taylor-type numerical differentiation formula is first presented to discretize the continuous-time Zhang neural network (ZNN), and obtain higher computational accuracy. Based on the Taylor-type formula, two Taylor-type discrete-time ZNN models (termed Taylor-type discrete-time ZNNK and Taylor-type discrete-time ZNNU models) are then proposed and discussed to perform online dynamic equality-constrained quadratic programming. For comparison, Euler-type discrete-time ZNN models (called Euler-type discrete-time ZNNK and Euler-type discrete-time ZNNU models) and Newton iteration, with interesting links being found, are also presented. It is proved herein that the steady-state residual errors of the proposed Taylor-type discrete-time ZNN models, Euler-type discrete-time ZNN models, and Newton iteration have the patterns of O(h(3)), O(h(2)), and O(h), respectively, with h denoting the sampling gap. Numerical experiments, including the application examples, are carried out, of which the results further substantiate the theoretical findings and the efficacy of Taylor-type discrete-time ZNN models. Finally, the comparisons with Taylor-type discrete-time derivative model and other Lagrange-type discrete-time ZNN models for dynamic equality-constrained quadratic programming substantiate the superiority of the proposed Taylor-type discrete-time ZNN models once again.

Fractal analysis of multiscale spatial autocorrelation among point data

USGS Publications Warehouse

De Cola, L.

1991-01-01

The analysis of spatial autocorrelation among point-data quadrats is a well-developed technique that has made limited but intriguing use of the multiscale aspects of pattern. In this paper are presented theoretical and algorithmic approaches to the analysis of aggregations of quadrats at or above a given density, in which these sets are treated as multifractal regions whose fractal dimension, D, may vary with phenomenon intensity, scale, and location. The technique is illustrated with Matui's quadrat house-count data, which yield measurements consistent with a nonautocorrelated simulated Poisson process but not with an orthogonal unit-step random walk. The paper concludes with a discussion of the implications of such analysis for multiscale geographic analysis systems. -Author

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.

Reliability-based design optimization using a generalized subset simulation method and posterior approximation

NASA Astrophysics Data System (ADS)

Ma, Yuan-Zhuo; Li, Hong-Shuang; Yao, Wei-Xing

2018-05-01

The evaluation of the probabilistic constraints in reliability-based design optimization (RBDO) problems has always been significant and challenging work, which strongly affects the performance of RBDO methods. This article deals with RBDO problems using a recently developed generalized subset simulation (GSS) method and a posterior approximation approach. The posterior approximation approach is used to transform all the probabilistic constraints into ordinary constraints as in deterministic optimization. The assessment of multiple failure probabilities required by the posterior approximation approach is achieved by GSS in a single run at all supporting points, which are selected by a proper experimental design scheme combining Sobol' sequences and Bucher's design. Sequentially, the transformed deterministic design optimization problem can be solved by optimization algorithms, for example, the sequential quadratic programming method. Three optimization problems are used to demonstrate the efficiency and accuracy of the proposed method.

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.

Optimization for minimum sensitivity to uncertain parameters

NASA Technical Reports Server (NTRS)

Pritchard, Jocelyn I.; Adelman, Howard M.; Sobieszczanski-Sobieski, Jaroslaw

1994-01-01

A procedure to design a structure for minimum sensitivity to uncertainties in problem parameters is described. The approach is to minimize directly the sensitivity derivatives of the optimum design with respect to fixed design parameters using a nested optimization procedure. The procedure is demonstrated for the design of a bimetallic beam for minimum weight with insensitivity to uncertainties in structural properties. The beam is modeled with finite elements based on two dimensional beam analysis. A sequential quadratic programming procedure used as the optimizer supplies the Lagrange multipliers that are used to calculate the optimum sensitivity derivatives. The method was perceived to be successful from comparisons of the optimization results with parametric studies.

Design and cost analysis of rapid aquifer restoration systems using flow simulation and quadratic programming.

USGS Publications Warehouse

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

1986-01-01

Detailed two-dimensional flow simulation of a complex ground-water system is combined with quadratic and linear programming to evaluate design alternatives for rapid aquifer restoration. Results show how treatment and pumping costs depend dynamically on the type of treatment process, and capacity of pumping and injection wells, and the number of wells. The design for an inexpensive treatment process minimizes pumping costs, while an expensive process results in the minimization of treatment costs. Substantial reductions in pumping costs occur with increases in injection capacity or in the number of wells. Treatment costs are reduced by expansions in pumping capacity or injecion capacity. The analysis identifies maximum pumping and injection capacities.-from Authors

Comparison of hexahedral and tetrahedral elements in finite element analysis of the foot and footwear.

PubMed

Tadepalli, Srinivas C; Erdemir, Ahmet; Cavanagh, Peter R

2011-08-11

Finite element analysis has been widely used in the field of foot and footwear biomechanics to determine plantar pressures as well as stresses and strains within soft tissue and footwear materials. When dealing with anatomical structures such as the foot, hexahedral mesh generation accounts for most of the model development time due to geometric complexities imposed by branching and embedded structures. Tetrahedral meshing, which can be more easily automated, has been the approach of choice to date in foot and footwear biomechanics. Here we use the nonlinear finite element program Abaqus (Simulia, Providence, RI) to examine the advantages and disadvantages of tetrahedral and hexahedral elements under compression and shear loading, material incompressibility, and frictional contact conditions, which are commonly seen in foot and footwear biomechanics. This study demonstrated that for a range of simulation conditions, hybrid hexahedral elements (Abaqus C3D8H) consistently performed well while hybrid linear tetrahedral elements (Abaqus C3D4H) performed poorly. On the other hand, enhanced quadratic tetrahedral elements with improved stress visualization (Abaqus C3D10I) performed as well as the hybrid hexahedral elements in terms of contact pressure and contact shear stress predictions. Although the enhanced quadratic tetrahedral element simulations were computationally expensive compared to hexahedral element simulations in both barefoot and footwear conditions, the enhanced quadratic tetrahedral element formulation seems to be very promising for foot and footwear applications as a result of decreased labor and expedited model development, all related to facilitated mesh generation. Copyright © 2011. Published by Elsevier Ltd.

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

Sequential quadratic programming-based fast path planning algorithm subject to no-fly zone constraints

NASA Astrophysics Data System (ADS)

Liu, Wei; Ma, Shunjian; Sun, Mingwei; Yi, Haidong; Wang, Zenghui; Chen, Zengqiang

2016-08-01

Path planning plays an important role in aircraft guided systems. Multiple no-fly zones in the flight area make path planning a constrained nonlinear optimization problem. It is necessary to obtain a feasible optimal solution in real time. In this article, the flight path is specified to be composed of alternate line segments and circular arcs, in order to reformulate the problem into a static optimization one in terms of the waypoints. For the commonly used circular and polygonal no-fly zones, geometric conditions are established to determine whether or not the path intersects with them, and these can be readily programmed. Then, the original problem is transformed into a form that can be solved by the sequential quadratic programming method. The solution can be obtained quickly using the Sparse Nonlinear OPTimizer (SNOPT) package. Mathematical simulations are used to verify the effectiveness and rapidity of the proposed algorithm.

Annual Review of Research Under the Joint Service Electronics Program.

DTIC Science & Technology

1979-10-01

Contents: Quadratic Optimization Problems; Nonlinear Control; Nonlinear Fault Analysis; Qualitative Analysis of Large Scale Systems; Multidimensional System Theory ; Optical Noise; and Pattern Recognition.

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

Exploring the joint measurability using an information-theoretic approach

NASA Astrophysics Data System (ADS)

Hsu, Li-Yi

2016-12-01

We explore the legal purity parameters for the joint measurements. Instead of direct unsharpening the measurements, we perform the quantum cloning before the sharp measurements. The necessary fuzziness in the unsharp measurements is equivalently introduced in the imperfect cloning process. Based on the information causality and the consequent noisy nonlocal computation, one can derive the information-theoretic quadratic inequalities that must be satisfied by any physical theory. On the other hand, to guarantee the classicality, the linear Bell-type inequalities deduced by these quadratic ones must be obeyed. As for the joint measurability, the purity parameters must be chosen to obey both types of inequalities. Finally, the quadratic inequalities for purity parameters in the joint measurability region are derived.

The algebraic decoding of the (41, 21, 9) quadratic residue code

NASA Technical Reports Server (NTRS)

Reed, Irving S.; Truong, T. K.; Chen, Xuemin; Yin, Xiaowei

1992-01-01

A new algebraic approach for decoding the quadratic residue (QR) codes, in particular the (41, 21, 9) QR code is presented. The key ideas behind this decoding technique are a systematic application of the Sylvester resultant method to the Newton identities associated with the code syndromes to find the error-locator polynomial, and next a method for determining error locations by solving certain quadratic, cubic and quartic equations over GF(2 exp m) in a new way which uses Zech's logarithms for the arithmetic. The algorithms developed here are suitable for implementation in a programmable microprocessor or special-purpose VLSI chip. It is expected that the algebraic methods developed here can apply generally to other codes such as the BCH and Reed-Solomon codes.

Analytical approximations for the oscillators with anti-symmetric quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Alal Hosen, Md.; Chowdhury, M. S. H.; Yeakub Ali, Mohammad; Faris Ismail, Ahmad

2017-12-01

A second-order ordinary differential equation involving anti-symmetric quadratic nonlinearity changes sign. The behaviour of the oscillators with an anti-symmetric quadratic nonlinearity is assumed to oscillate different in the positive and negative directions. In this reason, Harmonic Balance Method (HBM) cannot be directly applied. The main purpose of the present paper is to propose an analytical approximation technique based on the HBM for obtaining approximate angular frequencies and the corresponding periodic solutions of the oscillators with anti-symmetric quadratic nonlinearity. After applying HBM, a set of complicated nonlinear algebraic equations is found. Analytical approach is not always fruitful for solving such kinds of nonlinear algebraic equations. In this article, two small parameters are found, for which the power series solution produces desired results. Moreover, the amplitude-frequency relationship has also been determined in a novel analytical way. The presented technique gives excellent results as compared with the corresponding numerical results and is better than the existing ones.

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.

Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators

NASA Astrophysics Data System (ADS)

Ahmadiniaz, Naser; Gomez, Humberto; Lopez-Arcos, Cristhiam

2018-05-01

In this work we have studied the Kleiss-Kuijf relations for the recently introduced Parke-Taylor factors at one-loop in the CHY approach, that reproduce quadratic Feynman propagators. By doing this, we were able to identify the non-planar one-loop Parke-Taylor factors. In order to check that, in fact, these new factors can describe non-planar amplitudes, we applied them to the bi-adjoint Φ3 theory. As a byproduct, we found a new type of graphs that we called the non-planar CHY-graphs. These graphs encode all the information for the subleading order at one-loop, and there is not an equivalent of these in the Feynman formalism.

Quadratic correlation filters for optical correlators

NASA Astrophysics Data System (ADS)

Mahalanobis, Abhijit; Muise, Robert R.; Vijaya Kumar, Bhagavatula V. K.

2003-08-01

Linear correlation filters have been implemented in optical correlators and successfully used for a variety of applications. The output of an optical correlator is usually sensed using a square law device (such as a CCD array) which forces the output to be the squared magnitude of the desired correlation. It is however not a traditional practice to factor the effect of the square-law detector in the design of the linear correlation filters. In fact, the input-output relationship of an optical correlator is more accurately modeled as a quadratic operation than a linear operation. Quadratic correlation filters (QCFs) operate directly on the image data without the need for feature extraction or segmentation. In this sense, the QCFs retain the main advantages of conventional linear correlation filters while offering significant improvements in other respects. Not only is more processing required to detect peaks in the outputs of multiple linear filters, but choosing a winner among them is an error prone task. In contrast, all channels in a QCF work together to optimize the same performance metric and produce a combined output that leads to considerable simplification of the post-processing. In this paper, we propose a novel approach to the design of quadratic correlation based on the Fukunaga Koontz transform. Although quadratic filters are known to be optimum when the data is Gaussian, it is expected that they will perform as well as or better than linear filters in general. Preliminary performance results are provided that show that quadratic correlation filters perform better than their linear counterparts.

QUADrATiC: scalable gene expression connectivity mapping for repurposing FDA-approved therapeutics.

PubMed

O'Reilly, Paul G; Wen, Qing; Bankhead, Peter; Dunne, Philip D; McArt, Darragh G; McPherson, Suzanne; Hamilton, Peter W; Mills, Ken I; Zhang, Shu-Dong

2016-05-04

Gene expression connectivity mapping has proven to be a powerful and flexible tool for research. Its application has been shown in a broad range of research topics, most commonly as a means of identifying potential small molecule compounds, which may be further investigated as candidates for repurposing to treat diseases. The public release of voluminous data from the Library of Integrated Cellular Signatures (LINCS) programme further enhanced the utilities and potentials of gene expression connectivity mapping in biomedicine. We describe QUADrATiC ( http://go.qub.ac.uk/QUADrATiC ), a user-friendly tool for the exploration of gene expression connectivity on the subset of the LINCS data set corresponding to FDA-approved small molecule compounds. It enables the identification of compounds for repurposing therapeutic potentials. The software is designed to cope with the increased volume of data over existing tools, by taking advantage of multicore computing architectures to provide a scalable solution, which may be installed and operated on a range of computers, from laptops to servers. This scalability is provided by the use of the modern concurrent programming paradigm provided by the Akka framework. The QUADrATiC Graphical User Interface (GUI) has been developed using advanced Javascript frameworks, providing novel visualization capabilities for further analysis of connections. There is also a web services interface, allowing integration with other programs or scripts. QUADrATiC has been shown to provide an improvement over existing connectivity map software, in terms of scope (based on the LINCS data set), applicability (using FDA-approved compounds), usability and speed. It offers potential to biological researchers to analyze transcriptional data and generate potential therapeutics for focussed study in the lab. QUADrATiC represents a step change in the process of investigating gene expression connectivity and provides more biologically-relevant results than previous alternative solutions.

An Estimating Equations Approach for the LISCOMP Model.

ERIC Educational Resources Information Center

Reboussin, Beth A.; Liang, Kung-Lee

1998-01-01

A quadratic estimating equations approach for the LISCOMP model is proposed that only requires specification of the first two moments. This method is compared with a three-stage generalized least squares approach through a numerical study and application to a study of life events and neurotic illness. (SLD)

Rapid design and optimization of low-thrust rendezvous/interception trajectory for asteroid deflection missions

NASA Astrophysics Data System (ADS)

Li, Shuang; Zhu, Yongsheng; Wang, Yukai

2014-02-01

Asteroid deflection techniques are essential in order to protect the Earth from catastrophic impacts by hazardous asteroids. Rapid design and optimization of low-thrust rendezvous/interception trajectories is considered as one of the key technologies to successfully deflect potentially hazardous asteroids. In this paper, we address a general framework for the rapid design and optimization of low-thrust rendezvous/interception trajectories for future asteroid deflection missions. The design and optimization process includes three closely associated steps. Firstly, shape-based approaches and genetic algorithm (GA) are adopted to perform preliminary design, which provides a reasonable initial guess for subsequent accurate optimization. Secondly, Radau pseudospectral method is utilized to transcribe the low-thrust trajectory optimization problem into a discrete nonlinear programming (NLP) problem. Finally, sequential quadratic programming (SQP) is used to efficiently solve the nonlinear programming problem and obtain the optimal low-thrust rendezvous/interception trajectories. The rapid design and optimization algorithms developed in this paper are validated by three simulation cases with different performance indexes and boundary constraints.

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.

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.

Opera: reconstructing optimal genomic scaffolds with high-throughput paired-end sequences.

PubMed

Gao, Song; Sung, Wing-Kin; Nagarajan, Niranjan

2011-11-01

Scaffolding, the problem of ordering and orienting contigs, typically using paired-end reads, is a crucial step in the assembly of high-quality draft genomes. Even as sequencing technologies and mate-pair protocols have improved significantly, scaffolding programs still rely on heuristics, with no guarantees on the quality of the solution. In this work, we explored the feasibility of an exact solution for scaffolding and present a first tractable solution for this problem (Opera). We also describe a graph contraction procedure that allows the solution to scale to large scaffolding problems and demonstrate this by scaffolding several large real and synthetic datasets. In comparisons with existing scaffolders, Opera simultaneously produced longer and more accurate scaffolds demonstrating the utility of an exact approach. Opera also incorporates an exact quadratic programming formulation to precisely compute gap sizes (Availability: http://sourceforge.net/projects/operasf/ ).

Opera: Reconstructing Optimal Genomic Scaffolds with High-Throughput Paired-End Sequences

PubMed Central

Gao, Song; Sung, Wing-Kin

2011-01-01

Abstract Scaffolding, the problem of ordering and orienting contigs, typically using paired-end reads, is a crucial step in the assembly of high-quality draft genomes. Even as sequencing technologies and mate-pair protocols have improved significantly, scaffolding programs still rely on heuristics, with no guarantees on the quality of the solution. In this work, we explored the feasibility of an exact solution for scaffolding and present a first tractable solution for this problem (Opera). We also describe a graph contraction procedure that allows the solution to scale to large scaffolding problems and demonstrate this by scaffolding several large real and synthetic datasets. In comparisons with existing scaffolders, Opera simultaneously produced longer and more accurate scaffolds demonstrating the utility of an exact approach. Opera also incorporates an exact quadratic programming formulation to precisely compute gap sizes (Availability: http://sourceforge.net/projects/operasf/). PMID:21929371

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.

Soliton compression to few-cycle pulses with a high quality factor by engineering cascaded quadratic nonlinearities.

PubMed

Zeng, Xianglong; Guo, Hairun; Zhou, Binbin; Bache, Morten

2012-11-19

We propose an efficient approach to improve few-cycle soliton compression with cascaded quadratic nonlinearities by using an engineered multi-section structure of the nonlinear crystal. By exploiting engineering of the cascaded quadratic nonlinearities, in each section soliton compression with a low effective order is realized, and high-quality few-cycle pulses with large compression factors are feasible. Each subsequent section is designed so that the compressed pulse exiting the previous section experiences an overall effective self-defocusing cubic nonlinearity corresponding to a modest soliton order, which is kept larger than unity to ensure further compression. This is done by increasing the cascaded quadratic nonlinearity in the new section with an engineered reduced residual phase mismatch. The low soliton orders in each section ensure excellent pulse quality and high efficiency. Numerical results show that compressed pulses with less than three-cycle duration can be achieved even when the compression factor is very large, and in contrast to standard soliton compression, these compressed pulses have minimal pedestal and high quality factor.

Multivariable Hermite polynomials and phase-space dynamics

NASA Technical Reports Server (NTRS)

Dattoli, G.; Torre, Amalia; Lorenzutta, S.; Maino, G.; Chiccoli, C.

1994-01-01

The phase-space approach to classical and quantum systems demands for advanced analytical tools. Such an approach characterizes the evolution of a physical system through a set of variables, reducing to the canonically conjugate variables in the classical limit. It often happens that phase-space distributions can be written in terms of quadratic forms involving the above quoted variables. A significant analytical tool to treat these problems may come from the generalized many-variables Hermite polynomials, defined on quadratic forms in R(exp n). They form an orthonormal system in many dimensions and seem the natural tool to treat the harmonic oscillator dynamics in phase-space. In this contribution we discuss the properties of these polynomials and present some applications to physical problems.

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)

Support Vector Machine algorithm for regression and classification

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

Yu, Chenggang; Zavaljevski, Nela

2001-08-01

The software is an implementation of the Support Vector Machine (SVM) algorithm that was invented and developed by Vladimir Vapnik and his co-workers at AT&T Bell Laboratories. The specific implementation reported here is an Active Set method for solving a quadratic optimization problem that forms the major part of any SVM program. The implementation is tuned to specific constraints generated in the SVM learning. Thus, it is more efficient than general-purpose quadratic optimization programs. A decomposition method has been implemented in the software that enables processing large data sets. The size of the learning data is virtually unlimited by themore » capacity of the computer physical memory. The software is flexible and extensible. Two upper bounds are implemented to regulate the SVM learning for classification, which allow users to adjust the false positive and false negative rates. The software can be used either as a standalone, general-purpose SVM regression or classification program, or be embedded into a larger software system.« less

A superlinear interior points algorithm for engineering design optimization

NASA Technical Reports Server (NTRS)

Herskovits, J.; Asquier, J.

1990-01-01

We present a quasi-Newton interior points algorithm for nonlinear constrained optimization. It is based on a general approach consisting of the iterative solution in the primal and dual spaces of the equalities in Karush-Kuhn-Tucker optimality conditions. This is done in such a way to have primal and dual feasibility at each iteration, which ensures satisfaction of those optimality conditions at the limit points. This approach is very strong and efficient, since at each iteration it only requires the solution of two linear systems with the same matrix, instead of quadratic programming subproblems. It is also particularly appropriate for engineering design optimization inasmuch at each iteration a feasible design is obtained. The present algorithm uses a quasi-Newton approximation of the second derivative of the Lagrangian function in order to have superlinear asymptotic convergence. We discuss theoretical aspects of the algorithm and its computer implementation.

Identification of inelastic parameters based on deep drawing forming operations using a global-local hybrid Particle Swarm approach

NASA Astrophysics Data System (ADS)

Vaz, Miguel; Luersen, Marco A.; Muñoz-Rojas, Pablo A.; Trentin, Robson G.

2016-04-01

Application of optimization techniques to the identification of inelastic material parameters has substantially increased in recent years. The complex stress-strain paths and high nonlinearity, typical of this class of problems, require the development of robust and efficient techniques for inverse problems able to account for an irregular topography of the fitness surface. Within this framework, this work investigates the application of the gradient-based Sequential Quadratic Programming method, of the Nelder-Mead downhill simplex algorithm, of Particle Swarm Optimization (PSO), and of a global-local PSO-Nelder-Mead hybrid scheme to the identification of inelastic parameters based on a deep drawing operation. The hybrid technique has shown to be the best strategy by combining the good PSO performance to approach the global minimum basin of attraction with the efficiency demonstrated by the Nelder-Mead algorithm to obtain the minimum itself.

Dynamic metabolic modeling for a MAB bioprocess.

PubMed

Gao, Jianying; Gorenflo, Volker M; Scharer, Jeno M; Budman, Hector M

2007-01-01

Production of monoclonal antibodies (MAb) for diagnostic or therapeutic applications has become an important task in the pharmaceutical industry. The efficiency of high-density reactor systems can be potentially increased by model-based design and control strategies. Therefore, a reliable kinetic model for cell metabolism is required. A systematic procedure based on metabolic modeling is used to model nutrient uptake and key product formation in a MAb bioprocess during both the growth and post-growth phases. The approach combines the key advantages of stoichiometric and kinetic models into a complete metabolic network while integrating the regulation and control of cellular activity. This modeling procedure can be easily applied to any cell line during both the cell growth and post-growth phases. Quadratic programming (QP) has been identified as a suitable method to solve the underdetermined constrained problem related to model parameter identification. The approach is illustrated for the case of murine hybridoma cells cultivated in stirred spinners.

Observational constraints on cosmological models with Chaplygin gas and quadratic equation of state

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

Sharov, G.S., E-mail: german.sharov@mail.ru

Observational manifestations of accelerated expansion of the universe, in particular, recent data for Type Ia supernovae, baryon acoustic oscillations, for the Hubble parameter H ( z ) and cosmic microwave background constraints are described with different cosmological models. We compare the ΛCDM, the models with generalized and modified Chaplygin gas and the model with quadratic equation of state. For these models we estimate optimal model parameters and their permissible errors with different approaches to calculation of sound horizon scale r {sub s} ( z {sub d} ). Among the considered models the best value of χ{sup 2} is achieved formore » the model with quadratic equation of state, but it has 2 additional parameters in comparison with the ΛCDM and therefore is not favored by the Akaike information criterion.« less

L2CXCV: A Fortran 77 package for least squares convex/concave data smoothing

NASA Astrophysics Data System (ADS)

Demetriou, I. C.

2006-04-01

Fortran 77 software is given for least squares smoothing to data values contaminated by random errors subject to one sign change in the second divided differences of the smoothed values, where the location of the sign change is also unknown of the optimization problem. A highly useful description of the constraints is that they follow from the assumption of initially increasing and subsequently decreasing rates of change, or vice versa, of the process considered. The underlying algorithm partitions the data into two disjoint sets of adjacent data and calculates the required fit by solving a strictly convex quadratic programming problem for each set. The piecewise linear interpolant to the fit is convex on the first set and concave on the other one. The partition into suitable sets is achieved by a finite iterative algorithm, which is made quite efficient because of the interactions of the quadratic programming problems on consecutive data. The algorithm obtains the solution by employing no more quadratic programming calculations over subranges of data than twice the number of the divided differences constraints. The quadratic programming technique makes use of active sets and takes advantage of a B-spline representation of the smoothed values that allows some efficient updating procedures. The entire code required to implement the method is 2920 Fortran lines. The package has been tested on a variety of data sets and it has performed very efficiently, terminating in an overall number of active set changes over subranges of data that is only proportional to the number of data. The results suggest that the package can be used for very large numbers of data values. Some examples with output are provided to help new users and exhibit certain features of the software. Important applications of the smoothing technique may be found in calculating a sigmoid approximation, which is a common topic in various contexts in applications in disciplines like physics, economics, biology and engineering. Distribution material that includes single and double precision versions of the code, driver programs, technical details of the implementation of the software package and test examples that demonstrate the use of the software is available in an accompanying ASCII file. Program summaryTitle of program:L2CXCV Catalogue identifier:ADXM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXM_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer:PC Intel Pentium, Sun Sparc Ultra 5, Hewlett-Packard HP UX 11.0 Operating system:WINDOWS 98, 2000, Unix/Solaris 7, Unix/HP UX 11.0 Programming language used:FORTRAN 77 Memory required to execute with typical data:O(n), where n is the number of data No. of bits in a byte:8 No. of lines in distributed program, including test data, etc.:29 349 No. of bytes in distributed program, including test data, etc.:1 276 663 No. of processors used:1 Has the code been vectorized or parallelized?:no Distribution format:default tar.gz Separate documentation available:Yes Nature of physical problem:Analysis of processes that show initially increasing and then decreasing rates of change (sigmoid shape), as, for example, in heat curves, reactor stability conditions, evolution curves, photoemission yields, growth models, utility functions, etc. Identifying an unknown convex/concave (sigmoid) function from some measurements of its values that contain random errors. Also, identifying the inflection point of this sigmoid function. Method of solution:Univariate data smoothing by minimizing the sum of the squares of the residuals (least squares approximation) subject to the condition that the second order divided differences of the smoothed values change sign at most once. Ideally, this is the number of sign changes in the second derivative of the underlying function. The remarkable property of the smoothed values is that they consist of one separate section of optimal components that give nonnegative second divided differences (convexity) and one separate section of optimal components that give nonpositive second divided differences (concavity). The solution process finds the joint (that is the inflection point estimate of the underlying function) of the sections automatically. The underlying method is iterative, each iteration solving a structured strictly convex quadratic programming problem in order to obtain a convex or a concave section over a subrange of data. Restrictions on the complexity of the problem:Number of data, n, is not limited in the software package, but is limited to 2000 in the main driver. The total work of the method requires 2n-2 structured quadratic programming calculations over subranges of data, which in practice does not exceed the amount of O(n) computer operations. Typical running times:CPU time on a PC with an Intel 733 MHz processor operating in Windows 98: About 2 s to smooth n=1000 noisy measurements that follow the shape of the sine function over one period. Summary:L2CXCV is a package of Fortran 77 subroutines for least squares smoothing to n univariate data values contaminated by random errors subject to one sign change in the second divided differences of the smoothed values, where the location of the sign change is unknown. The piecewise linear interpolant to the smoothed values gives a convex/concave fit to the data. The underlying algorithm is based on the property that in this best convex/concave fit, the convex and the concave section are both optimal and separate. The algorithm is iterative, each iteration solving a strictly convex quadratic programming problem for the best convex fit to the first k data, starting from the best convex fit to the first k-1 data. By reversing the order and sign of the data, the algorithm obtains the best concave fit to the last n-k data. Then it chooses that k as the optimal position of the required sign change (which defines the inflection point of the fit), if the convex and the concave components to the first k and the last n-k data, respectively, form a convex/concave vector that gives the least sum of squares of residuals. In effect the algorithm requires at most 2n-2 quadratic programming calculations over subranges of data. The package employs a technique for quadratic programming, which takes advantage of a B-spline representation of the smoothed values and makes use of some efficient O(k) updating procedures, where k is the number of data of a subrange. The package has been tested on a variety of data sets and it has performed very efficiently, terminating in an overall number of active set changes that is about n, thus exhibiting quadratic performance in n. The Fortran codes have been designed to minimize the use of computing resources. Attention has been given to computer rounding errors details, which are essential to the robustness of the software package. Numerical examples with output are provided to help the use of the software and exhibit certain features of the method. Distribution material that includes driver programs, technical details of the installation of the package and test examples that demonstrate the use of the software is available in an ASCII file that accompanies this work.

A contracting-interval program for the Danilewski method. Ph.D. Thesis - Va. Univ.

NASA Technical Reports Server (NTRS)

Harris, J. D.

1971-01-01

The concept of contracting-interval programs is applied to finding the eigenvalues of a matrix. The development is a three-step process in which (1) a program is developed for the reduction of a matrix to Hessenberg form, (2) a program is developed for the reduction of a Hessenberg matrix to colleague form, and (3) the characteristic polynomial with interval coefficients is readily obtained from the interval of colleague matrices. This interval polynomial is then factored into quadratic factors so that the eigenvalues may be obtained. To develop a contracting-interval program for factoring this polynomial with interval coefficients it is necessary to have an iteration method which converges even in the presence of controlled rounding errors. A theorem is stated giving sufficient conditions for the convergence of Newton's method when both the function and its Jacobian cannot be evaluated exactly but errors can be made proportional to the square of the norm of the difference between the previous two iterates. This theorem is applied to prove the convergence of the generalization of the Newton-Bairstow method that is used to obtain quadratic factors of the characteristic polynomial.

The Comparison Study of Quadratic Infinite Beam Program on Optimization Instensity Modulated Radiation Therapy Treatment Planning (IMRTP) between Threshold and Exponential Scatter Method with CERR® In The Case of Lung Cancer

NASA Astrophysics Data System (ADS)

Hardiyanti, Y.; Haekal, M.; Waris, A.; Haryanto, F.

2016-08-01

This research compares the quadratic optimization program on Intensity Modulated Radiation Therapy Treatment Planning (IMRTP) with the Computational Environment for Radiotherapy Research (CERR) software. We assumed that the number of beams used for the treatment planner was about 9 and 13 beams. The case used the energy of 6 MV with Source Skin Distance (SSD) of 100 cm from target volume. Dose calculation used Quadratic Infinite beam (QIB) from CERR. CERR was used in the comparison study between Gauss Primary threshold method and Gauss Primary exponential method. In the case of lung cancer, the threshold variation of 0.01, and 0.004 was used. The output of the dose was distributed using an analysis in the form of DVH from CERR. The maximum dose distributions obtained were on the target volume (PTV) Planning Target Volume, (CTV) Clinical Target Volume, (GTV) Gross Tumor Volume, liver, and skin. It was obtained that if the dose calculation method used exponential and the number of beam 9. When the dose calculation method used the threshold and the number of beam 13, the maximum dose distributions obtained were on the target volume PTV, GTV, heart, and skin.

Fractional Programming for Communication Systems—Part I: Power Control and Beamforming

NASA Astrophysics Data System (ADS)

Shen, Kaiming; Yu, Wei

2018-05-01

This two-part paper explores the use of FP in the design and optimization of communication systems. Part I of this paper focuses on FP theory and on solving continuous problems. The main theoretical contribution is a novel quadratic transform technique for tackling the multiple-ratio concave-convex FP problem--in contrast to conventional FP techniques that mostly can only deal with the single-ratio or the max-min-ratio case. Multiple-ratio FP problems are important for the optimization of communication networks, because system-level design often involves multiple signal-to-interference-plus-noise ratio terms. This paper considers the applications of FP to solving continuous problems in communication system design, particularly for power control, beamforming, and energy efficiency maximization. These application cases illustrate that the proposed quadratic transform can greatly facilitate the optimization involving ratios by recasting the original nonconvex problem as a sequence of convex problems. This FP-based problem reformulation gives rise to an efficient iterative optimization algorithm with provable convergence to a stationary point. The paper further demonstrates close connections between the proposed FP approach and other well-known algorithms in the literature, such as the fixed-point iteration and the weighted minimum mean-square-error beamforming. The optimization of discrete problems is discussed in Part II of this paper.

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.

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.

Nonadiabatic rate constants for proton transfer and proton-coupled electron transfer reactions in solution: Effects of quadratic term in the vibronic coupling expansion

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

Soudackov, Alexander V.; Hammes-Schiffer, Sharon

2015-11-21

Rate constant expressions for vibronically nonadiabatic proton transfer and proton-coupled electron transfer reactions are presented and analyzed. The regimes covered include electronically adiabatic and nonadiabatic reactions, as well as high-frequency and low-frequency proton donor-acceptor vibrational modes. These rate constants differ from previous rate constants derived with the cumulant expansion approach in that the logarithmic expansion of the vibronic coupling in terms of the proton donor-acceptor distance includes a quadratic as well as a linear term. The analysis illustrates that inclusion of this quadratic term in the framework of the cumulant expansion framework may significantly impact the rate constants at highmore » temperatures for proton transfer interfaces with soft proton donor-acceptor modes that are associated with small force constants and weak hydrogen bonds. The effects of the quadratic term may also become significant in these regimes when using the vibronic coupling expansion in conjunction with a thermal averaging procedure for calculating the rate constant. In this case, however, the expansion of the coupling can be avoided entirely by calculating the couplings explicitly for the range of proton donor-acceptor distances sampled. The effects of the quadratic term for weak hydrogen-bonding systems are less significant for more physically realistic models that prevent the sampling of unphysical short proton donor-acceptor distances. Additionally, the rigorous relation between the cumulant expansion and thermal averaging approaches is clarified. In particular, the cumulant expansion rate constant includes effects from dynamical interference between the proton donor-acceptor and solvent motions and becomes equivalent to the thermally averaged rate constant when these dynamical effects are neglected. This analysis identifies the regimes in which each rate constant expression is valid and thus will be important for future applications to proton transfer and proton-coupled electron transfer in chemical and biological processes.« less

About the mechanism of ERP-system pilot test

NASA Astrophysics Data System (ADS)

Mitkov, V. V.; Zimin, V. V.

2018-05-01

In the paper the mathematical problem of defining the scope of pilot test is stated, which is a task of quadratic programming. The procedure of the problem solving includes the method of network programming based on the structurally similar network representation of the criterion and constraints and which reduces the original problem to a sequence of simpler evaluation tasks. The evaluation tasks are solved by the method of dichotomous programming.

Mixed-Integer Nonconvex Quadratic Optimization Relaxations and Performance Analysis

DTIC Science & Technology

2016-10-11

Analysis of Interior Point Algorithms for Non-Lipschitz and Nonconvex Minimization,” (W. Bian, X. Chen, and Ye), Math Programming, 149 (2015) 301-327...Chen, Ge, Wang, Ye), Math Programming, 143 (1-2) (2014) 371-383. This paper resolved an important open question in cardinality constrained...Statistical Performance, and Algorithmic Theory for Local Solutions,” (H. Liu, T. Yao, R. Li, Y. Ye) manuscript, 2nd revision in Math Programming

Missile Guidance Law Based on Robust Model Predictive Control Using Neural-Network Optimization.

PubMed

Li, Zhijun; Xia, Yuanqing; Su, Chun-Yi; Deng, Jun; Fu, Jun; He, Wei

2015-08-01

In this brief, the utilization of robust model-based predictive control is investigated for the problem of missile interception. Treating the target acceleration as a bounded disturbance, novel guidance law using model predictive control is developed by incorporating missile inside constraints. The combined model predictive approach could be transformed as a constrained quadratic programming (QP) problem, which may be solved using a linear variational inequality-based primal-dual neural network over a finite receding horizon. Online solutions to multiple parametric QP problems are used so that constrained optimal control decisions can be made in real time. Simulation studies are conducted to illustrate the effectiveness and performance of the proposed guidance control law for missile interception.

Improved Shaping Approach to the Preliminary Design of Low-Thrust Trajectories

NASA Astrophysics Data System (ADS)

Novak, D. M.; Vasile, M.

2011-01-01

This paper presents a general framework for the development of shape-based approaches to low-thrust trajectory design. A novel shaping method, based on a three-dimensional description of the trajectory in spherical coordinates, is developed within this general framework. Both the exponential sinusoid and the inverse polynomial shaping are demonstrated to be particular two-dimensional cases of the spherical one. The pseudoequinoctial shaping is revisited within the new framework, and the nonosculating nature of the pseudoequinoctial elements is analyzed. A two-step approach is introduced to solve the time of flight constraint, related to the design of low-thrust arcs with boundary constraints for both spherical and pseudoequinoctial shaping. The solution derived from the shaping approach is improved with a feedback linear-quadratic controller and compared against a direct collocation method based on finite elements in time. The new shaping approach and the combination of shaping and linear-quadratic controller are tested on three case studies: a mission to Mars, a mission to asteroid 1989ML, a mission to comet Tempel-1, and a mission to Neptune.

The application of quadratic optimal cooperative control synthesis to a CH-47 helicopter

NASA Technical Reports Server (NTRS)

Townsend, Barbara K.

1987-01-01

A control-system design method, quadratic optimal cooperative control synthesis (CCS), is applied to the design of a stability and control augmentation system (SCAS). The CCS design method is different from other design methods in that it does not require detailed a priori design criteria, but instead relies on an explicit optimal pilot-model to create desired performance. The design method, which was developed previously for fixed-wing aircraft, is simplified and modified for application to a Boeing CH-47 helicopter. Two SCAS designs are developed using the CCS design methodology. The resulting CCS designs are then compared with designs obtained using classical/frequency-domain methods and linear quadratic regulator (LQR) theory in a piloted fixed-base simulation. Results indicate that the CCS method, with slight modifications, can be used to produce controller designs which compare favorably with the frequency-domain approach.

The application of quadratic optimal cooperative control synthesis to a CH-47 helicopter

NASA Technical Reports Server (NTRS)

Townsend, Barbara K.

1986-01-01

A control-system design method, Quadratic Optimal Cooperative Control Synthesis (CCS), is applied to the design of a Stability and Control Augmentation Systems (SCAS). The CCS design method is different from other design methods in that it does not require detailed a priori design criteria, but instead relies on an explicit optimal pilot-model to create desired performance. The design model, which was developed previously for fixed-wing aircraft, is simplified and modified for application to a Boeing Vertol CH-47 helicopter. Two SCAS designs are developed using the CCS design methodology. The resulting CCS designs are then compared with designs obtained using classical/frequency-domain methods and Linear Quadratic Regulator (LQR) theory in a piloted fixed-base simulation. Results indicate that the CCS method, with slight modifications, can be used to produce controller designs which compare favorably with the frequency-domain approach.

Quadratic genetic modifications: a streamlined route to cosmological simulations with controlled merger history

NASA Astrophysics Data System (ADS)

Rey, Martin P.; Pontzen, Andrew

2018-02-01

Recent work has studied the interplay between a galaxy's history and its observable properties using `genetically modified' cosmological zoom simulations. The approach systematically generates alternative histories for a halo, while keeping its cosmological environment fixed. Applications to date altered linear properties of the initial conditions, such as the mean overdensity of specified regions; we extend the formulation to include quadratic features, such as local variance, that determines the overall importance of smooth accretion relative to mergers in a galaxy's history. We introduce an efficient algorithm for this new class of modification and demonstrate its ability to control the variance of a region in a one-dimensional toy model. Outcomes of this work are twofold: (i) a clarification of the formulation of genetic modifications and (ii) a proof of concept for quadratic modifications leading the way to a forthcoming implementation in cosmological simulations.

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.

Three-dimensional modeling of flexible pavements : executive summary, August 2001.

DOT National Transportation Integrated Search

2001-08-01

A linear viscoelastic model has been incorporated into a three-dimensional finite element program for analysis of flexible pavements. Linear and quadratic versions of hexahedral elements and quadrilateral axisymmetrix elements are provided. Dynamic p...

Three dimensional modeling of flexible pavements : final report, March 2002.

DOT National Transportation Integrated Search

2001-08-01

A linear viscoelastic model has been incorporated into a three-dimensional finite element program for analysis of flexible pavements. Linear and quadratic versions of hexahedral elements and quadrilateral axisymmetrix elements are provided. Dynamic p...

Interactive application of quadratic expansion of chi-square statistic to nonlinear curve fitting

NASA Technical Reports Server (NTRS)

Badavi, F. F.; Everhart, Joel L.

1987-01-01

This report contains a detailed theoretical description of an all-purpose, interactive curve-fitting routine that is based on P. R. Bevington's description of the quadratic expansion of the Chi-Square statistic. The method is implemented in the associated interactive, graphics-based computer program. Taylor's expansion of Chi-Square is first introduced, and justifications for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations is derived, then solved by matrix algebra. A brief description of the code is presented along with a limited number of changes that are required to customize the program of a particular task. To evaluate the performance of the method and the goodness of nonlinear curve fitting, two typical engineering problems are examined and the graphical and tabular output of each is discussed. A complete listing of the entire package is included as an appendix.

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.

The Use of Transformations in Solving Equations

ERIC Educational Resources Information Center

Libeskind, Shlomo

2010-01-01

Many workshops and meetings with the US high school mathematics teachers revealed a lack of familiarity with the use of transformations in solving equations and problems related to the roots of polynomials. This note describes two transformational approaches to the derivation of the quadratic formula as well as transformational approaches to…

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

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

Ibarra-Sierra, V.G.; Sandoval-Santana, J.C.; Cardoso, J.L.

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra ismore » later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a rotating quadrupole field ion trap are presented. •Exact solutions for magneto-transport in variable electromagnetic fields are shown.« less

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

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.

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.

A Maximum Likelihood Approach to Determine Sensor Radiometric Response Coefficients for NPP VIIRS Reflective Solar Bands

NASA Technical Reports Server (NTRS)

Lei, Ning; Chiang, Kwo-Fu; Oudrari, Hassan; Xiong, Xiaoxiong

2011-01-01

Optical sensors aboard Earth orbiting satellites such as the next generation Visible/Infrared Imager/Radiometer Suite (VIIRS) assume that the sensors radiometric response in the Reflective Solar Bands (RSB) is described by a quadratic polynomial, in relating the aperture spectral radiance to the sensor Digital Number (DN) readout. For VIIRS Flight Unit 1, the coefficients are to be determined before launch by an attenuation method, although the linear coefficient will be further determined on-orbit through observing the Solar Diffuser. In determining the quadratic polynomial coefficients by the attenuation method, a Maximum Likelihood approach is applied in carrying out the least-squares procedure. Crucial to the Maximum Likelihood least-squares procedure is the computation of the weight. The weight not only has a contribution from the noise of the sensor s digital count, with an important contribution from digitization error, but also is affected heavily by the mathematical expression used to predict the value of the dependent variable, because both the independent and the dependent variables contain random noise. In addition, model errors have a major impact on the uncertainties of the coefficients. The Maximum Likelihood approach demonstrates the inadequacy of the attenuation method model with a quadratic polynomial for the retrieved spectral radiance. We show that using the inadequate model dramatically increases the uncertainties of the coefficients. We compute the coefficient values and their uncertainties, considering both measurement and model errors.

Home Literacy Environment and Head Start Children's Language Development: The Role of Approaches to Learning

ERIC Educational Resources Information Center

Meng, Christine

2015-01-01

Research Findings: This study examined whether approaches to learning moderate the association between home literacy environment and English receptive vocabulary development. The Head Start Family and Child Experiences Survey (2003 cohort) was used for analysis. Latent growth curve modeling was utilized to test a quadratic model of English…

Bag-of-features based medical image retrieval via multiple assignment and visual words weighting.

PubMed

Wang, Jingyan; Li, Yongping; Zhang, Ying; Wang, Chao; Xie, Honglan; Chen, Guoling; Gao, Xin

2011-11-01

Bag-of-features based approaches have become prominent for image retrieval and image classification tasks in the past decade. Such methods represent an image as a collection of local features, such as image patches and key points with scale invariant feature transform (SIFT) descriptors. To improve the bag-of-features methods, we first model the assignments of local descriptors as contribution functions, and then propose a novel multiple assignment strategy. Assuming the local features can be reconstructed by their neighboring visual words in a vocabulary, reconstruction weights can be solved by quadratic programming. The weights are then used to build contribution functions, resulting in a novel assignment method, called quadratic programming (QP) assignment. We further propose a novel visual word weighting method. The discriminative power of each visual word is analyzed by the sub-similarity function in the bin that corresponds to the visual word. Each sub-similarity function is then treated as a weak classifier. A strong classifier is learned by boosting methods that combine those weak classifiers. The weighting factors of the visual words are learned accordingly. We evaluate the proposed methods on medical image retrieval tasks. The methods are tested on three well-known data sets, i.e., the ImageCLEFmed data set, the 304 CT Set, and the basal-cell carcinoma image set. Experimental results demonstrate that the proposed QP assignment outperforms the traditional nearest neighbor assignment, the multiple assignment, and the soft assignment, whereas the proposed boosting based weighting strategy outperforms the state-of-the-art weighting methods, such as the term frequency weights and the term frequency-inverse document frequency weights.

Mass Conservation and Positivity Preservation with Ensemble-type Kalman Filter Algorithms

NASA Technical Reports Server (NTRS)

Janjic, Tijana; McLaughlin, Dennis B.; Cohn, Stephen E.; Verlaan, Martin

2013-01-01

Maintaining conservative physical laws numerically has long been recognized as being important in the development of numerical weather prediction (NWP) models. In the broader context of data assimilation, concerted efforts to maintain conservation laws numerically and to understand the significance of doing so have begun only recently. In order to enforce physically based conservation laws of total mass and positivity in the ensemble Kalman filter, we incorporate constraints to ensure that the filter ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. We show that the analysis steps of ensemble transform Kalman filter (ETKF) algorithm and ensemble Kalman filter algorithm (EnKF) can conserve the mass integral, but do not preserve positivity. Further, if localization is applied or if negative values are simply set to zero, then the total mass is not conserved either. In order to ensure mass conservation, a projection matrix that corrects for localization effects is constructed. In order to maintain both mass conservation and positivity preservation through the analysis step, we construct a data assimilation algorithms based on quadratic programming and ensemble Kalman filtering. Mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate constraints. Some simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. The results show clear improvements in both analyses and forecasts, particularly in the presence of localized features. Behavior of the algorithm is also tested in presence of model error.

Exshall: A Turkel-Zwas explicit large time-step FORTRAN program for solving the shallow-water equations in spherical coordinates

NASA Astrophysics Data System (ADS)

Navon, I. M.; Yu, Jian

A FORTRAN computer program is presented and documented applying the Turkel-Zwas explicit large time-step scheme to a hemispheric barotropic model with constraint restoration of integral invariants of the shallow-water equations. We then proceed to detail the algorithms embodied in the code EXSHALL in this paper, particularly algorithms related to the efficiency and stability of T-Z scheme and the quadratic constraint restoration method which is based on a variational approach. In particular we provide details about the high-latitude filtering, Shapiro filtering, and Robert filtering algorithms used in the code. We explain in detail the various subroutines in the EXSHALL code with emphasis on algorithms implemented in the code and present the flowcharts of some major subroutines. Finally, we provide a visual example illustrating a 4-day run using real initial data, along with a sample printout and graphic isoline contours of the height field and velocity fields.

State dependent model predictive control for orbital rendezvous using pulse-width pulse-frequency modulated thrusters

NASA Astrophysics Data System (ADS)

Li, Peng; Zhu, Zheng H.; Meguid, S. A.

2016-07-01

This paper studies the pulse-width pulse-frequency modulation based trajectory planning for orbital rendezvous and proximity maneuvering near a non-cooperative spacecraft in an elliptical orbit. The problem is formulated by converting the continuous control input, output from the state dependent model predictive control, into a sequence of pulses of constant magnitude by controlling firing frequency and duration of constant-magnitude thrusters. The state dependent model predictive control is derived by minimizing the control error of states and control roughness of control input for a safe, smooth and fuel efficient approaching trajectory. The resulting nonlinear programming problem is converted into a series of quadratic programming problem and solved by numerical iteration using the receding horizon strategy. The numerical results show that the proposed state dependent model predictive control with the pulse-width pulse-frequency modulation is able to effectively generate optimized trajectories using equivalent control pulses for the proximity maneuvering with less energy consumption.

Influence of a Horizontal Approach on the Mechanical Output during Drop Jumps

ERIC Educational Resources Information Center

Ruan, Mianfang; Li, Li

2008-01-01

This study investigated the influence of a horizontal approach to mechanical output during drop jumps. Participants performed drop jumps from heights of 15, 30, 45, and 60 cm with zero, one, two, and three approach steps. The peak summed power during the push-off phase changed quadratically across heights (6.2 [plus or minus] 0.3, 6.7 [plus or…

Alternatives for Jet Engine Control

NASA Technical Reports Server (NTRS)

Leake, R. J.; Sain, M. K.

1976-01-01

Approaches are developed as alternatives to current design methods which rely heavily on linear quadratic and Riccati equation methods. The main alternatives are discussed in two broad categories, local multivariable frequency domain methods and global nonlinear optimal methods.

Constraint Optimization Problem For The Cutting Of A Cobalt Chrome Refractory Material

NASA Astrophysics Data System (ADS)

Lebaal, Nadhir; Schlegel, Daniel; Folea, Milena

2011-05-01

This paper shows a complete approach to solve a given problem, from the experimentation to the optimization of different cutting parameters. In response to an industrial problem of slotting FSX 414, a Cobalt-based refractory material, we have implemented a design of experiment to determine the most influent parameters on the tool life, the surface roughness and the cutting forces. After theses trials, an optimization approach has been implemented to find the lowest manufacturing cost while respecting the roughness constraints and cutting force limitation constraints. The optimization approach is based on the Response Surface Method (RSM) using the Sequential Quadratic programming algorithm (SQP) for a constrained problem. To avoid a local optimum and to obtain an accurate solution at low cost, an efficient strategy, which allows improving the RSM accuracy in the vicinity of the global optimum, is presented. With these models and these trials, we could apply and compare our optimization methods in order to get the lowest cost for the best quality, i.e. a satisfying surface roughness and limited cutting forces.

Mapping proteins in the presence of paralogs using units of coevolution

PubMed Central

2013-01-01

Background We study the problem of mapping proteins between two protein families in the presence of paralogs. This problem occurs as a difficult subproblem in coevolution-based computational approaches for protein-protein interaction prediction. Results Similar to prior approaches, our method is based on the idea that coevolution implies equal rates of sequence evolution among the interacting proteins, and we provide a first attempt to quantify this notion in a formal statistical manner. We call the units that are central to this quantification scheme the units of coevolution. A unit consists of two mapped protein pairs and its score quantifies the coevolution of the pairs. This quantification allows us to provide a maximum likelihood formulation of the paralog mapping problem and to cast it into a binary quadratic programming formulation. Conclusion CUPID, our software tool based on a Lagrangian relaxation of this formulation, makes it, for the first time, possible to compute state-of-the-art quality pairings in a few minutes of runtime. In summary, we suggest a novel alternative to the earlier available approaches, which is statistically sound and computationally feasible. PMID:24564758

Solution of quadratic matrix equations for free vibration analysis of structures.

NASA Technical Reports Server (NTRS)

Gupta, K. K.

1973-01-01

An efficient digital computer procedure and the related numerical algorithm are presented herein for the solution of quadratic matrix equations associated with free vibration analysis of structures. Such a procedure enables accurate and economical analysis of natural frequencies and associated modes of discretized structures. The numerically stable algorithm is based on the Sturm sequence method, which fully exploits the banded form of associated stiffness and mass matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be substantially more accurate and economical than other existing procedures of such analysis. Numerical examples are presented for two structures - a cantilever beam and a semicircular arch.

TWSVR: Regression via Twin Support Vector Machine.

PubMed

Khemchandani, Reshma; Goyal, Keshav; Chandra, Suresh

2016-02-01

Taking motivation from Twin Support Vector Machine (TWSVM) formulation, Peng (2010) attempted to propose Twin Support Vector Regression (TSVR) where the regressor is obtained via solving a pair of quadratic programming problems (QPPs). In this paper we argue that TSVR formulation is not in the true spirit of TWSVM. Further, taking motivation from Bi and Bennett (2003), we propose an alternative approach to find a formulation for Twin Support Vector Regression (TWSVR) which is in the true spirit of TWSVM. We show that our proposed TWSVR can be derived from TWSVM for an appropriately constructed classification problem. To check the efficacy of our proposed TWSVR we compare its performance with TSVR and classical Support Vector Regression(SVR) on various regression datasets. Copyright © 2015 Elsevier Ltd. All rights reserved.

VASP- VARIABLE DIMENSION AUTOMATIC SYNTHESIS PROGRAM

NASA Technical Reports Server (NTRS)

White, J. S.

1994-01-01

VASP is a variable dimension Fortran version of the Automatic Synthesis Program, ASP. The program is used to implement Kalman filtering and control theory. Basically, it consists of 31 subprograms for solving most modern control problems in linear, time-variant (or time-invariant) control systems. These subprograms include operations of matrix algebra, computation of the exponential of a matrix and its convolution integral, and the solution of the matrix Riccati equation. The user calls these subprograms by means of a FORTRAN main program, and so can easily obtain solutions to most general problems of extremization of a quadratic functional of the state of the linear dynamical system. Particularly, these problems include the synthesis of the Kalman filter gains and the optimal feedback gains for minimization of a quadratic performance index. VASP, as an outgrowth of the Automatic Synthesis Program, has the following improvements: more versatile programming language; more convenient input/output format; some new subprograms which consolidate certain groups of statements that are often repeated; and variable dimensioning. The pertinent difference between the two programs is that VASP has variable dimensioning and more efficient storage. The documentation for the VASP program contains a VASP dictionary and example problems. The dictionary contains a description of each subroutine and instructions on its use. The example problems include dynamic response, optimal control gain, solution of the sampled data matrix Riccati equation, matrix decomposition, and a pseudo-inverse of a matrix. This program is written in FORTRAN IV and has been implemented on the IBM 360. The VASP program was developed in 1971.

Low-Thrust Trajectory Optimization with Simplified SQP Algorithm

NASA Technical Reports Server (NTRS)

Parrish, Nathan L.; Scheeres, Daniel J.

2017-01-01

The problem of low-thrust trajectory optimization in highly perturbed dynamics is a stressing case for many optimization tools. Highly nonlinear dynamics and continuous thrust are each, separately, non-trivial problems in the field of optimal control, and when combined, the problem is even more difficult. This paper de-scribes a fast, robust method to design a trajectory in the CRTBP (circular restricted three body problem), beginning with no or very little knowledge of the system. The approach is inspired by the SQP (sequential quadratic programming) algorithm, in which a general nonlinear programming problem is solved via a sequence of quadratic problems. A few key simplifications make the algorithm presented fast and robust to initial guess: a quadratic cost function, neglecting the line search step when the solution is known to be far away, judicious use of end-point constraints, and mesh refinement on multiple shooting with fixed-step integration.In comparison to the traditional approach of plugging the problem into a “black-box” NLP solver, the methods shown converge even when given no knowledge of the solution at all. It was found that the only piece of information that the user needs to provide is a rough guess for the time of flight, as the transfer time guess will dictate which set of local solutions the algorithm could converge on. This robustness to initial guess is a compelling feature, as three-body orbit transfers are challenging to design with intuition alone. Of course, if a high-quality initial guess is available, the methods shown are still valid.We have shown that endpoints can be efficiently constrained to lie on 3-body repeating orbits, and that time of flight can be optimized as well. When optimizing the endpoints, we must make a trade between converging quickly on sub-optimal endpoints or converging more slowly on end-points that are arbitrarily close to optimal. It is easy for the mission design engineer to adjust this trade based on the problem at hand.The biggest limitation to the algorithm at this point is that multi-revolution transfers (greater than 2 revolutions) do not work nearly as well. This restriction comes in because the relationship between node 1 and node N becomes increasingly nonlinear as the angular distance grows. Trans-fers with more than about 1.5 complete revolutions generally require the line search to improve convergence. Future work includes: Comparison of this algorithm with other established tools; improvements to how multiple-revolution transfers are handled; parallelization of the Jacobian computation; in-creased efficiency for the line search; and optimization of many more trajectories between a variety of 3-body orbits.

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.

A mixed-mode traffic assignment model with new time-flow impedance function

NASA Astrophysics Data System (ADS)

Lin, Gui-Hua; Hu, Yu; Zou, Yuan-Yang

2018-01-01

Recently, with the wide adoption of electric vehicles, transportation network has shown different characteristics and been further developed. In this paper, we present a new time-flow impedance function, which may be more realistic than the existing time-flow impedance functions. Based on this new impedance function, we present an optimization model for a mixed-mode traffic network in which battery electric vehicles (BEVs) and gasoline vehicles (GVs) are chosen. We suggest two approaches to handle the model: One is to use the interior point (IP) algorithm and the other is to employ the sequential quadratic programming (SQP) algorithm. Three numerical examples are presented to illustrate the efficiency of these approaches. In particular, our numerical results show that more travelers prefer to choosing BEVs when the distance limit of BEVs is long enough and the unit operating cost of GVs is higher than that of BEVs, and the SQP algorithm is faster than the IP algorithm.

Analytic game—theoretic approach to ground-water extraction

NASA Astrophysics Data System (ADS)

Loáiciga, Hugo A.

2004-09-01

The roles of cooperation and non-cooperation in the sustainable exploitation of a jointly used groundwater resource have been quantified mathematically using an analytical game-theoretic formulation. Cooperative equilibrium arises when ground-water users respect water-level constraints and consider mutual impacts, which allows them to derive economic benefits from ground-water indefinitely, that is, to achieve sustainability. This work shows that cooperative equilibrium can be obtained from the solution of a quadratic programming problem. For cooperative equilibrium to hold, however, enforcement must be effective. Otherwise, according to the commonized costs-privatized profits paradox, there is a natural tendency towards non-cooperation and non-sustainable aquifer mining, of which overdraft is a typical symptom. Non-cooperative behavior arises when at least one ground-water user neglects the externalities of his adopted ground-water pumping strategy. In this instance, water-level constraints may be violated in a relatively short time and the economic benefits from ground-water extraction fall below those obtained with cooperative aquifer use. One example illustrates the game theoretic approach of this work.

Support Vector Machines Trained with Evolutionary Algorithms Employing Kernel Adatron for Large Scale Classification of Protein Structures.

PubMed

Arana-Daniel, Nancy; Gallegos, Alberto A; López-Franco, Carlos; Alanís, Alma Y; Morales, Jacob; López-Franco, Adriana

2016-01-01

With the increasing power of computers, the amount of data that can be processed in small periods of time has grown exponentially, as has the importance of classifying large-scale data efficiently. Support vector machines have shown good results classifying large amounts of high-dimensional data, such as data generated by protein structure prediction, spam recognition, medical diagnosis, optical character recognition and text classification, etc. Most state of the art approaches for large-scale learning use traditional optimization methods, such as quadratic programming or gradient descent, which makes the use of evolutionary algorithms for training support vector machines an area to be explored. The present paper proposes an approach that is simple to implement based on evolutionary algorithms and Kernel-Adatron for solving large-scale classification problems, focusing on protein structure prediction. The functional properties of proteins depend upon their three-dimensional structures. Knowing the structures of proteins is crucial for biology and can lead to improvements in areas such as medicine, agriculture and biofuels.

Generalized SMO algorithm for SVM-based multitask learning.

PubMed

Cai, Feng; Cherkassky, Vladimir

2012-06-01

Exploiting additional information to improve traditional inductive learning is an active research area in machine learning. In many supervised-learning applications, training data can be naturally separated into several groups, and incorporating this group information into learning may improve generalization. Recently, Vapnik proposed a general approach to formalizing such problems, known as "learning with structured data" and its support vector machine (SVM) based optimization formulation called SVM+. Liang and Cherkassky showed the connection between SVM+ and multitask learning (MTL) approaches in machine learning, and proposed an SVM-based formulation for MTL called SVM+MTL for classification. Training the SVM+MTL classifier requires the solution of a large quadratic programming optimization problem which scales as O(n(3)) with sample size n. So there is a need to develop computationally efficient algorithms for implementing SVM+MTL. This brief generalizes Platt's sequential minimal optimization (SMO) algorithm to the SVM+MTL setting. Empirical results show that, for typical SVM+MTL problems, the proposed generalized SMO achieves over 100 times speed-up, in comparison with general-purpose optimization routines.

Video stereolization: combining motion analysis with user interaction.

PubMed

Liao, Miao; Gao, Jizhou; Yang, Ruigang; Gong, Minglun

2012-07-01

We present a semiautomatic system that converts conventional videos into stereoscopic videos by combining motion analysis with user interaction, aiming to transfer as much as possible labeling work from the user to the computer. In addition to the widely used structure from motion (SFM) techniques, we develop two new methods that analyze the optical flow to provide additional qualitative depth constraints. They remove the camera movement restriction imposed by SFM so that general motions can be used in scene depth estimation-the central problem in mono-to-stereo conversion. With these algorithms, the user's labeling task is significantly simplified. We further developed a quadratic programming approach to incorporate both quantitative depth and qualitative depth (such as these from user scribbling) to recover dense depth maps for all frames, from which stereoscopic view can be synthesized. In addition to visual results, we present user study results showing that our approach is more intuitive and less labor intensive, while producing 3D effect comparable to that from current state-of-the-art interactive algorithms.

A symbiotic approach to fluid equations and non-linear flux-driven simulations of plasma dynamics

NASA Astrophysics Data System (ADS)

Halpern, Federico

2017-10-01

The fluid framework is ubiquitous in studies of plasma transport and stability. Typical forms of the fluid equations are motivated by analytical work dating several decades ago, before computer simulations were indispensable, and can be, therefore, not optimal for numerical computation. We demonstrate a new first-principles approach to obtaining manifestly consistent, skew-symmetric fluid models, ensuring internal consistency and conservation properties even in discrete form. Mass, kinetic, and internal energy become quadratic (and always positive) invariants of the system. The model lends itself to a robust, straightforward discretization scheme with inherent non-linear stability. A simpler, drift-ordered form of the equations is obtained, and first results of their numerical implementation as a binary framework for bulk-fluid global plasma simulations are demonstrated. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, Theory Program, under Award No. DE-FG02-95ER54309.

Physically founded phonon dispersions of few-layer materials and the case of borophene

DOE PAGES

Carrete, Jesús; Li, Wu; Lindsay, Lucas; ...

2016-04-21

By building physically sound interatomic force constants,we offer evidence of the universal presence of a quadratic phonon branch in all unstrained 2D materials, thus contradicting much of the existing literature. Through a reformulation of the interatomic force constants (IFCs) in terms of internal coordinates, we find that a delicate balance between the IFCs is responsible for this quadraticity. We use this approach to predict the thermal conductivity of Pmmn borophene, which is comparable to that of MoS 2, and displays a remarkable in-plane anisotropy. Ultimately, these qualities may enable the efficient heat management of borophene devices in potential nanoelectronic applications

Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

Optimization of cascade blade mistuning. I - Equations of motion and basic inherent properties

NASA Technical Reports Server (NTRS)

Nissim, E.

1985-01-01

Attention is given to the derivation of the equations of motion of mistuned compressor blades, interpolating aerodynamic coefficients by means of quadratic expressions in the reduced frequency. If the coefficients of the quadratic expressions are permitted to assume complex values, excellent accuracy is obtained and Pade rational expressions are obviated. On the basis of the resulting equations, it is shown analytically that the sum of all the real parts of the eigenvalues is independent of the mistuning introduced into the system. Blade mistuning is further treated through the aerodynamic energy approach, and the limiting vibration modes associated with alternative mistunings are identified.

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.

Regge trajectories for heavy quarkonia from the quadratic form of the spinless Salpeter-type equation

NASA Astrophysics Data System (ADS)

Chen, Jiao-Kai

2018-03-01

In this paper, we present one new form of the Regge trajectories for heavy quarkonia which is obtained from the quadratic form of the spinless Salpeter-type equation (QSSE) by employing the Bohr-Sommerfeld quantization approach. The obtained Regge trajectories take the parameterized form M^2={β }({c_l}l+{π }n_r+c_0)^{2/3}+c_1, which are different from the present Regge trajectories. Then we apply the obtained Regge trajectories to fit the spectra of charmonia and bottomonia. The fitted Regge trajectories are in good agreement with the experimental data and the theoretical predictions.

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.

Gain scheduled linear quadratic control for quadcopter

NASA Astrophysics Data System (ADS)

Okasha, M.; Shah, J.; Fauzi, W.; Hanouf, Z.

2017-12-01

This study exploits the dynamics and control of quadcopters using Linear Quadratic Regulator (LQR) control approach. The quadcopter’s mathematical model is derived using the Newton-Euler method. It is a highly manoeuvrable, nonlinear, coupled with six degrees of freedom (DOF) model, which includes aerodynamics and detailed gyroscopic moments that are often ignored in many literatures. The linearized model is obtained and characterized by the heading angle (i.e. yaw angle) of the quadcopter. The adopted control approach utilizes LQR method to track several reference trajectories including circle and helix curves with significant variation in the yaw angle. The controller is modified to overcome difficulties related to the continuous changes in the operating points and eliminate chattering and discontinuity that is observed in the control input signal. Numerical non-linear simulations are performed using MATLAB and Simulink to illustrate to accuracy and effectiveness of the proposed controller.

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.

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.

Aggregation of LoD 1 building models as an optimization problem

NASA Astrophysics Data System (ADS)

Guercke, R.; Götzelmann, T.; Brenner, C.; Sester, M.

3D city models offered by digital map providers typically consist of several thousands or even millions of individual buildings. Those buildings are usually generated in an automated fashion from high resolution cadastral and remote sensing data and can be very detailed. However, not in every application such a high degree of detail is desirable. One way to remove complexity is to aggregate individual buildings, simplify the ground plan and assign an appropriate average building height. This task is computationally complex because it includes the combinatorial optimization problem of determining which subset of the original set of buildings should best be aggregated to meet the demands of an application. In this article, we introduce approaches to express different aspects of the aggregation of LoD 1 building models in the form of Mixed Integer Programming (MIP) problems. The advantage of this approach is that for linear (and some quadratic) MIP problems, sophisticated software exists to find exact solutions (global optima) with reasonable effort. We also propose two different heuristic approaches based on the region growing strategy and evaluate their potential for optimization by comparing their performance to a MIP-based approach.

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

Development of Quadratic Programming Algorithm Based on Interior Point Method with Estimation Mechanism of Active Constraints

NASA Astrophysics Data System (ADS)

Hashimoto, Hiroyuki; Takaguchi, Yusuke; Nakamura, Shizuka

Instability of calculation process and increase of calculation time caused by increasing size of continuous optimization problem remain the major issues to be solved to apply the technique to practical industrial systems. This paper proposes an enhanced quadratic programming algorithm based on interior point method mainly for improvement of calculation stability. The proposed method has dynamic estimation mechanism of active constraints on variables, which fixes the variables getting closer to the upper/lower limit on them and afterwards releases the fixed ones as needed during the optimization process. It is considered as algorithm-level integration of the solution strategy of active-set method into the interior point method framework. We describe some numerical results on commonly-used bench-mark problems called “CUTEr” to show the effectiveness of the proposed method. Furthermore, the test results on large-sized ELD problem (Economic Load Dispatching problems in electric power supply scheduling) are also described as a practical industrial application.

Documentation of the Fourth Order Band Model

NASA Technical Reports Server (NTRS)

Kalnay-Rivas, E.; Hoitsma, D.

1979-01-01

A general circulation model is presented which uses quadratically conservative, fourth order horizontal space differences on an unstaggered grid and second order vertical space differences with a forward-backward or a smooth leap frog time scheme to solve the primitive equations of motion. The dynamic equations for motion, finite difference equations, a discussion of the structure and flow chart of the program code, a program listing, and three relevent papers are given.

Application of Sequential Quadratic Programming to Minimize Smart Active Flap Rotor Hub Loads

NASA Technical Reports Server (NTRS)

Kottapalli, Sesi; Leyland, Jane

2014-01-01

In an analytical study, SMART active flap rotor hub loads have been minimized using nonlinear programming constrained optimization methodology. The recently developed NLPQLP system (Schittkowski, 2010) that employs Sequential Quadratic Programming (SQP) as its core algorithm was embedded into a driver code (NLP10x10) specifically designed to minimize active flap rotor hub loads (Leyland, 2014). Three types of practical constraints on the flap deflections have been considered. To validate the current application, two other optimization methods have been used: i) the standard, linear unconstrained method, and ii) the nonlinear Generalized Reduced Gradient (GRG) method with constraints. The new software code NLP10x10 has been systematically checked out. It has been verified that NLP10x10 is functioning as desired. The following are briefly covered in this paper: relevant optimization theory; implementation of the capability of minimizing a metric of all, or a subset, of the hub loads as well as the capability of using all, or a subset, of the flap harmonics; and finally, solutions for the SMART rotor. The eventual goal is to implement NLP10x10 in a real-time wind tunnel environment.

Optimization strategies based on sequential quadratic programming applied for a fermentation process for butanol production.

PubMed

Pinto Mariano, Adriano; Bastos Borba Costa, Caliane; de Franceschi de Angelis, Dejanira; Maugeri Filho, Francisco; Pires Atala, Daniel Ibraim; Wolf Maciel, Maria Regina; Maciel Filho, Rubens

2009-11-01

In this work, the mathematical optimization of a continuous flash fermentation process for the production of biobutanol was studied. The process consists of three interconnected units, as follows: fermentor, cell-retention system (tangential microfiltration), and vacuum flash vessel (responsible for the continuous recovery of butanol from the broth). The objective of the optimization was to maximize butanol productivity for a desired substrate conversion. Two strategies were compared for the optimization of the process. In one of them, the process was represented by a deterministic model with kinetic parameters determined experimentally and, in the other, by a statistical model obtained using the factorial design technique combined with simulation. For both strategies, the problem was written as a nonlinear programming problem and was solved with the sequential quadratic programming technique. The results showed that despite the very similar solutions obtained with both strategies, the problems found with the strategy using the deterministic model, such as lack of convergence and high computational time, make the use of the optimization strategy with the statistical model, which showed to be robust and fast, more suitable for the flash fermentation process, being recommended for real-time applications coupling optimization and control.

Monitoring post-fire vegetation rehabilitation projects: A common approach for non-forested ecosystems

USGS Publications Warehouse

Wirth, Troy A.; Pyke, David A.

2007-01-01

Emergency Stabilization and Rehabilitation (ES&R) and Burned Area Emergency Response (BAER) treatments are short-term, high-intensity treatments designed to mitigate the adverse effects of wildfire on public lands. The federal government expends significant resources implementing ES&R and BAER treatments after wildfires; however, recent reviews have found that existing data from monitoring and research are insufficient to evaluate the effects of these activities. The purpose of this report is to: (1) document what monitoring methods are generally used by personnel in the field; (2) describe approaches and methods for post-fire vegetation and soil monitoring documented in agency manuals; (3) determine the common elements of monitoring programs recommended in these manuals; and (4) describe a common monitoring approach to determine the effectiveness of future ES&R and BAER treatments in non-forested regions. Both qualitative and quantitative methods to measure effectiveness of ES&R treatments are used by federal land management agencies. Quantitative methods are used in the field depending on factors such as funding, personnel, and time constraints. There are seven vegetation monitoring manuals produced by the federal government that address monitoring methods for (primarily) vegetation and soil attributes. These methods vary in their objectivity and repeatability. The most repeatable methods are point-intercept, quadrat-based density measurements, gap intercepts, and direct measurement of soil erosion. Additionally, these manuals recommend approaches for designing monitoring programs for the state of ecosystems or the effect of management actions. The elements of a defensible monitoring program applicable to ES&R and BAER projects that most of these manuals have in common are objectives, stratification, control areas, random sampling, data quality, and statistical analysis. The effectiveness of treatments can be determined more accurately if data are gathered using an approach that incorporates these six monitoring program design elements and objectives, as well as repeatable procedures to measure cover, density, gap intercept, and soil erosion within each ecoregion and plant community. Additionally, using a common monitoring program design with comparable methods, consistently documenting results, and creating and maintaining a central database for query and reporting, will ultimately allow a determination of the effectiveness of post-fire rehabilitation activities region-wide.

NOLIN: A nonlinear laminate analysis program

NASA Technical Reports Server (NTRS)

Kibler, J. J.

1975-01-01

A nonlinear, plane-stress, laminate analysis program, NOLIN, was developed which accounts for laminae nonlinearity under inplane shear and transverse extensional stress. The program determines the nonlinear stress-strain behavior of symmetric laminates subjected to any combination of inplane shear and biaxial extensional loadings. The program has the ability to treat different stress-strain behavior in tension and compression, and predicts laminate failure using any or all of maximum stress, maximum strain, and quadratic interaction failure criteria. A brief description of the program is presented including discussion of the flow of information and details of the input required. Sample problems and a complete listing of the program is also provided.

QuBiLS-MAS, open source multi-platform software for atom- and bond-based topological (2D) and chiral (2.5D) algebraic molecular descriptors computations.

PubMed

Valdés-Martiní, José R; Marrero-Ponce, Yovani; García-Jacas, César R; Martinez-Mayorga, Karina; Barigye, Stephen J; Vaz d'Almeida, Yasser Silveira; Pham-The, Hai; Pérez-Giménez, Facundo; Morell, Carlos A

2017-06-07

In previous reports, Marrero-Ponce et al. proposed algebraic formalisms for characterizing topological (2D) and chiral (2.5D) molecular features through atom- and bond-based ToMoCoMD-CARDD (acronym for Topological Molecular Computational Design-Computer Aided Rational Drug Design) molecular descriptors. These MDs codify molecular information based on the bilinear, quadratic and linear algebraic forms and the graph-theoretical electronic-density and edge-adjacency matrices in order to consider atom- and bond-based relations, respectively. These MDs have been successfully applied in the screening of chemical compounds of different therapeutic applications ranging from antimalarials, antibacterials, tyrosinase inhibitors and so on. To compute these MDs, a computational program with the same name was initially developed. However, this in house software barely offered the functionalities required in contemporary molecular modeling tasks, in addition to the inherent limitations that made its usability impractical. Therefore, the present manuscript introduces the QuBiLS-MAS (acronym for Quadratic, Bilinear and N-Linear mapS based on graph-theoretic electronic-density Matrices and Atomic weightingS) software designed to compute topological (0-2.5D) molecular descriptors based on bilinear, quadratic and linear algebraic forms for atom- and bond-based relations. The QuBiLS-MAS module was designed as standalone software, in which extensions and generalizations of the former ToMoCoMD-CARDD 2D-algebraic indices are implemented, considering the following aspects: (a) two new matrix normalization approaches based on double-stochastic and mutual probability formalisms; (b) topological constraints (cut-offs) to take into account particular inter-atomic relations; (c) six additional atomic properties to be used as weighting schemes in the calculation of the molecular vectors; (d) four new local-fragments to consider molecular regions of interest; (e) number of lone-pair electrons in chemical structure defined by diagonal coefficients in matrix representations; and (f) several aggregation operators (invariants) applied over atom/bond-level descriptors in order to compute global indices. This software permits the parallel computation of the indices, contains a batch processing module and data curation functionalities. This program was developed in Java v1.7 using the Chemistry Development Kit library (version 1.4.19). The QuBiLS-MAS software consists of two components: a desktop interface (GUI) and an API library allowing for the easy integration of the latter in chemoinformatics applications. The relevance of the novel extensions and generalizations implemented in this software is demonstrated through three studies. Firstly, a comparative Shannon's entropy based variability study for the proposed QuBiLS-MAS and the DRAGON indices demonstrates superior performance for the former. A principal component analysis reveals that the QuBiLS-MAS approach captures chemical information orthogonal to that codified by the DRAGON descriptors. Lastly, a QSAR study for the binding affinity to the corticosteroid-binding globulin using Cramer's steroid dataset is carried out. From these analyses, it is revealed that the QuBiLS-MAS approach for atom-pair relations yields similar-to-superior performance with regard to other QSAR methodologies reported in the literature. Therefore, the QuBiLS-MAS approach constitutes a useful tool for the diversity analysis of chemical compound datasets and high-throughput screening of structure-activity data.

Feasibility of Decentralized Linear-Quadratic-Gaussian Control of Autonomous Distributed Spacecraft

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

1999-01-01

A distributed satellite formation, modeled as an arbitrary number of fully connected nodes in a network, could be controlled using a decentralized controller framework that distributes operations in parallel over the network. For such problems, a solution that minimizes data transmission requirements, in the context of linear-quadratic-Gaussian (LQG) control theory, was given by Speyer. This approach is advantageous because it is non-hierarchical, detected failures gracefully degrade system performance, fewer local computations are required than for a centralized controller, and it is optimal with respect to the standard LQG cost function. Disadvantages of the approach are the need for a fully connected communications network, the total operations performed over all the nodes are greater than for a centralized controller, and the approach is formulated for linear time-invariant systems. To investigate the feasibility of the decentralized approach to satellite formation flying, a simple centralized LQG design for a spacecraft orbit control problem is adapted to the decentralized framework. The simple design uses a fixed reference trajectory (an equatorial, Keplerian, circular orbit), and by appropriate choice of coordinates and measurements is formulated as a linear time-invariant system.

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,…

Elastic Model Transitions: a Hybrid Approach Utilizing Quadratic Inequality Constrained Least Squares (LSQI) and Direct Shape Mapping (DSM)

NASA Technical Reports Server (NTRS)

Jurenko, Robert J.; Bush, T. Jason; Ottander, John A.

2014-01-01

A method for transitioning linear time invariant (LTI) models in time varying simulation is proposed that utilizes both quadratically constrained least squares (LSQI) and Direct Shape Mapping (DSM) algorithms to determine physical displacements. This approach is applicable to the simulation of the elastic behavior of launch vehicles and other structures that utilize multiple LTI finite element model (FEM) derived mode sets that are propagated throughout time. The time invariant nature of the elastic data for discrete segments of the launch vehicle trajectory presents a problem of how to properly transition between models while preserving motion across the transition. In addition, energy may vary between flex models when using a truncated mode set. The LSQI-DSM algorithm can accommodate significant changes in energy between FEM models and carries elastic motion across FEM model transitions. Compared with previous approaches, the LSQI-DSM algorithm shows improvements ranging from a significant reduction to a complete removal of transients across FEM model transitions as well as maintaining elastic motion from the prior state.

Nonlinear Curve-Fitting Program

NASA Technical Reports Server (NTRS)

Everhart, Joel L.; Badavi, Forooz F.

1989-01-01

Nonlinear optimization algorithm helps in finding best-fit curve. Nonlinear Curve Fitting Program, NLINEAR, interactive curve-fitting routine based on description of quadratic expansion of X(sup 2) statistic. Utilizes nonlinear optimization algorithm calculating best statistically weighted values of parameters of fitting function and X(sup 2) minimized. Provides user with such statistical information as goodness of fit and estimated values of parameters producing highest degree of correlation between experimental data and mathematical model. Written in FORTRAN 77.

A Centered Projective Algorithm for Linear Programming

DTIC Science & Technology

1988-02-01

zx/l to (PA Karmarkar’s algorithm iterates this procedure. An alternative method, the so-called affine variant (first proposed by Dikin [6] in 1967...trajectories, II. Legendre transform coordinates . central trajectories," manuscripts, to appear in Transactions of the American [6] I.I. Dikin ...34Iterative solution of problems of linear and quadratic programming," Soviet Mathematics Dokladv 8 (1967), 674-675. [7] I.I. Dikin , "On the speed of an

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…

A Sequential Quadratic Programming Algorithm Using an Incomplete Solution of the Subproblem

DTIC Science & Technology

1990-09-01

Electr6nica e Inform’itica Industrial E.T.S. Ingenieros Industriales Universidad Polit6cnica, Madrid Technical Report SOL 90-12 September 1990 -Y...MURRAY* AND FRANCISCO J. PRIETOt *Systems Optimization Laboratory Department of Operations Research Stanford University tDept. de Automitica, Ingenieria

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.

Frequency-independent approach to calculate physical optics radiations with the quadratic concave phase variations

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

Wu, Yu Mao, E-mail: yumaowu@fudan.edu.cn; Teng, Si Jia, E-mail: sjteng12@fudan.edu.cn

In this work, we develop the numerical steepest descent path (NSDP) method to calculate the physical optics (PO) radiations with the quadratic concave phase variations. With the surface integral equation method, the physical optics (PO) scattered fields are formulated and further reduced to the surface integrals. The high frequency physical critical points contributions, including the stationary phase points, the boundary resonance points and the vertex points are comprehensively studied via the proposed NSDP method. The key contributions of this work are twofold. One is that together with the PO integrals taking the quadratic parabolic and hyperbolic phase terms, this workmore » makes the NSDP theory be complete for treating the PO integrals with quadratic phase variations. Another is that, in order to illustrate the transition effect of the high frequency physical critical points, in this work, we consider and further extend the NSDP method to calculate the PO integrals with the coalescence of the high frequency critical points. Numerical results for the highly oscillatory PO integral with the coalescence of the critical points are given to verify the efficiency of the proposed NSDP method. The NSDP method could achieve the frequency independent computational workload and error controllable accuracy in all the numerical experiments, especially for the case of the coalescence of the high frequency critical points.« less

The role of modern control theory in the design of controls for aircraft turbine engines

NASA Technical Reports Server (NTRS)

Zeller, J.; Lehtinen, B.; Merrill, W.

1982-01-01

The development, applications, and current research in modern control theory (MCT) are reviewed, noting the importance for fuel-efficient operation of turbines with variable inlet guide vanes, compressor stators, and exhaust nozzle area. The evolution of multivariable propulsion control design is examined, noting a basis in a matrix formulation of the differential equations defining the process, leading to state space formulations. Reports and papers which appeared from 1970-1982 which dealt with problems in MCT applications to turbine engine control design are outlined, including works on linear quadratic regulator methods, frequency domain methods, identification, estimation, and model reduction, detection, isolation, and accommodation, and state space control, adaptive control, and optimization approaches. Finally, NASA programs in frequency domain design, sensor failure detection, computer-aided control design, and plant modeling are explored

An optimization program based on the method of feasible directions: Theory and users guide

NASA Technical Reports Server (NTRS)

Belegundu, Ashok D.; Berke, Laszlo; Patnaik, Surya N.

1994-01-01

The theory and user instructions for an optimization code based on the method of feasible directions are presented. The code was written for wide distribution and ease of attachment to other simulation software. Although the theory of the method of feasible direction was developed in the 1960's, many considerations are involved in its actual implementation as a computer code. Included in the code are a number of features to improve robustness in optimization. The search direction is obtained by solving a quadratic program using an interior method based on Karmarkar's algorithm. The theory is discussed focusing on the important and often overlooked role played by the various parameters guiding the iterations within the program. Also discussed is a robust approach for handling infeasible starting points. The code was validated by solving a variety of structural optimization test problems that have known solutions obtained by other optimization codes. It has been observed that this code is robust: it has solved a variety of problems from different starting points. However, the code is inefficient in that it takes considerable CPU time as compared with certain other available codes. Further work is required to improve its efficiency while retaining its robustness.

Evaluating the efficiency of a one-square-meter quadrat sampler for riffle-dwelling fish

USGS Publications Warehouse

Peterson, J.T.; Rabeni, C.F.

2001-01-01

We evaluated the efficacy of a 1-m2 quadrat sampler for collecting riffle-dwelling fishes in an Ozark stream. We used a dual-gear approach to evaluate sampler efficiency in relation to species, fish size, and habitat variables. Quasi-likelihood regression showed sampling efficiency to differ significantly (P 0.05). Sampling efficiency was significantly influenced by physical habitat characteristics. Mean current velocity negatively influenced sampling efficiencies for Cyprinidae (P = 0.009), Cottidae (P = 0.006), and Percidae (P < 0.001), and the amount of cobble substrate negatively influenced sampling efficiencies for Cyprinidae (P = 0.025), Ictaluridae (P < 0.001), and Percidae (P < 0.001). Water temperature negatively influenced sampling efficiency for Cyprinidae (P = 0.009) and Ictaluridae (P = 0.006). Species-richness efficiency was positively influenced (P = 0.002) by percentage of riffle sampled. Under average habitat conditions encountered in stream riffles, the 1-m2 quadrat sampler was most efficient at estimating the densities of Cyprinidae (84%) and Cottidae (80%) and least efficient for Percidae (57%) and Ictaluridae (31%).

Users manual for flight control design programs

NASA Technical Reports Server (NTRS)

Nalbandian, J. Y.

1975-01-01

Computer programs for the design of analog and digital flight control systems are documented. The program DIGADAPT uses linear-quadratic-gaussian synthesis algorithms in the design of command response controllers and state estimators, and it applies covariance propagation analysis to the selection of sampling intervals for digital systems. Program SCHED executes correlation and regression analyses for the development of gain and trim schedules to be used in open-loop explicit-adaptive control laws. A linear-time-varying simulation of aircraft motions is provided by the program TVHIS, which includes guidance and control logic, as well as models for control actuator dynamics. The programs are coded in FORTRAN and are compiled and executed on both IBM and CDC computers.

Stochastic model of the NASA/MSFC ground facility for large space structures with uncertain parameters: The maximum entropy approach, part 2

NASA Technical Reports Server (NTRS)

Hsia, Wei Shen

1989-01-01

A validated technology data base is being developed in the areas of control/structures interaction, deployment dynamics, and system performance for Large Space Structures (LSS). A Ground Facility (GF), in which the dynamics and control systems being considered for LSS applications can be verified, was designed and built. One of the important aspects of the GF is to verify the analytical model for the control system design. The procedure is to describe the control system mathematically as well as possible, then to perform tests on the control system, and finally to factor those results into the mathematical model. The reduction of the order of a higher order control plant was addressed. The computer program was improved for the maximum entropy principle adopted in Hyland's MEOP method. The program was tested against the testing problem. It resulted in a very close match. Two methods of model reduction were examined: Wilson's model reduction method and Hyland's optimal projection (OP) method. Design of a computer program for Hyland's OP method was attempted. Due to the difficulty encountered at the stage where a special matrix factorization technique is needed in order to obtain the required projection matrix, the program was successful up to the finding of the Linear Quadratic Gaussian solution but not beyond. Numerical results along with computer programs which employed ORACLS are presented.

Convergence of the standard RLS method and UDUT factorisation of covariance matrix for solving the algebraic Riccati equation of the DLQR via heuristic approximate dynamic programming

NASA Astrophysics Data System (ADS)

Moraes Rêgo, Patrícia Helena; Viana da Fonseca Neto, João; Ferreira, Ernesto M.

2015-08-01

The main focus of this article is to present a proposal to solve, via UDUT factorisation, the convergence and numerical stability problems that are related to the covariance matrix ill-conditioning of the recursive least squares (RLS) approach for online approximations of the algebraic Riccati equation (ARE) solution associated with the discrete linear quadratic regulator (DLQR) problem formulated in the actor-critic reinforcement learning and approximate dynamic programming context. The parameterisations of the Bellman equation, utility function and dynamic system as well as the algebra of Kronecker product assemble a framework for the solution of the DLQR problem. The condition number and the positivity parameter of the covariance matrix are associated with statistical metrics for evaluating the approximation performance of the ARE solution via RLS-based estimators. The performance of RLS approximators is also evaluated in terms of consistence and polarisation when associated with reinforcement learning methods. The used methodology contemplates realisations of online designs for DLQR controllers that is evaluated in a multivariable dynamic system model.

Spatial taxation effects on regional coal economic activities

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

Yang, C.W.; Labys, W.C.

1982-01-01

Taxation effects on resource production, consumption and prices are seldom evaluated especially in the field of spatial commodity modeling. The most commonly employed linear programming model has fixed-point estimated demands and capacity constraints; hence it makes taxation effects difficult to be modeled. The second type of resource allocation model, the interregional input-output models does not include a direct and explicit price mechanism. Therefore, it is not suitable for analyzing taxation effects. The third type or spatial commodity model has been econometric in nature. While such an approach has a good deal of flexibility in modeling political and non-economic variables, itmore » treats taxation (or tariff) effects loosely using only dummy variables, and, in many cases, must sacrifice the consistency criterion important for spatial commodity modeling. This leaves model builders only one legitimate choice for analyzing taxation effects: the quadratic programming model which explicitly allows the interplay of regional demand and supply relations via a continuous spatial price constructed by the authors related to the regional demand for and supply of coal from Appalachian markets.« less

Optimization Based Data Mining Approah for Forecasting Real-Time Energy Demand

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

Omitaomu, Olufemi A; Li, Xueping; Zhou, Shengchao

The worldwide concern over environmental degradation, increasing pressure on electric utility companies to meet peak energy demand, and the requirement to avoid purchasing power from the real-time energy market are motivating the utility companies to explore new approaches for forecasting energy demand. Until now, most approaches for forecasting energy demand rely on monthly electrical consumption data. The emergence of smart meters data is changing the data space for electric utility companies, and creating opportunities for utility companies to collect and analyze energy consumption data at a much finer temporal resolution of at least 15-minutes interval. While the data granularity providedmore » by smart meters is important, there are still other challenges in forecasting energy demand; these challenges include lack of information about appliances usage and occupants behavior. Consequently, in this paper, we develop an optimization based data mining approach for forecasting real-time energy demand using smart meters data. The objective of our approach is to develop a robust estimation of energy demand without access to these other building and behavior data. Specifically, the forecasting problem is formulated as a quadratic programming problem and solved using the so-called support vector machine (SVM) technique in an online setting. The parameters of the SVM technique are optimized using simulated annealing approach. The proposed approach is applied to hourly smart meters data for several residential customers over several days.« less

N-person differential games. Part 1: Duality-finite element methods

NASA Technical Reports Server (NTRS)

Chen, G.; Zheng, Q.

1983-01-01

The duality approach, which is motivated by computational needs and is done by introducing N + 1 Language multipliers is addressed. For N-person linear quadratic games, the primal min-max problem is shown to be equivalent to the dual min-max problem.

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.

Equations with Parameters: A Locus Approach

ERIC Educational Resources Information Center

Abramovich, Sergei; Norton, Anderson

2006-01-01

This paper introduces technology-based teaching ideas that facilitate the development of qualitative reasoning techniques in the context of quadratic equations with parameters. It reflects on activities designed for and used with prospective secondary mathematics teachers in accord with standards for teaching and recommendations for teachers in…

A game theoretic approach to a finite-time disturbance attenuation problem

NASA Technical Reports Server (NTRS)

Rhee, Ihnseok; Speyer, Jason L.

1991-01-01

A disturbance attenuation problem over a finite-time interval is considered by a game theoretic approach where the control, restricted to a function of the measurement history, plays against adversaries composed of the process and measurement disturbances, and the initial state. A zero-sum game, formulated as a quadratic cost criterion subject to linear time-varying dynamics and measurements, is solved by a calculus of variation technique. By first maximizing the quadratic cost criterion with respect to the process disturbance and initial state, a full information game between the control and the measurement residual subject to the estimator dynamics results. The resulting solution produces an n-dimensional compensator which expresses the controller as a linear combination of the measurement history. A disturbance attenuation problem is solved based on the results of the game problem. For time-invariant systems it is shown that under certain conditions the time-varying controller becomes time-invariant on the infinite-time interval. The resulting controller satisfies an H(infinity) norm bound.

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

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.

EVALUATION OF A MEASUREMENT METHOD FOR FOREST VEGETATION IN A LARGE-SCALE ECOLOGICAL SURVEY

EPA Science Inventory

We evaluate a field method for determining species richness and canopy cover of vascular plants for the Forest Health Monitoring Program (FHM), an ecological survey of U.S. forests. Measurements are taken within 12 1-m2 quadrats on 1/15 ha plots in FHM. Species richness and cover...

Primal Barrier Methods for Linear Programming

DTIC Science & Technology

1989-06-01

A Theoretical Bound Concerning the difficulties introduced by an ill-conditioned H- 1, Dikin [Dik67] and Stewart [Stew87] show for a full-rank A...Dik67] I. I. Dikin (1967). Iterative solution of problems of linear and quadratic pro- gramming, Doklady Akademii Nauk SSSR, Tom 174, No. 4. [Fia79] A. V

Interior-Point Methods for Linear Programming: A Challenge to the Simplex Method

DTIC Science & Technology

1988-07-01

subsequently found that the method was first proposed by Dikin in 1967 [6]. Search directions are generated by the same system (5). Any hint of quadratic...1982). Inexact Newton methods, SIAM Journal on Numerical Analysis 19, 400-408. [6] I. I. Dikin (1967). Iterative solution of problems of linear and

Optimization of a bundle divertor for FED

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

Hively, L.M.; Rothe, K.E.; Minkoff, M.

1982-01-01

Optimal double-T bundle divertor configurations have been obtained for the Fusion Engineering Device (FED). On-axis ripple is minimized, while satisfying a series of engineering constraints. The ensuing non-linear optimization problem is solved via a sequence of quadratic programming subproblems, using the VMCON algorithm. The resulting divertor designs are substantially improved over previous configurations.

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…

Adaptive dynamic programming for discrete-time linear quadratic regulation based on multirate generalised policy iteration

NASA Astrophysics Data System (ADS)

Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho

2018-06-01

In this paper, we propose two multirate generalised policy iteration (GPI) algorithms applied to discrete-time linear quadratic regulation problems. The proposed algorithms are extensions of the existing GPI algorithm that consists of the approximate policy evaluation and policy improvement steps. The two proposed schemes, named heuristic dynamic programming (HDP) and dual HDP (DHP), based on multirate GPI, use multi-step estimation (M-step Bellman equation) at the approximate policy evaluation step for estimating the value function and its gradient called costate, respectively. Then, we show that these two methods with the same update horizon can be considered equivalent in the iteration domain. Furthermore, monotonically increasing and decreasing convergences, so called value iteration (VI)-mode and policy iteration (PI)-mode convergences, are proved to hold for the proposed multirate GPIs. Further, general convergence properties in terms of eigenvalues are also studied. The data-driven online implementation methods for the proposed HDP and DHP are demonstrated and finally, we present the results of numerical simulations performed to verify the effectiveness of the proposed methods.

Studies on spatial modes and the correlation anisotropy of entangled photons generated from 2D quadratic nonlinear photonic crystals

NASA Astrophysics Data System (ADS)

Luo, X. W.; Xu, P.; Sun, C. W.; Jin, H.; Hou, R. J.; Leng, H. Y.; Zhu, S. N.

2017-06-01

Concurrent spontaneous parametric down-conversion (SPDC) processes have proved to be an appealing approach for engineering the path-entangled photonic state with designable and tunable spatial modes. In this work, we propose a general scheme to construct high-dimensional path entanglement and demonstrate the basic properties of concurrent SPDC processes from domain-engineered quadratic nonlinear photonic crystals, including the spatial modes and the photon flux, as well as the anisotropy of spatial correlation under noncollinear quasi-phase-matching geometry. The overall understanding about the performance of concurrent SPDC processes will give valuable references to the construction of compact path entanglement and the development of new types of photonic quantum technologies.

Single-photon transport through a waveguide coupling to a quadratic optomechanical system

NASA Astrophysics Data System (ADS)

Qiao, Lei

2017-07-01

We study the coherent transport of a single photon, which propagates in a one-dimensional waveguide and is scattered by a quadratic optomechanical system. Our approach, which is based on the Lippmann-Schwinger equation, gives an analytical solution to describe the single-photon transmission and reflection properties. We analyze the transport spectra and find they are not only related to the optomechanical system's energy-level structure, but also dependent on the optomechanical system's inherent parameters. For the existence of atomic degrees of freedom, we get a Rabi-splitting-like or an electromagnetically induced transparency (EIT)-like spectrum, depending on the atom-cavity coupling strength. Here, we focus on the single-photon strong-coupling regime so that single-quantum effects could be seen.

Microgravity vibration isolation: Optimal preview and feedback control

NASA Technical Reports Server (NTRS)

Hampton, R. D.; Knospe, C. R.; Grodsinsky, C. M.; Allaire, P. E.; Lewis, D. W.

1992-01-01

In order to achieve adequate low-frequency vibration isolation for certain space experiments an active control is needed, due to inherent passive-isolator limitations. Proposed here are five possible state-space models for a one-dimensional vibration isolation system with a quadratic performance index. The five models are subsets of a general set of nonhomogeneous state space equations which includes disturbance terms. An optimal control is determined, using a differential equations approach, for this class of problems. This control is expressed in terms of constant, Linear Quadratic Regulator (LQR) feedback gains and constant feedforward (preview) gains. The gains can be easily determined numerically. They result in a robust controller and offers substantial improvements over a control that uses standard LQR feedback alone.

Computation and analysis for a constrained entropy optimization problem in finance

NASA Astrophysics Data System (ADS)

He, Changhong; Coleman, Thomas F.; Li, Yuying

2008-12-01

In [T. Coleman, C. He, Y. Li, Calibrating volatility function bounds for an uncertain volatility model, Journal of Computational Finance (2006) (submitted for publication)], an entropy minimization formulation has been proposed to calibrate an uncertain volatility option pricing model (UVM) from market bid and ask prices. To avoid potential infeasibility due to numerical error, a quadratic penalty function approach is applied. In this paper, we show that the solution to the quadratic penalty problem can be obtained by minimizing an objective function which can be evaluated via solving a Hamilton-Jacobian-Bellman (HJB) equation. We prove that the implicit finite difference solution of this HJB equation converges to its viscosity solution. In addition, we provide computational examples illustrating accuracy of calibration.

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.

An LQR controller design approach for a Large Gap Magnetic Suspension System (LGMSS)

NASA Technical Reports Server (NTRS)

Groom, Nelson J.; Schaffner, Philip R.

1990-01-01

Two control approaches for a Large Gap Magnetic Suspension System (LGMSS) are investigated and numerical results are presented. The approaches are based on Linear Quadratic Regulator (LQR) control theory and include a nonzero set point regulator with constant disturbance input and an integral feedback regulator. The LGMSS provides five degree of freedom control of a cylindrical suspended element which is composed of permanent magnet material. The magnetic actuators are air core electromagnets mounted in a planar way.

A neural network based implementation of an MPC algorithm applied in the control systems of electromechanical plants

NASA Astrophysics Data System (ADS)

Marusak, Piotr M.; Kuntanapreeda, Suwat

2018-01-01

The paper considers application of a neural network based implementation of a model predictive control (MPC) control algorithm to electromechanical plants. Properties of such control plants implicate that a relatively short sampling time should be used. However, in such a case, finding the control value numerically may be too time-consuming. Therefore, the current paper tests the solution based on transforming the MPC optimization problem into a set of differential equations whose solution is the same as that of the original optimization problem. This set of differential equations can be interpreted as a dynamic neural network. In such an approach, the constraints can be introduced into the optimization problem with relative ease. Moreover, the solution of the optimization problem can be obtained faster than when the standard numerical quadratic programming routine is used. However, a very careful tuning of the algorithm is needed to achieve this. A DC motor and an electrohydraulic actuator are taken as illustrative examples. The feasibility and effectiveness of the proposed approach are demonstrated through numerical simulations.

A General Formulation for Robust and Efficient Integration of Finite Differences and Phase Unwrapping on Sparse Multidimensional Domains

NASA Astrophysics Data System (ADS)

Costantini, Mario; Malvarosa, Fabio; Minati, Federico

2010-03-01

Phase unwrapping and integration of finite differences are key problems in several technical fields. In SAR interferometry and differential and persistent scatterers interferometry digital elevation models and displacement measurements can be obtained after unambiguously determining the phase values and reconstructing the mean velocities and elevations of the observed targets, which can be performed by integrating differential estimates of these quantities (finite differences between neighboring points).In this paper we propose a general formulation for robust and efficient integration of finite differences and phase unwrapping, which includes standard techniques methods as sub-cases. The proposed approach allows obtaining more reliable and accurate solutions by exploiting redundant differential estimates (not only between nearest neighboring points) and multi-dimensional information (e.g. multi-temporal, multi-frequency, multi-baseline observations), or external data (e.g. GPS measurements). The proposed approach requires the solution of linear or quadratic programming problems, for which computationally efficient algorithms exist.The validation tests obtained on real SAR data confirm the validity of the method, which was integrated in our production chain and successfully used also in massive productions.

Multi-Constraint Multi-Variable Optimization of Source-Driven Nuclear Systems

NASA Astrophysics Data System (ADS)

Watkins, Edward Francis

1995-01-01

A novel approach to the search for optimal designs of source-driven nuclear systems is investigated. Such systems include radiation shields, fusion reactor blankets and various neutron spectrum-shaping assemblies. The novel approach involves the replacement of the steepest-descents optimization algorithm incorporated in the code SWAN by a significantly more general and efficient sequential quadratic programming optimization algorithm provided by the code NPSOL. The resulting SWAN/NPSOL code system can be applied to more general, multi-variable, multi-constraint shield optimization problems. The constraints it accounts for may include simple bounds on variables, linear constraints, and smooth nonlinear constraints. It may also be applied to unconstrained, bound-constrained and linearly constrained optimization. The shield optimization capabilities of the SWAN/NPSOL code system is tested and verified in a variety of optimization problems: dose minimization at constant cost, cost minimization at constant dose, and multiple-nonlinear constraint optimization. The replacement of the optimization part of SWAN with NPSOL is found feasible and leads to a very substantial improvement in the complexity of optimization problems which can be efficiently handled.

Physician performance assessment using a composite quality index.

PubMed

Liu, Kaibo; Jain, Shabnam; Shi, Jianjun

2013-07-10

Assessing physician performance is important for the purposes of measuring and improving quality of service and reducing healthcare delivery costs. In recent years, physician performance scorecards have been used to provide feedback on individual measures; however, one key challenge is how to develop a composite quality index that combines multiple measures for overall physician performance evaluation. A controversy arises over establishing appropriate weights to combine indicators in multiple dimensions, and cannot be easily resolved. In this study, we proposed a generic unsupervised learning approach to develop a single composite index for physician performance assessment by using non-negative principal component analysis. We developed a new algorithm named iterative quadratic programming to solve the numerical issue in the non-negative principal component analysis approach. We conducted real case studies to demonstrate the performance of the proposed method. We provided interpretations from both statistical and clinical perspectives to evaluate the developed composite ranking score in practice. In addition, we implemented the root cause assessment techniques to explain physician performance for improvement purposes. Copyright © 2012 John Wiley & Sons, Ltd.

Solving portfolio selection problems with minimum transaction lots based on conditional-value-at-risk

NASA Astrophysics Data System (ADS)

Setiawan, E. P.; Rosadi, D.

2017-01-01

Portfolio selection problems conventionally means ‘minimizing the risk, given the certain level of returns’ from some financial assets. This problem is frequently solved with quadratic or linear programming methods, depending on the risk measure that used in the objective function. However, the solutions obtained by these method are in real numbers, which may give some problem in real application because each asset usually has its minimum transaction lots. In the classical approach considering minimum transaction lots were developed based on linear Mean Absolute Deviation (MAD), variance (like Markowitz’s model), and semi-variance as risk measure. In this paper we investigated the portfolio selection methods with minimum transaction lots with conditional value at risk (CVaR) as risk measure. The mean-CVaR methodology only involves the part of the tail of the distribution that contributed to high losses. This approach looks better when we work with non-symmetric return probability distribution. Solution of this method can be found with Genetic Algorithm (GA) methods. We provide real examples using stocks from Indonesia stocks market.

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...

Comparison of the quadratic configuration interaction and coupled cluster approaches to electron correlation including the effect of triple excitations

NASA Technical Reports Server (NTRS)

Taylor, Peter R.; Lee, Timothy J.; Rendell, Alistair P.

1990-01-01

The recently proposed quadratic configuration interaction (QCI) method is compared with the more rigorous coupled cluster (CC) approach for a variety of chemical systems. Some of these systems are well represented by a single-determinant reference function and others are not. The finite order singles and doubles correlation energy, the perturbational triples correlation energy, and a recently devised diagnostic for estimating the importance of multireference effects are considered. The spectroscopic constants of CuH, the equilibrium structure of cis-(NO)2 and the binding energies of Be3, Be4, Mg3, and Mg4 were calculated using both approaches. The diagnostic for estimating multireference character clearly demonstrates that the QCI method becomes less satisfactory than the CC approach as non-dynamical correlation becomes more important, in agreement with a perturbational analysis of the two methods and the numerical estimates of the triple excitation energies they yield. The results for CuH show that the differences between the two methods become more apparent as the chemical systems under investigation becomes more multireference in nature and the QCI results consequently become less reliable. Nonetheless, when the system of interest is dominated by a single reference determinant both QCI and CC give very similar results.

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.

Implications of a quadratic stream definition in radiative transfer theory.

NASA Technical Reports Server (NTRS)

Whitney, C.

1972-01-01

An explicit definition of the radiation-stream concept is stated and applied to approximate the integro-differential equation of radiative transfer with a set of twelve coupled differential equations. Computational efficiency is enhanced by distributing the corresponding streams in three-dimensional space in a totally symmetric way. Polarization is then incorporated in this model. A computer program based on the model is briefly compared with a Monte Carlo program for simulation of horizon scans of the earth's atmosphere. It is found to be considerably faster.

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.

Optimization of spatiotemporally fractionated radiotherapy treatments with bounds on the achievable benefit

NASA Astrophysics Data System (ADS)

Gaddy, Melissa R.; Yıldız, Sercan; Unkelbach, Jan; Papp, Dávid

2018-01-01

Spatiotemporal fractionation schemes, that is, treatments delivering different dose distributions in different fractions, can potentially lower treatment side effects without compromising tumor control. This can be achieved by hypofractionating parts of the tumor while delivering approximately uniformly fractionated doses to the surrounding tissue. Plan optimization for such treatments is based on biologically effective dose (BED); however, this leads to computationally challenging nonconvex optimization problems. Optimization methods that are in current use yield only locally optimal solutions, and it has hitherto been unclear whether these plans are close to the global optimum. We present an optimization framework to compute rigorous bounds on the maximum achievable normal tissue BED reduction for spatiotemporal plans. The approach is demonstrated on liver tumors, where the primary goal is to reduce mean liver BED without compromising any other treatment objective. The BED-based treatment plan optimization problems are formulated as quadratically constrained quadratic programming (QCQP) problems. First, a conventional, uniformly fractionated reference plan is computed using convex optimization. Then, a second, nonconvex, QCQP model is solved to local optimality to compute a spatiotemporally fractionated plan that minimizes mean liver BED, subject to the constraints that the plan is no worse than the reference plan with respect to all other planning goals. Finally, we derive a convex relaxation of the second model in the form of a semidefinite programming problem, which provides a rigorous lower bound on the lowest achievable mean liver BED. The method is presented on five cases with distinct geometries. The computed spatiotemporal plans achieve 12-35% mean liver BED reduction over the optimal uniformly fractionated plans. This reduction corresponds to 79-97% of the gap between the mean liver BED of the uniform reference plans and our lower bounds on the lowest achievable mean liver BED. The results indicate that spatiotemporal treatments can achieve substantial reductions in normal tissue dose and BED, and that local optimization techniques provide high-quality plans that are close to realizing the maximum potential normal tissue dose reduction.

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

SU-G-TeP3-01: A New Approach for Calculating Variable Relative Biological Effectiveness in IMPT Optimization

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

Cao, W; Randeniya, K; Grosshans, D

2016-06-15

Purpose: To investigate the impact of a new approach for calculating relative biological effectiveness (RBE) in intensity-modulated proton therapy (IMPT) optimization on RBE-weighted dose distributions. This approach includes the nonlinear RBE for the high linear energy transfer (LET) region, which was revealed by recent experiments at our institution. In addition, this approach utilizes RBE data as a function of LET without using dose-averaged LET in calculating RBE values. Methods: We used a two-piece function for calculating RBE from LET. Within the Bragg peak, RBE is linearly correlated to LET. Beyond the Bragg peak, we use a nonlinear (quadratic) RBE functionmore » of LET based on our experimental. The IMPT optimization was devised to incorporate variable RBE by maximizing biological effect (based on the Linear Quadratic model) in tumor and minimizing biological effect in normal tissues. Three glioblastoma patients were retrospectively selected from our institution in this study. For each patient, three optimized IMPT plans were created based on three RBE resolutions, i.e., fixed RBE of 1.1 (RBE-1.1), variable RBE based on linear RBE and LET relationship (RBE-L), and variable RBE based on linear and quadratic relationship (RBE-LQ). The RBE weighted dose distributions of each optimized plan were evaluated in terms of different RBE values, i.e., RBE-1.1, RBE-L and RBE-LQ. Results: The RBE weighted doses recalculated from RBE-1.1 based optimized plans demonstrated an increasing pattern from using RBE-1.1, RBE-L to RBE-LQ consistently for all three patients. The variable RBE (RBE-L and RBE-LQ) weighted dose distributions recalculated from RBE-L and RBE-LQ based optimization were more homogenous within the targets and better spared in the critical structures than the ones recalculated from RBE-1.1 based optimization. Conclusion: We implemented a new approach for RBE calculation and optimization and demonstrated potential benefits of improving tumor coverage and normal sparing in IMPT planning.« less

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.

Optimal marker-assisted selection to increase the effective size of small populations.

PubMed

Wang, J

2001-02-01

An approach to the optimal utilization of marker and pedigree information in minimizing the rates of inbreeding and genetic drift at the average locus of the genome (not just the marked loci) in a small diploid population is proposed, and its efficiency is investigated by stochastic simulations. The approach is based on estimating the expected pedigree of each chromosome by using marker and individual pedigree information and minimizing the average coancestry of selected chromosomes by quadratic integer programming. It is shown that the approach is much more effective and much less computer demanding in implementation than previous ones. For pigs with 10 offspring per mother genotyped for two markers (each with four alleles at equal initial frequency) per chromosome of 100 cM, the approach can increase the average effective size for the whole genome by approximately 40 and 55% if mating ratios (the number of females mated with a male) are 3 and 12, respectively, compared with the corresponding values obtained by optimizing between-family selection using pedigree information only. The efficiency of the marker-assisted selection method increases with increasing amount of marker information (number of markers per chromosome, heterozygosity per marker) and family size, but decreases with increasing genome size. For less prolific species, the approach is still effective if the mating ratio is large so that a high marker-assisted selection pressure on the rarer sex can be maintained.

Classicalization by phase space measurements

NASA Astrophysics Data System (ADS)

Bolaños, Marduk

2018-05-01

This article provides an illustration of the measurement approach to the quantum–classical transition suitable for beginning graduate students. As an example, we apply this framework to a quantum system with a general quadratic Hamiltonian, and obtain the exact solution of the dynamics for an arbitrary measurement strength using phase space methods.

Meta-Regression Approximations to Reduce Publication Selection Bias

ERIC Educational Resources Information Center

Stanley, T. D.; Doucouliagos, Hristos

2014-01-01

Publication selection bias is a serious challenge to the integrity of all empirical sciences. We derive meta-regression approximations to reduce this bias. Our approach employs Taylor polynomial approximations to the conditional mean of a truncated distribution. A quadratic approximation without a linear term, precision-effect estimate with…

Secondary School Advanced Mathematics, Chapter 8, Systems of Equations. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the last of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. In this volume the solution of systems of linear and quadratic equations and inequalities in…

User's guide for the northern hardwood stand models: SIMSAP and SIMTIM

Treesearch

Dale S. Solomon; Richard A. Hosmer; Richard A. Hosmer

1987-01-01

SIMSAP and SlMTlM are computer programs that have been developed to simulate the stand growth and development of natural and treated evenaged northern hardwood stands. SIMSAP begins with species distributions by quality classes in sapling stands after regeneration. SIMTIM, the poletimber-sawtimber-harvest phase, uses stocking guides based on quadratic mean stand...

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…

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…

[Application of GIS and integrated mathematic models on estimating forest land wood productiveness and solar energy use efficiency].

PubMed

Xing, Shihe; Lin, Dexi; Shen, Jinquan; Cao, Rongbin

2005-10-01

Based on the meteorological elements observation and mountain soil survey in Fujian Province, this paper approached the application of geographic information system (GIS) and integrated mathematic models on estimating the grid wood productiveness and solar energy use efficiency (SEUE) of regional forest land. The results showed that there was a significant quadratic correlation of annual mean temperature, precipitation and total solar radiation energy(TSRE) with longitude, latitude and altitude, and their multiple correlation coefficients ranged from 0.692 to 0.981. The regional annual mean TSRE, temperature and precipitation could be well estimated by GIS and integrated models of quadratic tendency curve, and linear, quadratic and quartic inverse distance weighted interpolation. These annual means estimated by the models did not differ greatly from observed data, and the t test values were 1.29, 0.12 and 0.06, respectively. The grid wood productiveness and SEUE of regional forest land in Fujian could also be well estimated with the aid of GIS and integrated models, which ranged from 2.32 m3 x hm(-2) yr(-1) to 18.61 m3 x hm(-2) yr(-1) and from 0.11% to 0.91%, respectively.

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.

Nonadiabatic rate constants for proton transfer and proton-coupled electron transfer reactions in solution: Effects of quadratic term in the vibronic coupling expansion

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

Soudackov, Alexander; Hammes-Schiffer, Sharon

2015-11-17

Rate constant expressions for vibronically nonadiabatic proton transfer and proton-coupled electron transfer reactions are presented and analyzed. The regimes covered include electronically adiabatic and nonadiabatic reactions, as well as high-frequency and low-frequency regimes for the proton donor-acceptor vibrational mode. These rate constants differ from previous rate constants derived with the cumulant expansion approach in that the logarithmic expansion of the vibronic coupling in terms of the proton donor-acceptor distance includes a quadratic as well as a linear term. The analysis illustrates that inclusion of this quadratic term does not significantly impact the rate constants derived using the cumulant expansion approachmore » in any of the regimes studied. The effects of the quadratic term may become significant when using the vibronic coupling expansion in conjunction with a thermal averaging procedure for calculating the rate constant, however, particularly at high temperatures and for proton transfer interfaces with extremely soft proton donor-acceptor modes that are associated with extraordinarily weak hydrogen bonds. Even with the thermal averaging procedure, the effects of the quadratic term for weak hydrogen-bonding systems are less significant for more physically realistic models that prevent the sampling of unphysical short proton donor-acceptor distances, and the expansion of the coupling can be avoided entirely by calculating the couplings explicitly for the range of proton donor-acceptor distances. This analysis identifies the regimes in which each rate constant expression is valid and thus will be important for future applications to proton transfer and proton-coupled electron transfer in chemical and biological processes. We are grateful for support from National Institutes of Health Grant GM056207 (applications to enzymes) and the Center for Molecular Electrocatalysis, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences (applications to molecular electrocatalysts).« less

A Path Algorithm for Constrained Estimation

PubMed Central

Zhou, Hua; Lange, Kenneth

2013-01-01

Many least-square problems involve affine equality and inequality constraints. Although there are a variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current article proposes a new path-following algorithm for quadratic programming that replaces hard constraints by what are called exact penalties. Similar penalties arise in l1 regularization in model selection. In the regularization setting, penalties encapsulate prior knowledge, and penalized parameter estimates represent a trade-off between the observed data and the prior knowledge. Classical penalty methods of optimization, such as the quadratic penalty method, solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties!are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. The exact path-following method starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. Path following in Lasso penalized regression, in contrast, starts with a large value of the penalty constant and works its way downward. In both settings, inspection of the entire solution path is revealing. Just as with the Lasso and generalized Lasso, it is possible to plot the effective degrees of freedom along the solution path. For a strictly convex quadratic program, the exact penalty algorithm can be framed entirely in terms of the sweep operator of regression analysis. A few well-chosen examples illustrate the mechanics and potential of path following. This article has supplementary materials available online. PMID:24039382

Clinical implementation of stereotaxic brain implant optimization

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

Rosenow, U.F.; Wojcicka, J.B.

1991-03-01

This optimization method for stereotaxic brain implants is based on seed/strand configurations of the basic type developed for the National Cancer Institute (NCI) atlas of regular brain implants. Irregular target volume shapes are determined from delineation in a stack of contrast enhanced computed tomography scans. The neurosurgeon may then select up to ten directions, or entry points, of surgical approach of which the program finds the optimal one under the criterion of smallest target volume diameter. Target volume cross sections are then reconstructed in 5-mm-spaced planes perpendicular to the implantation direction defined by the entry point and the target volumemore » center. This information is used to define a closed line in an implant cross section along which peripheral seed strands are positioned and which has now an irregular shape. Optimization points are defined opposite peripheral seeds on the target volume surface to which the treatment dose rate is prescribed. Three different optimization algorithms are available: linear least-squares programming, quadratic programming with constraints, and a simplex method. The optimization routine is implemented into a commercial treatment planning system. It generates coordinate and source strength information of the optimized seed configurations for further dose rate distribution calculation with the treatment planning system, and also the coordinate settings for the stereotaxic Brown-Roberts-Wells (BRW) implantation device.« less

Development of failure criterion for Kevlar-epoxy fabric laminates

NASA Technical Reports Server (NTRS)

Tennyson, R. C.; Elliott, W. G.

1984-01-01

The development of the tensor polynomial failure criterion for composite laminate analysis is discussed. In particular, emphasis is given to the fabrication and testing of Kevlar-49 fabric (Style 285)/Narmco 5208 Epoxy. The quadratic-failure criterion with F(12)=0 provides accurate estimates of failure stresses for the Kevlar/Epoxy investigated. The cubic failure criterion was re-cast into an operationally easier form, providing the engineer with design curves that can be applied to laminates fabricated from unidirectional prepregs. In the form presented no interaction strength tests are required, although recourse to the quadratic model and the principal strength parameters is necessary. However, insufficient test data exists at present to generalize this approach for all undirectional prepregs and its use must be restricted to the generic materials investigated to-date.

Direct Optimal Control of Duffing Dynamics

NASA Technical Reports Server (NTRS)

Oz, Hayrani; Ramsey, John K.

2002-01-01

The "direct control method" is a novel concept that is an attractive alternative and competitor to the differential-equation-based methods. The direct method is equally well applicable to nonlinear, linear, time-varying, and time-invariant systems. For all such systems, the method yields explicit closed-form control laws based on minimization of a quadratic control performance measure. We present an application of the direct method to the dynamics and optimal control of the Duffing system where the control performance measure is not restricted to a quadratic form and hence may include a quartic energy term. The results we present in this report also constitute further generalizations of our earlier work in "direct optimal control methodology." The approach is demonstrated for the optimal control of the Duffing equation with a softening nonlinear stiffness.

A different approach to X-ray stress analysis

NASA Astrophysics Data System (ADS)

Ogilvie, Robert E.

2007-07-01

A different approach to X-ray stress analysis has been developed. At the outset, it must be noted that the material to be analyzed is assumed homogeneous and isotropic. If a sphere with radius r within a specimen is subjected to a state of stress, the sphere is deformed into an ellipsoid. The semi-axes of the ellipsoid have the values of ( r + ɛx), ( r + ɛy), and ( r + ɛz), which are replaced by dx, dy, and dz, or for the cubic case, ax, ay, and az. In this technique, at a particular ϕ angle (see Fig. 1), the two-theta position of a high angle (hkl) peak is determined at ψ angles of 0, 15, 30, and 45°. These measurements are repeated for 3 to 6 ϕ angles in steps of 30°. The dϕψ or aϕψ values are then determined from the peak positions. The data is then fitted to the general quadratic equation for an ellipsoid by the method of least squares. From the coefficients of the quadratic equation, the angle between the laboratory and the specimen coordinates (direction of the principle stress) can be determined. Applying the general rotation of axes equations to the quadratic, the equation of the ellipse in the x- y plane is determined. The ax, ay, and az values for the principal axes of the lattice parameter ellipsoid are then evaluated. It is then possible to determine the unstressed a0 value from Hooke's Law using ax, ay, and az. The magnitude of the principal strains/stresses is then determined.

SERS assay of telomerase activity at single-cell level and colon cancer tissues via quadratic signal amplification.

PubMed

Shi, Muling; Zheng, Jing; Liu, Changhui; Tan, Guixiang; Qing, Zhihe; Yang, Sheng; Yang, Jinfeng; Tan, Yongjun; Yang, Ronghua

2016-03-15

As an important biomarker and therapeutic target, telomerase has attracted extensive attention concerning its detection and monitoring. Recently, enzyme-assisted amplification approaches have provided useful platforms for the telomerase activity detection, however, further improvement in sensitivity is still hindered by the single-step signal amplification. Herein, we develop a quadratic signal amplification strategy for ultrasensitive surface-enhanced Raman scattering (SERS) detection of telomerase activity. The central idea of our design is using telomerase-induced silver nanoparticles (AgNPs) assembly and silver ions (Ag(+))-mediated cascade amplification. In our approach, each telomerase-aided DNA sequence extension could trigger the formation of a long double-stranded DNA (dsDNA), making numerous AgNPs assembling along with this long strand through specific Ag-S bond, to form a primary amplification element. For secondary amplification, each conjugated AgNP was dissolved into Ag(+), which can effectively induce the 4-aminobenzenethiol (4-ABT) modified gold nanoparticles (AuNPs@4-ABT) to undergo aggregation to form numerous "hot-spots". Through quadratic amplifications, a limit of detection down to single HeLa cell was achieved. More importantly, this method demonstrated good performance when applied to tissues from colon cancer patients, which exhibits great potential in the practical application of telomerase-based cancer diagnosis in early stages. To demonstrate the potential in screening the telomerase inhibitors and telomerase-targeted drugs, the proposed design is successfully employed to measure the inhibition of telomerase activity by 3'-azido-3'-deoxythymidine. Copyright © 2015 Elsevier B.V. All rights reserved.

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.

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

An empirical probability model of detecting species at low densities.

PubMed

Delaney, David G; Leung, Brian

2010-06-01

False negatives, not detecting things that are actually present, are an important but understudied problem. False negatives are the result of our inability to perfectly detect species, especially those at low density such as endangered species or newly arriving introduced species. They reduce our ability to interpret presence-absence survey data and make sound management decisions (e.g., rapid response). To reduce the probability of false negatives, we need to compare the efficacy and sensitivity of different sampling approaches and quantify an unbiased estimate of the probability of detection. We conducted field experiments in the intertidal zone of New England and New York to test the sensitivity of two sampling approaches (quadrat vs. total area search, TAS), given different target characteristics (mobile vs. sessile). Using logistic regression we built detection curves for each sampling approach that related the sampling intensity and the density of targets to the probability of detection. The TAS approach reduced the probability of false negatives and detected targets faster than the quadrat approach. Mobility of targets increased the time to detection but did not affect detection success. Finally, we interpreted two years of presence-absence data on the distribution of the Asian shore crab (Hemigrapsus sanguineus) in New England and New York, using our probability model for false negatives. The type of experimental approach in this paper can help to reduce false negatives and increase our ability to detect species at low densities by refining sampling approaches, which can guide conservation strategies and management decisions in various areas of ecology such as conservation biology and invasion ecology.

FASTER 3: A generalized-geometry Monte Carlo computer program for the transport of neutrons and gamma rays. Volume 1: Summary report

NASA Technical Reports Server (NTRS)

Jordan, T. M.

1970-01-01

The theory used in FASTER-III, a Monte Carlo computer program for the transport of neutrons and gamma rays in complex geometries, is outlined. The program includes the treatment of geometric regions bounded by quadratic and quadric surfaces with multiple radiation sources which have specified space, angle, and energy dependence. The program calculates, using importance sampling, the resulting number and energy fluxes at specified point, surface, and volume detectors. It can also calculate minimum weight shield configuration meeting a specified dose rate constraint. Results are presented for sample problems involving primary neutron, and primary and secondary photon, transport in a spherical reactor shield configuration.

Two controller design approaches for decentralized systems

NASA Technical Reports Server (NTRS)

Ozguner, U.; Khorrami, F.; Iftar, A.

1988-01-01

Two different philosophies for designing the controllers of decentralized systems are considered within a quadratic regulator framework which is generalized to admit decentralized frequency weighting. In the first approach, the total system model is examined, and the feedback strategy for each channel or subsystem is determined. In the second approach, separate, possibly overlapping, and uncoupled models are analyzed for each channel, and the results can be combined to study the original system. The two methods are applied to the example of a model of the NASA COFS Mast Flight System.

The Boltzmann Constant from a Snifter

ERIC Educational Resources Information Center

Tyukodi, B.; Sarkozi, Zs.; Neda, Z.; Tunyagi, A.; Gyorke, E.

2012-01-01

Evaporation of a small glass of ethylic alcohol is studied both experimentally and through an elementary thermal physics approach. For a cylindrical beaker and no air flow in the room, a simple quadratic relation is found between the evaporation time and the mass of evaporated liquid. This problem and the obtained results offer excellent…

Minimum mean squared error (MSE) adjustment and the optimal Tykhonov-Phillips regularization parameter via reproducing best invariant quadratic uniformly unbiased estimates (repro-BIQUUE)

NASA Astrophysics Data System (ADS)

Schaffrin, Burkhard

2008-02-01

In a linear Gauss-Markov model, the parameter estimates from BLUUE (Best Linear Uniformly Unbiased Estimate) are not robust against possible outliers in the observations. Moreover, by giving up the unbiasedness constraint, the mean squared error (MSE) risk may be further reduced, in particular when the problem is ill-posed. In this paper, the α-weighted S-homBLE (Best homogeneously Linear Estimate) is derived via formulas originally used for variance component estimation on the basis of the repro-BIQUUE (reproducing Best Invariant Quadratic Uniformly Unbiased Estimate) principle in a model with stochastic prior information. In the present model, however, such prior information is not included, which allows the comparison of the stochastic approach (α-weighted S-homBLE) with the well-established algebraic approach of Tykhonov-Phillips regularization, also known as R-HAPS (Hybrid APproximation Solution), whenever the inverse of the “substitute matrix” S exists and is chosen as the R matrix that defines the relative impact of the regularizing term on the final result.

Semisupervised Support Vector Machines With Tangent Space Intrinsic Manifold Regularization.

PubMed

Sun, Shiliang; Xie, Xijiong

2016-09-01

Semisupervised learning has been an active research topic in machine learning and data mining. One main reason is that labeling examples is expensive and time-consuming, while there are large numbers of unlabeled examples available in many practical problems. So far, Laplacian regularization has been widely used in semisupervised learning. In this paper, we propose a new regularization method called tangent space intrinsic manifold regularization. It is intrinsic to data manifold and favors linear functions on the manifold. Fundamental elements involved in the formulation of the regularization are local tangent space representations, which are estimated by local principal component analysis, and the connections that relate adjacent tangent spaces. Simultaneously, we explore its application to semisupervised classification and propose two new learning algorithms called tangent space intrinsic manifold regularized support vector machines (TiSVMs) and tangent space intrinsic manifold regularized twin SVMs (TiTSVMs). They effectively integrate the tangent space intrinsic manifold regularization consideration. The optimization of TiSVMs can be solved by a standard quadratic programming, while the optimization of TiTSVMs can be solved by a pair of standard quadratic programmings. The experimental results of semisupervised classification problems show the effectiveness of the proposed semisupervised learning algorithms.

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 Optimisation with One Quadratic Equality Constraint

DTIC Science & Technology

2010-06-01

This report presents a theoretical framework for minimising a quadratic objective function subject to a quadratic equality constraint. The first part of the report gives a detailed algorithm which computes the global minimiser without calling special nonlinear optimisation solvers. The second part of the report shows how the developed theory can be applied to solve the time of arrival geolocation problem.

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.

An improved multiple linear regression and data analysis computer program package

NASA Technical Reports Server (NTRS)

Sidik, S. M.

1972-01-01

NEWRAP, an improved version of a previous multiple linear regression program called RAPIER, CREDUC, and CRSPLT, allows for a complete regression analysis including cross plots of the independent and dependent variables, correlation coefficients, regression coefficients, analysis of variance tables, t-statistics and their probability levels, rejection of independent variables, plots of residuals against the independent and dependent variables, and a canonical reduction of quadratic response functions useful in optimum seeking experimentation. A major improvement over RAPIER is that all regression calculations are done in double precision arithmetic.

Using state variables to model the response of tumour cells to radiation and heat: a novel multi-hit-repair approach.

PubMed

Scheidegger, Stephan; Fuchs, Hans U; Zaugg, Kathrin; Bodis, Stephan; Füchslin, Rudolf M

2013-01-01

In order to overcome the limitations of the linear-quadratic model and include synergistic effects of heat and radiation, a novel radiobiological model is proposed. The model is based on a chain of cell populations which are characterized by the number of radiation induced damages (hits). Cells can shift downward along the chain by collecting hits and upward by a repair process. The repair process is governed by a repair probability which depends upon state variables used for a simplistic description of the impact of heat and radiation upon repair proteins. Based on the parameters used, populations up to 4-5 hits are relevant for the calculation of the survival. The model describes intuitively the mathematical behaviour of apoptotic and nonapoptotic cell death. Linear-quadratic-linear behaviour of the logarithmic cell survival, fractionation, and (with one exception) the dose rate dependencies are described correctly. The model covers the time gap dependence of the synergistic cell killing due to combined application of heat and radiation, but further validation of the proposed approach based on experimental data is needed. However, the model offers a work bench for testing different biological concepts of damage induction, repair, and statistical approaches for calculating the variables of state.

Quadratic trigonometric B-spline for image interpolation using GA

PubMed Central

Abbas, Samreen; Irshad, Misbah

2017-01-01

In this article, a new quadratic trigonometric B-spline with control parameters is constructed to address the problems related to two dimensional digital image interpolation. The newly constructed spline is then used to design an image interpolation scheme together with one of the soft computing techniques named as Genetic Algorithm (GA). The idea of GA has been formed to optimize the control parameters in the description of newly constructed spline. The Feature SIMilarity (FSIM), Structure SIMilarity (SSIM) and Multi-Scale Structure SIMilarity (MS-SSIM) indices along with traditional Peak Signal-to-Noise Ratio (PSNR) are employed as image quality metrics to analyze and compare the outcomes of approach offered in this work, with three of the present digital image interpolation schemes. The upshots show that the proposed scheme is better choice to deal with the problems associated to image interpolation. PMID:28640906

Quadratic trigonometric B-spline for image interpolation using GA.

PubMed

Hussain, Malik Zawwar; Abbas, Samreen; Irshad, Misbah

2017-01-01

In this article, a new quadratic trigonometric B-spline with control parameters is constructed to address the problems related to two dimensional digital image interpolation. The newly constructed spline is then used to design an image interpolation scheme together with one of the soft computing techniques named as Genetic Algorithm (GA). The idea of GA has been formed to optimize the control parameters in the description of newly constructed spline. The Feature SIMilarity (FSIM), Structure SIMilarity (SSIM) and Multi-Scale Structure SIMilarity (MS-SSIM) indices along with traditional Peak Signal-to-Noise Ratio (PSNR) are employed as image quality metrics to analyze and compare the outcomes of approach offered in this work, with three of the present digital image interpolation schemes. The upshots show that the proposed scheme is better choice to deal with the problems associated to image interpolation.

A generalised optimal linear quadratic tracker with universal applications. Part 2: discrete-time systems

NASA Astrophysics Data System (ADS)

Ebrahimzadeh, Faezeh; Tsai, Jason Sheng-Hong; Chung, Min-Ching; Liao, Ying Ting; Guo, Shu-Mei; Shieh, Leang-San; Wang, Li

2017-01-01

Contrastive to Part 1, Part 2 presents a generalised optimal linear quadratic digital tracker (LQDT) with universal applications for the discrete-time (DT) systems. This includes (1) a generalised optimal LQDT design for the system with the pre-specified trajectories of the output and the control input and additionally with both the input-to-output direct-feedthrough term and known/estimated system disturbances or extra input/output signals; (2) a new optimal filter-shaped proportional plus integral state-feedback LQDT design for non-square non-minimum phase DT systems to achieve a minimum-phase-like tracking performance; (3) a new approach for computing the control zeros of the given non-square DT systems; and (4) a one-learning-epoch input-constrained iterative learning LQDT design for the repetitive DT systems.

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.

Estimating the quadratic mean diameter of fine woody debris for forest type groups of the United States

Treesearch

Christopher W. Woodall; Vicente J. Monleon

2009-01-01

The Forest Inventory and Analysis program of the Forest Service, U.S. Department of Agriculture conducts a national inventory of fine woody debris (FWD); however, the sampling protocols involve tallying only the number of FWD pieces by size class that intersect a sampling transect with no measure of actual size. The line intersect estimator used with those samples...

A design procedure and handling quality criteria for lateral directional flight control systems

NASA Technical Reports Server (NTRS)

Stein, G.; Henke, A. H.

1972-01-01

A practical design procedure for aircraft augmentation systems is described based on quadratic optimal control technology and handling-quality-oriented cost functionals. The procedure is applied to the design of a lateral-directional control system for the F4C aircraft. The design criteria, design procedure, and final control system are validated with a program of formal pilot evaluation experiments.

Do Negative Acts in Italian Academia Have a Quadratic Relationship with Determinants of Health?

ERIC Educational Resources Information Center

Fadda, Salvatore; Giorgi, Gabriele; Benitez Muñoz, Juan Luis; Justicia Justicia, Fernando; Solinas, Giuliana

2015-01-01

Purpose: The purpose of this paper is to investigate the prevalence of workplace bullying in an Italian university. Design/methodology/approach: More than 200 workers have completed the Italian version of the Negative Acts Questionnaire and the General Health Questionnaire. Findings: The results show a spread of low to medium negative actions in…

The Director Circle of a Central Conic Section

ERIC Educational Resources Information Center

Ayoub, Ayoub B.

2007-01-01

Each ellipse and hyperbola has a circle associated with it called the director circle. In this article, the author derives the equations of the circle for the ellipse and hyperbola through a different approach. Then the author concentrates on the director circle of the central conic given by the general quadratic equation. The content of this…

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...

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.

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.

Hybrid BEM/empirical approach for scattering of correlated sources in rocket noise prediction

NASA Astrophysics Data System (ADS)

Barbarino, Mattia; Adamo, Francesco P.; Bianco, Davide; Bartoccini, Daniele

2017-09-01

Empirical models such as the Eldred standard model are commonly used for rocket noise prediction. Such models directly provide a definition of the Sound Pressure Level through the quadratic pressure term by uncorrelated sources. In this paper, an improvement of the Eldred Standard model has been formulated. This new formulation contains an explicit expression for the acoustic pressure of each noise source, in terms of amplitude and phase, in order to investigate the sources correlation effects and to propagate them through a wave equation. In particular, the correlation effects between adjacent and not-adjacent sources have been modeled and analyzed. The noise prediction obtained with the revised Eldred-based model has then been used for formulating an empirical/BEM (Boundary Element Method) hybrid approach that allows an evaluation of the scattering effects. In the framework of the European Space Agency funded program VECEP (VEga Consolidation and Evolution Programme), these models have been applied for the prediction of the aeroacoustics loads of the VEGA (Vettore Europeo di Generazione Avanzata - Advanced Generation European Carrier Rocket) launch vehicle at lift-off and the results have been compared with experimental data.

Automatic classification of small bowel mucosa alterations in celiac disease for confocal laser endomicroscopy

NASA Astrophysics Data System (ADS)

Boschetto, Davide; Di Claudio, Gianluca; Mirzaei, Hadis; Leong, Rupert; Grisan, Enrico

2016-03-01

Celiac disease (CD) is an immune-mediated enteropathy triggered by exposure to gluten and similar proteins, affecting genetically susceptible persons, increasing their risk of different complications. Small bowels mucosa damage due to CD involves various degrees of endoscopically relevant lesions, which are not easily recognized: their overall sensitivity and positive predictive values are poor even when zoom-endoscopy is used. Confocal Laser Endomicroscopy (CLE) allows skilled and trained experts to qualitative evaluate mucosa alteration such as a decrease in goblet cells density, presence of villous atrophy or crypt hypertrophy. We present a method for automatically classifying CLE images into three different classes: normal regions, villous atrophy and crypt hypertrophy. This classification is performed after a features selection process, in which four features are extracted from each image, through the application of homomorphic filtering and border identification through Canny and Sobel operators. Three different classifiers have been tested on a dataset of 67 different images labeled by experts in three classes (normal, VA and CH): linear approach, Naive-Bayes quadratic approach and a standard quadratic analysis, all validated with a ten-fold cross validation. Linear classification achieves 82.09% accuracy (class accuracies: 90.32% for normal villi, 82.35% for VA and 68.42% for CH, sensitivity: 0.68, specificity 1.00), Naive Bayes analysis returns 83.58% accuracy (90.32% for normal villi, 70.59% for VA and 84.21% for CH, sensitivity: 0.84 specificity: 0.92), while the quadratic analysis achieves a final accuracy of 94.03% (96.77% accuracy for normal villi, 94.12% for VA and 89.47% for CH, sensitivity: 0.89, specificity: 0.98).

Determinants of Paracentrotus lividus sea urchin recruitment under oligotrophic conditions: Implications for conservation management.

PubMed

Oliva, Silvia; Farina, Simone; Pinna, Stefania; Guala, Ivan; Agnetta, Davide; Ariotti, Pierre Antoine; Mura, Francesco; Ceccherelli, Giulia

2016-06-01

Sea urchins may deeply shape the structure of macrophyte-dominated communities and require the implementation of sustainable management strategies. In the Mediterranean, the identification of the major recruitment determinants of the keystone sea urchin species Paracentrotus lividus is required, so that source areas of the populations can be identified and exploitation or programmed harvesting can be spatially managed. In this study a collection of eight possible determinants, these encompassing both the biotic (larvae, adult sea urchins, fish, encrusting coralline algae, habitat type and spatial arrangement of habitats) and abiotic (substrate complexity and nutritional status) realms was considered at different spatial scales (site, area, transect and quadrat). Data from a survey including sites subject to different levels of human influence (i.e. from urbanized to protected areas), but all corresponding to an oligotrophic and low-populated region were fitted by means of a generalized linear mixed model. Despite the extensive sampling effort of benthic quadrats, an overall paucity of recruits was found, recruits being aggregated in a very small number of quadrats and in few areas. The analysis of data detected substrate complexity, and adult sea urchin and predatory fish abundances as the momentous determinants of Paracentrotus lividus recruitment. Possible mechanisms of influence are discussed beyond the implications of conservation management. Copyright © 2016 Elsevier Ltd. All rights reserved.

On a Microscopic Representation of Space-Time V

NASA Astrophysics Data System (ADS)

Dahm, R.

2017-01-01

In previous parts of this publication series, starting from the Dirac algebra and SU*(4), the ’dual’ compact rank-3 group SU(4) and Lie theory, we have developed some arguments and the reasoning to use (real) projective and (line) Complex geometry directly. Here, we want to extend this approach further in terms of line and Complex geometry and give some analytical examples. As such, we start from quadratic Complexe which we’ve identified in parts III and IV already as yielding naturally the ’light cone’ x_12 + x_22 + x_32 - x_02 = 0 when being related to (homogeneous) point coordinates x_α ^2 and infinitesimal dynamics by tetrahedral Complexe (or line elements). This introduces naturally projective transformations by preserving anharmonic ratios. We summarize some old work of Plücker relating quadratic Complexe to optics and discuss briefly their relation to spherical (and Schrödinger-type) equations as well as an obvious interpretation based on homogeneous coordinates and relations to conics and second order surfaces. Discussing (linear) symplectic symmetry and line coordinates, the main purpose and thread within this paper, however, is the identification and discussion of special relativity as direct invariance properties of line/Complex coordinates as well as their relation to ’quantum field theory’ by complexification of point coordinates or Complexe. This can be established by the Lie mapping1 which relates lines/Complexe to sphere geometry so that SU(2), SU(2)×U(1), SU(2)×SU(2) and the Dirac spinor description emerge without additional assumptions. We give a short outlook in that quadratic Complexe are related to dynamics e.g. power expressions in terms of six-vector products of Complexe, and action principles may be applied. (Quadratic) products like {Fμ ν }{Fμ ν }{{ or }}{Fα {{ }μ ν }}Fμ ν ^α ,1 ≤ α ≤ 3 are natural quadratic Complex expressions which may be extended by line constraints λk · ɛ = 0 with respect to an ’action principle’ so that we identify ’quantum field theory’ with projective or line/Complex geometry having applied the Lie mapping.

Importance of sampling design and analysis in animal population studies: a comment on Sergio et al

USGS Publications Warehouse

Kery, M.; Royle, J. Andrew; Schmid, Hans

2008-01-01

1. The use of predators as indicators and umbrellas in conservation has been criticized. In the Trentino region, Sergio et al. (2006; hereafter SEA) counted almost twice as many bird species in quadrats located in raptor territories than in controls. However, SEA detected astonishingly few species. We used contemporary Swiss Breeding Bird Survey data from an adjacent region and a novel statistical model that corrects for overlooked species to estimate the expected number of bird species per quadrat in that region. 2. There are two anomalies in SEA which render their results ambiguous. First, SEA detected on average only 6.8 species, whereas a value of 32 might be expected. Hence, they probably overlooked almost 80% of all species. Secondly, the precision of their mean species counts was greater in two-thirds of cases than in the unlikely case that all quadrats harboured exactly the same number of equally detectable species. This suggests that they detected consistently only a biased, unrepresentative subset of species. 3. Conceptually, expected species counts are the product of true species number and species detectability p. Plenty of factors may affect p, including date, hour, observer, previous knowledge of a site and mobbing behaviour of passerines in the presence of predators. Such differences in p between raptor and control quadrats could have easily created the observed effects. Without a method that corrects for such biases, or without quantitative evidence that species detectability was indeed similar between raptor and control quadrats, the meaning of SEA's counts is hard to evaluate. Therefore, the evidence presented by SEA in favour of raptors as indicator species for enhanced levels of biodiversity remains inconclusive. 4. Synthesis and application. Ecologists should pay greater attention to sampling design and analysis in animal population estimation. Species richness estimation means sampling a community. Samples should be representative for the community studied and the sampling fraction among communities compared should be the same on average, otherwise formal estimation approaches must be applied to avoid misleading inference.

Performance Analysis and Design Synthesis (PADS) computer program. Volume 2: Program description, part 2

NASA Technical Reports Server (NTRS)

1972-01-01

The QL module of the Performance Analysis and Design Synthesis (PADS) computer program is described. Execution of this module is initiated when and if subroutine PADSI calls subroutine GROPE. Subroutine GROPE controls the high level logical flow of the QL module. The purpose of the module is to determine a trajectory that satisfies the necessary variational conditions for optimal performance. The module achieves this by solving a nonlinear multi-point boundary value problem. The numerical method employed is described. It is an iterative technique that converges quadratically when it does converge. The three basic steps of the module are: (1) initialization, (2) iteration, and (3) culmination. For Volume 1 see N73-13199.

Learning locality preserving graph from data.

PubMed

Zhang, Yan-Ming; Huang, Kaizhu; Hou, Xinwen; Liu, Cheng-Lin

2014-11-01

Machine learning based on graph representation, or manifold learning, has attracted great interest in recent years. As the discrete approximation of data manifold, the graph plays a crucial role in these kinds of learning approaches. In this paper, we propose a novel learning method for graph construction, which is distinct from previous methods in that it solves an optimization problem with the aim of directly preserving the local information of the original data set. We show that the proposed objective has close connections with the popular Laplacian Eigenmap problem, and is hence well justified. The optimization turns out to be a quadratic programming problem with n(n-1)/2 variables (n is the number of data points). Exploiting the sparsity of the graph, we further propose a more efficient cutting plane algorithm to solve the problem, making the method better scalable in practice. In the context of clustering and semi-supervised learning, we demonstrated the advantages of our proposed method by experiments.

Data-Driven Engineering of Social Dynamics: Pattern Matching and Profit Maximization

PubMed Central

Peng, Huan-Kai; Lee, Hao-Chih; Pan, Jia-Yu; Marculescu, Radu

2016-01-01

In this paper, we define a new problem related to social media, namely, the data-driven engineering of social dynamics. More precisely, given a set of observations from the past, we aim at finding the best short-term intervention that can lead to predefined long-term outcomes. Toward this end, we propose a general formulation that covers two useful engineering tasks as special cases, namely, pattern matching and profit maximization. By incorporating a deep learning model, we derive a solution using convex relaxation and quadratic-programming transformation. Moreover, we propose a data-driven evaluation method in place of the expensive field experiments. Using a Twitter dataset, we demonstrate the effectiveness of our dynamics engineering approach for both pattern matching and profit maximization, and study the multifaceted interplay among several important factors of dynamics engineering, such as solution validity, pattern-matching accuracy, and intervention cost. Finally, the method we propose is general enough to work with multi-dimensional time series, so it can potentially be used in many other applications. PMID:26771830

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.

Integration of Libration Point Orbit Dynamics into a Universal 3-D Autonomous Formation Flying Algorithm

NASA Technical Reports Server (NTRS)

Folta, David; Bauer, Frank H. (Technical Monitor)

2001-01-01

The autonomous formation flying control algorithm developed by the Goddard Space Flight Center (GSFC) for the New Millennium Program (NMP) Earth Observing-1 (EO-1) mission is investigated for applicability to libration point orbit formations. In the EO-1 formation-flying algorithm, control is accomplished via linearization about a reference transfer orbit with a state transition matrix (STM) computed from state inputs. The effect of libration point orbit dynamics on this algorithm architecture is explored via computation of STMs using the flight proven code, a monodromy matrix developed from a N-body model of a libration orbit, and a standard STM developed from the gravitational and coriolis effects as measured at the libration point. A comparison of formation flying Delta-Vs calculated from these methods is made to a standard linear quadratic regulator (LQR) method. The universal 3-D approach is optimal in the sense that it can be accommodated as an open-loop or closed-loop control using only state information.

Data-Driven Engineering of Social Dynamics: Pattern Matching and Profit Maximization.

PubMed

Peng, Huan-Kai; Lee, Hao-Chih; Pan, Jia-Yu; Marculescu, Radu

2016-01-01

In this paper, we define a new problem related to social media, namely, the data-driven engineering of social dynamics. More precisely, given a set of observations from the past, we aim at finding the best short-term intervention that can lead to predefined long-term outcomes. Toward this end, we propose a general formulation that covers two useful engineering tasks as special cases, namely, pattern matching and profit maximization. By incorporating a deep learning model, we derive a solution using convex relaxation and quadratic-programming transformation. Moreover, we propose a data-driven evaluation method in place of the expensive field experiments. Using a Twitter dataset, we demonstrate the effectiveness of our dynamics engineering approach for both pattern matching and profit maximization, and study the multifaceted interplay among several important factors of dynamics engineering, such as solution validity, pattern-matching accuracy, and intervention cost. Finally, the method we propose is general enough to work with multi-dimensional time series, so it can potentially be used in many other applications.

A waveform diversity method for optimizing 3-d power depositions generated by ultrasound phased arrays.

PubMed

Zeng, Xiaozheng Jenny; Li, Jian; McGough, Robert J

2010-01-01

A waveform-diversity-based approach for 3-D tumor heating is compared to spot scanning for hyperthermia applications. The waveform diversity method determines the excitation signals applied to the phased array elements and produces a beam pattern that closely matches the desired power distribution. The optimization algorithm solves the covariance matrix of the excitation signals through semidefinite programming subject to a series of quadratic cost functions and constraints on the control points. A numerical example simulates a 1444-element spherical-section phased array that delivers heat to a 3-cm-diameter spherical tumor located 12 cm from the array aperture, and the results show that waveform diversity combined with mode scanning increases the heated volume within the tumor while simultaneously decreasing normal tissue heating. Whereas standard single focus and multiple focus methods are often associated with unwanted intervening tissue heating, the waveform diversity method combined with mode scanning shifts energy away from intervening tissues where hotspots otherwise accumulate to improve temperature localization in deep-seated tumors.

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.

Periodicity analysis of tourist arrivals to Banda Aceh using smoothing SARIMA approach

NASA Astrophysics Data System (ADS)

Miftahuddin, Helida, Desri; Sofyan, Hizir

2017-11-01

Forecasting the number of tourist arrivals who enters a region is needed for tourism businesses, economic and industrial policies, so that the statistical modeling needs to be conducted. Banda Aceh is the capital of Aceh province more economic activity is driven by the services sector, one of which is the tourism sector. Therefore, the prediction of the number of tourist arrivals is needed to develop further policies. The identification results indicate that the data arrival of foreign tourists to Banda Aceh to contain the trend and seasonal nature. Allegedly, the number of arrivals is influenced by external factors, such as economics, politics, and the holiday season caused the structural break in the data. Trend patterns are detected by using polynomial regression with quadratic and cubic approaches, while seasonal is detected by a periodic regression polynomial with quadratic and cubic approach. To model the data that has seasonal effects, one of the statistical methods that can be used is SARIMA (Seasonal Autoregressive Integrated Moving Average). The results showed that the smoothing, a method to detect the trend pattern is cubic polynomial regression approach, with the modified model and the multiplicative periodicity of 12 months. The AIC value obtained was 70.52. While the method for detecting the seasonal pattern is a periodic regression polynomial cubic approach, with the modified model and the multiplicative periodicity of 12 months. The AIC value obtained was 73.37. Furthermore, the best model to predict the number of foreign tourist arrivals to Banda Aceh in 2017 to 2018 is SARIMA (0,1,1)(1,1,0) with MAPE is 26%.

Reliable numerical computation in an optimal output-feedback design

NASA Technical Reports Server (NTRS)

Vansteenwyk, Brett; Ly, Uy-Loi

1991-01-01

A reliable algorithm is presented for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters. The algorithm is a part of a design algorithm for optimal linear dynamic output-feedback controller that minimizes a finite-time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control-law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed-loop eigensystem. This approach through the use of an accurate Pade series approximation does not require the closed-loop system matrix to be diagonalizable. The algorithm was included in a control design package for optimal robust low-order controllers. Usefulness of the proposed numerical algorithm was demonstrated using numerous practical design cases where degeneracies occur frequently in the closed-loop system under an arbitrary controller design initialization and during the numerical search.

Evaluation of failure criterion for graphite/epoxy fabric laminates

NASA Technical Reports Server (NTRS)

Tennyson, R. C.; Wharram, G. E.

1985-01-01

The development and application of the tensor polynomial failure criterion for composite laminate analysis is described. Emphasis is given to the fabrication and testing of Narmco Rigidite 5208-WT300, a plain weave fabric of Thornel 300 Graphite fibers impregnated with Narmco 5208 Resin. The quadratic-failure criterion with F sub 12=0 provides accurate estimates of failure stresses for the graphite/epoxy investigated. The cubic failure criterion was recast into an operationally easier form, providing design curves that can be applied to laminates fabricated from orthotropic woven fabric prepregs. In the form presented, no interaction strength tests are required, although recourse to the quadratic model and the principal strength parameters is necessary. However, insufficient test data exist at present to generalize this approach for all prepreg constructions, and its use must be restricted to the generic materials and configurations investigated to date.

Investigations into the shape-preserving interpolants using symbolic computation

NASA Technical Reports Server (NTRS)

Lam, Maria

1988-01-01

Shape representation is a central issue in computer graphics and computer-aided geometric design. Many physical phenomena involve curves and surfaces that are monotone (in some directions) or are convex. The corresponding representation problem is given some monotone or convex data, and a monotone or convex interpolant is found. Standard interpolants need not be monotone or convex even though they may match monotone or convex data. Most of the methods of investigation of this problem involve the utilization of quadratic splines or Hermite polynomials. In this investigation, a similar approach is adopted. These methods require derivative information at the given data points. The key to the problem is the selection of the derivative values to be assigned to the given data points. Schemes for choosing derivatives were examined. Along the way, fitting given data points by a conic section has also been investigated as part of the effort to study shape-preserving quadratic splines.

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.

Virtue Quadratic Male Sling for stress incontinence—surgical guide for placement and delayed revision

PubMed Central

Rubin, Rachel S.; Xavier, Keith R.

2017-01-01

The algorithm for surgical management of post prostatectomy incontinence classically includes male slings and artificial urinary sphincter (AUS) placement. The Virtue Quadratic Male Sling was designed to provide both urethral elevation and prepubic compression making it a viable option for a wider spectrum of incontinent men whose symptoms range from mild to severe. With a focus on two key steps of the surgery, (I) sling fixation (II) use of intraoperative retrograde leak point pressure (RLPP), this guide is intended to outline a safe and efficacious treatment for post-prostatectomy incontinence. Intriguingly, the sling can be revised in the event of refractory or worsening leakage, and does not preclude the placement of an AUS should it be needed. This paper describes a step by step approach to performing the procedure as well as expert tips to improve outcomes and avoid/manage complications that have been learned over the years. PMID:28904899

Advanced rotorcraft control using parameter optimization

NASA Technical Reports Server (NTRS)

Vansteenwyk, Brett; Ly, Uy-Loi

1991-01-01

A reliable algorithm for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters is presented. The algorithm is part of a design algorithm for an optimal linear dynamic output feedback controller that minimizes a finite time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed loop eigensystem. This approach through the use of a accurate Pade series approximation does not require the closed loop system matrix to be diagonalizable. The algorithm has been included in a control design package for optimal robust low order controllers. Usefulness of the proposed numerical algorithm has been demonstrated using numerous practical design cases where degeneracies occur frequently in the closed loop system under an arbitrary controller design initialization and during the numerical search.

Secondary School Advanced Mathematics, Chapter 6, The Complex Number System, Chapter 7, Equations of the First and Second Degree in Two Variables. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the fourth of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. This text begins with a brief discussion of quadratic equations which motivates the…

Cheetah: Starspot modeling code

NASA Astrophysics Data System (ADS)

Walkowicz, Lucianne; Thomas, Michael; Finkestein, Adam

2014-12-01

Cheetah models starspots in photometric data (lightcurves) by calculating the modulation of a light curve due to starspots. The main parameters of the program are the linear and quadratic limb darkening coefficients, stellar inclination, spot locations and sizes, and the intensity ratio of the spots to the stellar photosphere. Cheetah uses uniform spot contrast and the minimum number of spots needed to produce a good fit and ignores bright regions for the sake of simplicity.

Controllability of semi-infinite rod heating by a point source

NASA Astrophysics Data System (ADS)

Khurshudyan, A.

2018-04-01

The possibility of control over heating of a semi-infinite thin rod by a point source concentrated at an inner point of the rod, is studied. Quadratic and piecewise constant solutions of the problem are derived, and the possibilities of solving appropriate problems of optimal control are indicated. Determining of the parameters of the piecewise constant solution is reduced to a problem of nonlinear programming. Numerical examples are considered.

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…

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.

Scalable Effective Approaches for Quadratic Assignment Problems Based on Conic Optimization and Applications

DTIC Science & Technology

2012-02-09

1nclud1ng suggestions for reduc1ng the burden. to the Department of Defense. ExecutiVe Serv1ce D>rectorate (0704-0188) Respondents should be aware...benchmark problem we contacted Bertrand LeCun who in their poject CHOC from 2005-2008 had applied their parallel B&B framework BOB++ to the RLT1

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

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.

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…

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.

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.

MM Algorithms for Geometric and Signomial Programming

PubMed Central

Lange, Kenneth; Zhou, Hua

2013-01-01

This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates. PMID:24634545

MM Algorithms for Geometric and Signomial Programming.

PubMed

Lange, Kenneth; Zhou, Hua

2014-02-01

This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.

Gradient optimization and nonlinear control

NASA Technical Reports Server (NTRS)

Hasdorff, L.

1976-01-01

The book represents an introduction to computation in control by an iterative, gradient, numerical method, where linearity is not assumed. The general language and approach used are those of elementary functional analysis. The particular gradient method that is emphasized and used is conjugate gradient descent, a well known method exhibiting quadratic convergence while requiring very little more computation than simple steepest descent. Constraints are not dealt with directly, but rather the approach is to introduce them as penalty terms in the criterion. General conjugate gradient descent methods are developed and applied to problems in control.

Space construction base control system

NASA Technical Reports Server (NTRS)

Kaczynski, R. F.

1979-01-01

Several approaches for an attitude control system are studied and developed for a large space construction base that is structurally flexible. Digital simulations were obtained using the following techniques: (1) the multivariable Nyquist array method combined with closed loop pole allocation, (2) the linear quadratic regulator method. Equations for the three-axis simulation using the multilevel control method were generated and are presented. Several alternate control approaches are also described. A technique is demonstrated for obtaining the dynamic structural properties of a vehicle which is constructed of two or more submodules of known dynamic characteristics.

UAV Control on the Basis of 3D Landmark Bearing-Only Observations.

PubMed

Karpenko, Simon; Konovalenko, Ivan; Miller, Alexander; Miller, Boris; Nikolaev, Dmitry

2015-11-27

The article presents an approach to the control of a UAV on the basis of 3D landmark observations. The novelty of the work is the usage of the 3D RANSAC algorithm developed on the basis of the landmarks' position prediction with the aid of a modified Kalman-type filter. Modification of the filter based on the pseudo-measurements approach permits obtaining unbiased UAV position estimation with quadratic error characteristics. Modeling of UAV flight on the basis of the suggested algorithm shows good performance, even under significant external perturbations.

Formation Flying With Decentralized Control in Libration Point Orbits

NASA Technical Reports Server (NTRS)

Folta, David; Carpenter, J. Russell; Wagner, Christoph

2000-01-01

A decentralized control framework is investigated for applicability of formation flying control in libration orbits. The decentralized approach, being non-hierarchical, processes only direct measurement data, in parallel with the other spacecraft. Control is accomplished via linearization about a reference libration orbit with standard control using a Linear Quadratic Regulator (LQR) or the GSFC control algorithm. Both are linearized about the current state estimate as with the extended Kalman filter. Based on this preliminary work, the decentralized approach appears to be feasible for upcoming libration missions using distributed spacecraft.

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.

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.

Response surface modeling of acid activation of raw diatomite using in sunflower oil bleaching by: Box-Behnken experimental design.

PubMed

Larouci, M; Safa, M; Meddah, B; Aoues, A; Sonnet, P

2015-03-01

The optimum conditions for acid activation of diatomite for maximizing bleaching efficiency of the diatomite in sun flower oil treatment were studied. Box-Behnken experimental design combining with response surface modeling (RSM) and quadratic programming (QP) was employed to obtain the optimum conditions of three independent variables (acid concentration, activation time and solid to liquid) for acid activation of diatomite. The significance of independent variables and their interactions were tested by means of the analysis of variance (ANOVA) with 95 % confidence limits (α = 0.05). The optimum values of the selected variables were obtained by solving the quadratic regression model, as well as by analyzing the response surface contour plots. The experimental conditions at this global point were determined to be acid concentration = 8.963 N, activation time = 11.9878 h, and solid to liquid ratio = 221.2113 g/l, the corresponding bleaching efficiency was found to be about 99 %.

Chemical library subset selection algorithms: a unified derivation using spatial statistics.

PubMed

Hamprecht, Fred A; Thiel, Walter; van Gunsteren, Wilfred F

2002-01-01

If similar compounds have similar activity, rational subset selection becomes superior to random selection in screening for pharmacological lead discovery programs. Traditional approaches to this experimental design problem fall into two classes: (i) a linear or quadratic response function is assumed (ii) some space filling criterion is optimized. The assumptions underlying the first approach are clear but not always defendable; the second approach yields more intuitive designs but lacks a clear theoretical foundation. We model activity in a bioassay as realization of a stochastic process and use the best linear unbiased estimator to construct spatial sampling designs that optimize the integrated mean square prediction error, the maximum mean square prediction error, or the entropy. We argue that our approach constitutes a unifying framework encompassing most proposed techniques as limiting cases and sheds light on their underlying assumptions. In particular, vector quantization is obtained, in dimensions up to eight, in the limiting case of very smooth response surfaces for the integrated mean square error criterion. Closest packing is obtained for very rough surfaces under the integrated mean square error and entropy criteria. We suggest to use either the integrated mean square prediction error or the entropy as optimization criteria rather than approximations thereof and propose a scheme for direct iterative minimization of the integrated mean square prediction error. Finally, we discuss how the quality of chemical descriptors manifests itself and clarify the assumptions underlying the selection of diverse or representative subsets.

Numerical calculation of thermo-mechanical problems at large strains based on complex step derivative approximation of tangent stiffness matrices

NASA Astrophysics Data System (ADS)

Balzani, Daniel; Gandhi, Ashutosh; Tanaka, Masato; Schröder, Jörg

2015-05-01

In this paper a robust approximation scheme for the numerical calculation of tangent stiffness matrices is presented in the context of nonlinear thermo-mechanical finite element problems and its performance is analyzed. The scheme extends the approach proposed in Kim et al. (Comput Methods Appl Mech Eng 200:403-413, 2011) and Tanaka et al. (Comput Methods Appl Mech Eng 269:454-470, 2014 and bases on applying the complex-step-derivative approximation to the linearizations of the weak forms of the balance of linear momentum and the balance of energy. By incorporating consistent perturbations along the imaginary axis to the displacement as well as thermal degrees of freedom, we demonstrate that numerical tangent stiffness matrices can be obtained with accuracy up to computer precision leading to quadratically converging schemes. The main advantage of this approach is that contrary to the classical forward difference scheme no round-off errors due to floating-point arithmetics exist within the calculation of the tangent stiffness. This enables arbitrarily small perturbation values and therefore leads to robust schemes even when choosing small values. An efficient algorithmic treatment is presented which enables a straightforward implementation of the method in any standard finite-element program. By means of thermo-elastic and thermo-elastoplastic boundary value problems at finite strains the performance of the proposed approach is analyzed.

Broiler responses to increasing selenium supplementation using Zn-L-selenomethionine with special attention to breast myopathies.

PubMed

Cemin, H S; Vieira, S L; Stefanello, C; Kindlein, L; Ferreira, T Z; Fireman, A K

2018-05-01

A study was conducted to evaluate growth performance, carcass and breast yields, and the occurrence and severity of white striping (WS) and wooden breast (WB) myopathies of broilers fed diets supplemented with increasing dietary levels of an organic source of selenium (Zn-L-SeMet). Broilers were fed 6 treatments with 12 replications of 26 birds in a 4-phase feeding program from 1 to 42 days. Corn-soy-based diets were supplemented with 0, 0.2, 0.4, 0.6, 0.8, and 1.0 ppm of Zn-L-SeMet. At 42 d, 6 birds were randomly selected from each pen (n = 72) and processed for carcass and breast yields. Breast fillets were scored for WS and WB at 42 days. Increasing Zn-L-SeMet led to quadratic responses (P < 0.05) for FCR from 1 to 7 d, BWG from 22 to 35 d, and for both responses from 8 to 21 d and 36 to 42 d, as well as in the overall period of 42 days. Carcass and breast yields presented a quadratic improvement (P < 0.01) with increasing Zn-L-SeMet supplementation and Se requirements were estimated at 0.85 and 0.86 ppm, respectively. In the overall period, estimates of Se requirements were 0.64 ppm for BWG and 0.67 ppm for FCR. White striping and WB scores presented quadratic increases (P < 0.01), and maximum scores were observed at 0.68 and 0.67 ppm, respectively. Broilers fed diets formulated without Se supplementation had a higher percentage of normal fillets compared to other Se supplementation levels (quadratic, P < 0.05). In conclusion, increasing Se supplementation to reach maximum growth performance led to higher degrees of severity of WS and WB. Selenium requirements determined in the present study were significantly higher than the present commercial recommendations.

Quadratic String Method for Locating Instantons in Tunneling Splitting Calculations.

PubMed

Cvitaš, Marko T

2018-03-13

The ring-polymer instanton (RPI) method is an efficient technique for calculating approximate tunneling splittings in high-dimensional molecular systems. In the RPI method, tunneling splitting is evaluated from the properties of the minimum action path (MAP) connecting the symmetric wells, whereby the extensive sampling of the full potential energy surface of the exact quantum-dynamics methods is avoided. Nevertheless, the search for the MAP is usually the most time-consuming step in the standard numerical procedures. Recently, nudged elastic band (NEB) and string methods, originaly developed for locating minimum energy paths (MEPs), were adapted for the purpose of MAP finding with great efficiency gains [ J. Chem. Theory Comput. 2016 , 12 , 787 ]. In this work, we develop a new quadratic string method for locating instantons. The Euclidean action is minimized by propagating the initial guess (a path connecting two wells) over the quadratic potential energy surface approximated by means of updated Hessians. This allows the algorithm to take many minimization steps between the potential/gradient calls with further reductions in the computational effort, exploiting the smoothness of potential energy surface. The approach is general, as it uses Cartesian coordinates, and widely applicable, with computational effort of finding the instanton usually lower than that of determining the MEP. It can be combined with expensive potential energy surfaces or on-the-fly electronic-structure methods to explore a wide variety of molecular systems.

Run-off-road and recovery - state estimation and vehicle control strategies

NASA Astrophysics Data System (ADS)

Freeman, P.; Wagner, J.; Alexander, K.

2016-09-01

Despite many advances in vehicle safety technology, traffic fatalities remain a devastating burden on society. With over two-thirds of all fatal single-vehicle crashes occurring off the roadway, run-off-road (ROR) crashes have become the focus of much roadway safety research. Current countermeasures, including roadway infrastructure modifications and some on-board vehicle safety systems, remain limited in their approach as they do not directly address the critical factor of driver behaviour. It has been shown that ROR crashes are often the result of poor driver performance leading up to the crash. In this study, the performance of two control algorithms, sliding control and linear quadratic control, was investigated for use in an autonomous ROR vehicle recovery system. The two controllers were simulated amongst a variety of ROR conditions where typical driver performance was inadequate to safely operate the vehicle. The sliding controller recovered the fastest within the nominal conditions but exhibited large variability in performance amongst the more extreme ROR scenarios. Despite some small sacrifices in lateral error and yaw rate, the linear quadratic controller demonstrated a higher level of consistency and stability amongst the various conditions examined. Overall, the linear quadratic controller recovered the vehicle 25% faster than the sliding controller while using 70% less steering, which combined with its robust performance, indicates its high potential as an autonomous ROR countermeasure.

Robust decentralized power system controller design: Integrated approach

NASA Astrophysics Data System (ADS)

Veselý, Vojtech

2017-09-01

A unique approach to the design of gain scheduled controller (GSC) is presented. The proposed design procedure is based on the Bellman-Lyapunov equation, guaranteed cost and robust stability conditions using the parameter dependent quadratic stability approach. The obtained feasible design procedures for robust GSC design are in the form of BMI with guaranteed convex stability conditions. The obtained design results and their properties are illustrated in the simultaneously design of controllers for simple model (6-order) turbogenerator. The results of the obtained design procedure are a PI automatic voltage regulator (AVR) for synchronous generator, a PI governor controller and a power system stabilizer for excitation system.

Design of integrated autopilot/autothrottle for NASA TSRV airplane using integral LQG methodology. [transport systems research vehicle

NASA Technical Reports Server (NTRS)

Kaminer, Isaac; Benson, Russell A.

1989-01-01

An integrated autopilot/autothrottle control system has been developed for the NASA transport system research vehicle using a two-degree-of-freedom approach. Based on this approach, the feedback regulator was designed using an integral linear quadratic regulator design technique, which offers a systematic approach to satisfy desired feedback performance requirements and guarantees stability margins in both control and sensor loops. The resulting feedback controller was discretized and implemented using a delta coordinate concept, which allows for transient free controller switching by initializing all controller states to zero and provides a simple solution for dealing with throttle limiting cases.

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…

Period changes of 7 bright RR Lyrae variables included in the BAV standard program.

NASA Astrophysics Data System (ADS)

Wunder, E.

1995-11-01

On the basis of 1578 times of maxima historical and present period changes of the RR Lyrae stars SW And, SW Aqr, AA Aql, X Ari, RS Boo, RR Cet and XZ Cyg are analysed. In tables the period jumps and the quadratic terms of the elements are quantified and timed; elements are given to describe the historical O-C-curves; instant elements are listed to support nowadays observations.

Guidance/Navigation Requirements Study Final Report. Volume III. Appendices

DTIC Science & Technology

1978-04-30

shown Figure G-2. The free-flight simulation program FFSIM uses quaternions to calculate the body attitude as a function of time. To calculate the...the lack of open-loop damping, the existence of a feedback controller which will stabilize the closed-loon system depends upon the satisfaction of a...re-entry vehicle has dynamic pecularitles which tend to discourage the use of "linear-quadratic" feedback regulators in guidance. The disadvantageous

Lump solutions to nonlinear partial differential equations via Hirota bilinear forms

NASA Astrophysics Data System (ADS)

Ma, Wen-Xiu; Zhou, Yuan

2018-02-01

Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is the Hirota bilinear formulation and the primary object is the class of positive multivariate quadratic functions. A complete determination of quadratic functions positive in space and time is given, and positive quadratic functions are characterized as sums of squares of linear functions. Necessary and sufficient conditions for positive quadratic functions to solve Hirota bilinear equations are presented, and such polynomial solutions yield lump solutions to nonlinear partial differential equations under the dependent variable transformations u = 2(ln ⁡ f) x and u = 2(ln ⁡ f) xx, where x is one spatial variable. Applications are made for a few generalized KP and BKP equations.

The degenerate parametric oscillator and Ince's equation

NASA Astrophysics Data System (ADS)

Cordero-Soto, Ricardo; Suslov, Sergei K.

2011-01-01

We construct Green's function for the quantum degenerate parametric oscillator in the coordinate representation in terms of standard solutions of Ince's equation in a framework of a general approach to variable quadratic Hamiltonians. Exact time-dependent wavefunctions and their connections with dynamical invariants and SU(1, 1) group are also discussed. An extension to the degenerate parametric oscillator with time-dependent amplitude and phase is also mentioned.

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.

TRANSP-based Trajectory Optimization of the Current Profile Evolution to Facilitate Robust Non-inductive Ramp-up in NSTX-U

NASA Astrophysics Data System (ADS)

Wehner, William; Schuster, Eugenio; Poli, Francesca

2016-10-01

Initial progress towards the design of non-inductive current ramp-up scenarios in the National Spherical Torus Experiment Upgrade (NSTX-U) has been made through the use of TRANSP predictive simulations. The strategy involves, first, ramping the plasma current with high harmonic fast waves (HHFW) to about 400 kA, and then further ramping to 900 kA with neutral beam injection (NBI). However, the early ramping of neutral beams and application of HHFW leads to an undesirably peaked current profile making the plasma unstable to ballooning modes. We present an optimization-based control approach to improve on the non-inductive ramp-up strategy. We combine the TRANSP code with an optimization algorithm based on sequential quadratic programming to search for time evolutions of the NBI powers, the HHFW powers, and the line averaged density that define an open-loop actuator strategy that maximizes the non-inductive current while satisfying constraints associated with the current profile evolution for MHD stable plasmas. This technique has the potential of playing a critical role in achieving robustly stable non-inductive ramp-up, which will ultimately be necessary to demonstrate applicability of the spherical torus concept to larger devices without sufficient room for a central coil. Supported by the US DOE under the SCGSR Program.

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…

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…

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…

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.

Partial discharge localization in power transformers based on the sequential quadratic programming-genetic algorithm adopting acoustic emission techniques

NASA Astrophysics Data System (ADS)

Liu, Hua-Long; Liu, Hua-Dong

2014-10-01

Partial discharge (PD) in power transformers is one of the prime reasons resulting in insulation degradation and power faults. Hence, it is of great importance to study the techniques of the detection and localization of PD in theory and practice. The detection and localization of PD employing acoustic emission (AE) techniques, as a kind of non-destructive testing, plus due to the advantages of powerful capability of locating and high precision, have been paid more and more attention. The localization algorithm is the key factor to decide the localization accuracy in AE localization of PD. Many kinds of localization algorithms exist for the PD source localization adopting AE techniques including intelligent and non-intelligent algorithms. However, the existed algorithms possess some defects such as the premature convergence phenomenon, poor local optimization ability and unsuitability for the field applications. To overcome the poor local optimization ability and easily caused premature convergence phenomenon of the fundamental genetic algorithm (GA), a new kind of improved GA is proposed, namely the sequence quadratic programming-genetic algorithm (SQP-GA). For the hybrid optimization algorithm, SQP-GA, the sequence quadratic programming (SQP) algorithm which is used as a basic operator is integrated into the fundamental GA, so the local searching ability of the fundamental GA is improved effectively and the premature convergence phenomenon is overcome. Experimental results of the numerical simulations of benchmark functions show that the hybrid optimization algorithm, SQP-GA, is better than the fundamental GA in the convergence speed and optimization precision, and the proposed algorithm in this paper has outstanding optimization effect. At the same time, the presented SQP-GA in the paper is applied to solve the ultrasonic localization problem of PD in transformers, then the ultrasonic localization method of PD in transformers based on the SQP-GA is proposed. And localization results based on the SQP-GA are compared with some algorithms such as the GA, some other intelligent and non-intelligent algorithms. The results of calculating examples both stimulated and spot experiments demonstrate that the localization method based on the SQP-GA can effectively prevent the results from getting trapped into the local optimum values, and the localization method is of great feasibility and very suitable for the field applications, and the precision of localization is enhanced, and the effectiveness of localization is ideal and satisfactory.

A novel approach to enhance the accuracy of vibration control of Frames

NASA Astrophysics Data System (ADS)

Toloue, Iraj; Shahir Liew, Mohd; Harahap, I. S. H.; Lee, H. E.

2018-03-01

All structures built within known seismically active regions are typically designed to endure earthquake forces. Despite advances in earthquake resistant structures, it can be inferred from hindsight that no structure is entirely immune to damage from earthquakes. Active vibration control systems, unlike the traditional methods which enlarge beams and columns, are highly effective countermeasures to reduce the effects of earthquake loading on a structure. It requires fast computation of nonlinear structural analysis in near time and has historically demanded advanced programming hosted on powerful computers. This research aims to develop a new approach for active vibration control of frames, which is applicable over both elastic and plastic material behavior. In this study, the Force Analogy Method (FAM), which is based on Hook's Law is further extended using the Timoshenko element which considers shear deformations to increase the reliability and accuracy of the controller. The proposed algorithm is applied to a 2D portal frame equipped with linear actuator, which is designed based on full state Linear Quadratic Regulator (LQR). For comparison purposes, the portal frame is analysed by both the Euler Bernoulli and Timoshenko element respectively. The results clearly demonstrate the superiority of the Timoshenko element over Euler Bernoulli for application in nonlinear analysis.

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…

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.

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.

SUBOPT: A CAD program for suboptimal linear regulators

NASA Technical Reports Server (NTRS)

Fleming, P. J.

1985-01-01

An interactive software package which provides design solutions for both standard linear quadratic regulator (LQR) and suboptimal linear regulator problems is described. Intended for time-invariant continuous systems, the package is easily modified to include sampled-data systems. LQR designs are obtained by established techniques while the large class of suboptimal problems containing controller and/or performance index options is solved using a robust gradient minimization technique. Numerical examples demonstrate features of the package and recent developments are described.

Sparse Recovery via Differential Inclusions

DTIC Science & Technology

2014-07-01

2242. [Wai09] Martin J. Wainwright, Sharp thresholds for high-dimensional and noisy spar- sity recovery using l1 -constrained quadratic programming...solution, (1.11) βt = { 0, if t < 1/y; y(1− e−κ(t−1/y)), otherwise, which converges to the unbiased Bregman ISS estimator exponentially fast. Let us ...are not given the support set S, so the following two prop- erties are used to evaluate the performance of an estimator β̂. 1. Model selection

Structural Optimization of a Distributed Actuation System in a Flexible In-Plane Morphing Wing

DTIC Science & Technology

2007-06-01

Captain, USAF Approved: /signed/ 11 Jun 2007 Dr. Robert Canfield (Chairman) date /signed/ 11 Jun 2007 Dr. Brian Sanders (Member) date /signed/ 11 Jun...can be seen here at the Camp Roberts Flight Test Range [11]. separation, which ultimately increased the overall lift. During wind tunnel tests, the...Matlabr . The outermost loop was written by Mark Spillman and Dr. Robert Canfield and was based on Schittkowski’s Sequential Quadratic Programming (SQP

New Decentralized Algorithms for Spacecraft Formation Control Based on a Cyclic Approach

DTIC Science & Technology

2010-06-01

space framework. As metric of performance, a common quadratic norm that weights the performance error and the control effort is traded with the cost...R = DTD, then the metric of interest is (’J)",,, the square of the 2-norm from input w to output z. Given a system G with state space description A ... spaced logarithmic spiral formation. These results are derived for

Adiabatic Quantum Computing with Neutral Atoms

NASA Astrophysics Data System (ADS)

Hankin, Aaron; Biedermann, Grant; Burns, George; Jau, Yuan-Yu; Johnson, Cort; Kemme, Shanalyn; Landahl, Andrew; Mangan, Michael; Parazzoli, L. Paul; Schwindt, Peter; Armstrong, Darrell

2012-06-01

We are developing, both theoretically and experimentally, a neutral atom qubit approach to adiabatic quantum computation. Using our microfabricated diffractive optical elements, we plan to implement an array of optical traps for cesium atoms and use Rydberg-dressed ground states to provide a controlled atom-atom interaction. We will develop this experimental capability to generate a two-qubit adiabatic evolution aimed specifically toward demonstrating the two-qubit quadratic unconstrained binary optimization (QUBO) routine.

Modeling the pressure-strain correlation of turbulence: An invariant dynamical systems approach

NASA Technical Reports Server (NTRS)

Speziale, Charles G.; Sarkar, Sutanu; Gatski, Thomas B.

1990-01-01

The modeling of the pressure-strain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved second-order closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressure-strain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model - the SSG model - is shown to outperform the Launder, Reece, and Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in a variety of homogeneous turbulent flows. Some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modeling of the pressure-strain correlation. Possible alternative approaches are discussed briefly.

Modelling the pressure-strain correlation of turbulence - An invariant dynamical systems approach

NASA Technical Reports Server (NTRS)

Speziale, Charles G.; Sarkar, Sutanu; Gatski, Thomas B.

1991-01-01

The modeling of the pressure-strain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved second-order closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressure-strain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model - the SSG model - is shown to outperform the Launder, Reece, and Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in a variety of homogeneous turbulent flows. Some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modeling of the pressure-strain correlation. Possible alternative approaches are discussed briefly.

Design of asymptotic estimators: an approach based on neural networks and nonlinear programming.

PubMed

Alessandri, Angelo; Cervellera, Cristiano; Sanguineti, Marcello

2007-01-01

A methodology to design state estimators for a class of nonlinear continuous-time dynamic systems that is based on neural networks and nonlinear programming is proposed. The estimator has the structure of a Luenberger observer with a linear gain and a parameterized (in general, nonlinear) function, whose argument is an innovation term representing the difference between the current measurement and its prediction. The problem of the estimator design consists in finding the values of the gain and of the parameters that guarantee the asymptotic stability of the estimation error. Toward this end, if a neural network is used to take on this function, the parameters (i.e., the neural weights) are chosen, together with the gain, by constraining the derivative of a quadratic Lyapunov function for the estimation error to be negative definite on a given compact set. It is proved that it is sufficient to impose the negative definiteness of such a derivative only on a suitably dense grid of sampling points. The gain is determined by solving a Lyapunov equation. The neural weights are searched for via nonlinear programming by minimizing a cost penalizing grid-point constraints that are not satisfied. Techniques based on low-discrepancy sequences are applied to deal with a small number of sampling points, and, hence, to reduce the computational burden required to optimize the parameters. Numerical results are reported and comparisons with those obtained by the extended Kalman filter are made.

Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel

PubMed Central

Shanhua, Xu; Songbo, Ren; Youde, Wang

2015-01-01

To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel. PMID:26121468

Precision measurement of the local bias of dark matter halos

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

Lazeyras, Titouan; Wagner, Christian; Schmidt, Fabian

2016-02-01

We present accurate measurements of the linear, quadratic, and cubic local bias of dark matter halos, using curved 'separate universe' N-body simulations which effectively incorporate an infinite-wavelength overdensity. This can be seen as an exact implementation of the peak-background split argument. We compare the results with the linear and quadratic bias measured from the halo-matter power spectrum and bispectrum, and find good agreement. On the other hand, the standard peak-background split applied to the Sheth and Tormen (1999) and Tinker et al. (2008) halo mass functions matches the measured linear bias parameter only at the level of 10%. The predictionmore » from the excursion set-peaks approach performs much better, which can be attributed to the stochastic moving barrier employed in the excursion set-peaks prediction. We also provide convenient fitting formulas for the nonlinear bias parameters b{sub 2}(b{sub 1}) and b{sub 3}(b{sub 1}), which work well over a range of redshifts.« less

Wind turbine power tracking using an improved multimodel quadratic approach.

PubMed

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

2010-07-01

In this paper, an improved multimodel optimal quadratic control structure for variable speed, pitch regulated wind turbines (operating at high wind speeds) is proposed in order to integrate high levels of wind power to actively provide a primary reserve for frequency control. On the basis of the nonlinear model of the studied plant, and taking into account the wind speed fluctuations, and the electrical power variation, a multimodel linear description is derived for the wind turbine, and is used for the synthesis of an optimal control law involving a state feedback, an integral action and an output reference model. This new control structure allows a rapid transition of the wind turbine generated power between different desired set values. This electrical power tracking is ensured with a high-performance behavior for all other state variables: turbine and generator rotational speeds and mechanical shaft torque; and smooth and adequate evolution of the control variables. 2010 ISA. Published by Elsevier Ltd. All rights reserved.

Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares

NASA Technical Reports Server (NTRS)

Orr, Jeb S.

2012-01-01

A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed

Characterization of DBD Plasma Actuators Performance without External Flow . Part I; Thrust-Voltage Quadratic Relationship in Logarithmic Space for Sinusoidal Excitation

NASA Technical Reports Server (NTRS)

Ashpis, David E.; Laun, Matthew C.

2016-01-01

We present results of thrust measurements of Dielectric Barrier Discharge (DBD) plasma actuators. We have used a test setup, measurement, and data processing methodology that we developed in prior work. The tests were conducted with High Density Polyethylene (HDPE) actuators of three thicknesses. The applied voltage driving the actuators was a pure sinusoidal waveform. The test setup was suspended actuators with a partial liquid interface. The tests were conducted at low ambient humidity. The thrust was measured with an analytical balance and the results were corrected for anti-thrust to isolate the plasma generated thrust. Applying this approach resulted in smooth and repeatable data. It also enabled curve fitting that yielded quadratic relations between the plasma thrust and voltage in log-log space at constant frequencies. The results contrast power law relationships developed in literature that appear to be a rough approximation over a limited voltage range.

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.

Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel.

PubMed

Shanhua, Xu; Songbo, Ren; Youde, Wang

2015-01-01

To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel.

Are rapid population estimates accurate? A field trial of two different assessment methods.

PubMed

Grais, Rebecca F; Coulombier, Denis; Ampuero, Julia; Lucas, Marcelino E S; Barretto, Avertino T; Jacquier, Guy; Diaz, Francisco; Balandine, Serge; Mahoudeau, Claude; Brown, Vincent

2006-09-01

Emergencies resulting in large-scale displacement often lead to populations resettling in areas where basic health services and sanitation are unavailable. To plan relief-related activities quickly, rapid population size estimates are needed. The currently recommended Quadrat method estimates total population by extrapolating the average population size living in square blocks of known area to the total site surface. An alternative approach, the T-Square, provides a population estimate based on analysis of the spatial distribution of housing units taken throughout a site. We field tested both methods and validated the results against a census in Esturro Bairro, Beira, Mozambique. Compared to the census (population: 9,479), the T-Square yielded a better population estimate (9,523) than the Quadrat method (7,681; 95% confidence interval: 6,160-9,201), but was more difficult for field survey teams to implement. Although applicable only to similar sites, several general conclusions can be drawn for emergency planning.

Analytical and simulator study of advanced transport

NASA Technical Reports Server (NTRS)

Levison, W. H.; Rickard, W. W.

1982-01-01

An analytic methodology, based on the optimal-control pilot model, was demonstrated for assessing longitidunal-axis handling qualities of transport aircraft in final approach. Calibration of the methodology is largely in terms of closed-loop performance requirements, rather than specific vehicle response characteristics, and is based on a combination of published criteria, pilot preferences, physical limitations, and engineering judgment. Six longitudinal-axis approach configurations were studied covering a range of handling qualities problems, including the presence of flexible aircraft modes. The analytical procedure was used to obtain predictions of Cooper-Harper ratings, a solar quadratic performance index, and rms excursions of important system variables.

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.

UAV Control on the Basis of 3D Landmark Bearing-Only Observations

PubMed Central

Karpenko, Simon; Konovalenko, Ivan; Miller, Alexander; Miller, Boris; Nikolaev, Dmitry

2015-01-01

The article presents an approach to the control of a UAV on the basis of 3D landmark observations. The novelty of the work is the usage of the 3D RANSAC algorithm developed on the basis of the landmarks’ position prediction with the aid of a modified Kalman-type filter. Modification of the filter based on the pseudo-measurements approach permits obtaining unbiased UAV position estimation with quadratic error characteristics. Modeling of UAV flight on the basis of the suggested algorithm shows good performance, even under significant external perturbations. PMID:26633394

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…

A Parallel Implicit Reconstructed Discontinuous Galerkin Method for Compressible Flows on Hybrid Grids

NASA Astrophysics Data System (ADS)

Xia, Yidong

The objective this work is to develop a parallel, implicit reconstructed discontinuous Galerkin (RDG) method using Taylor basis for the solution of the compressible Navier-Stokes equations on 3D hybrid grids. This third-order accurate RDG method is based on a hierarchical weighed essentially non- oscillatory reconstruction scheme, termed as HWENO(P1P 2) to indicate that a quadratic polynomial solution is obtained from the underlying linear polynomial DG solution via a hierarchical WENO reconstruction. The HWENO(P1P2) is designed not only to enhance the accuracy of the underlying DG(P1) method but also to ensure non-linear stability of the RDG method. In this reconstruction scheme, a quadratic polynomial (P2) solution is first reconstructed using a least-squares approach from the underlying linear (P1) discontinuous Galerkin solution. The final quadratic solution is then obtained using a Hermite WENO reconstruction, which is necessary to ensure the linear stability of the RDG method on 3D unstructured grids. The first derivatives of the quadratic polynomial solution are then reconstructed using a WENO reconstruction in order to eliminate spurious oscillations in the vicinity of strong discontinuities, thus ensuring the non-linear stability of the RDG method. The parallelization in the RDG method is based on a message passing interface (MPI) programming paradigm, where the METIS library is used for the partitioning of a mesh into subdomain meshes of approximately the same size. Both multi-stage explicit Runge-Kutta and simple implicit backward Euler methods are implemented for time advancement in the RDG method. In the implicit method, three approaches: analytical differentiation, divided differencing (DD), and automatic differentiation (AD) are developed and implemented to obtain the resulting flux Jacobian matrices. The automatic differentiation is a set of techniques based on the mechanical application of the chain rule to obtain derivatives of a function given as a computer program. By using an AD tool, the manpower can be significantly reduced for deriving the flux Jacobians, which can be quite complicated, tedious, and error-prone if done by hand or symbolic arithmetic software, depending on the complexity of the numerical flux scheme. In addition, the workload for code maintenance can also be largely reduced in case the underlying flux scheme is updated. The approximate system of linear equations arising from the Newton linearization is solved by the general minimum residual (GMRES) algorithm with lower-upper symmetric gauss-seidel (LUSGS) preconditioning. This GMRES+LU-SGS linear solver is the most robust and efficient for implicit time integration of the discretized Navier-Stokes equations when the AD-based flux Jacobians are provided other than the other two approaches. The developed HWENO(P1P2) method is used to compute a variety of well-documented compressible inviscid and viscous flow test cases on 3D hybrid grids, including some standard benchmark test cases such as the Sod shock tube, flow past a circular cylinder, and laminar flow past a at plate. The computed solutions are compared with either analytical solutions or experimental data, if available to assess the accuracy of the HWENO(P 1P2) method. Numerical results demonstrate that the HWENO(P 1P2) method is able to not only enhance the accuracy of the underlying HWENO(P1) method, but also ensure the linear and non-linear stability at the presence of strong discontinuities. An extensive study of grid convergence analysis on various types of elements: tetrahedron, prism, hexahedron, and hybrid prism/hexahedron, for a number of test cases indicates that the developed HWENO(P1P2) method is able to achieve the designed third-order accuracy of spatial convergence for smooth inviscid flows: one order higher than the underlying second-order DG(P1) method without significant increase in computing costs and storage requirements. The performance of the the developed GMRES+LU-SGS implicit method is compared with the multi-stage Runge-Kutta time stepping scheme for a number of test cases in terms of the timestep and CPU time. Numerical results indicate that the overall performance of the implicit method with AD-based Jacobians is order of magnitude better than the its explicit counterpart. Finally, a set of parallel scaling tests for both explicit and implicit methods is conducted on North Carolina State University's ARC cluster, demonstrating almost an ideal scalability of the RDG method. (Abstract shortened by UMI.)

Structural optimization with approximate sensitivities

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Hopkins, D. A.; Coroneos, R.

1994-01-01

Computational efficiency in structural optimization can be enhanced if the intensive computations associated with the calculation of the sensitivities, that is, gradients of the behavior constraints, are reduced. Approximation to gradients of the behavior constraints that can be generated with small amount of numerical calculations is proposed. Structural optimization with these approximate sensitivities produced correct optimum solution. Approximate gradients performed well for different nonlinear programming methods, such as the sequence of unconstrained minimization technique, method of feasible directions, sequence of quadratic programming, and sequence of linear programming. Structural optimization with approximate gradients can reduce by one third the CPU time that would otherwise be required to solve the problem with explicit closed-form gradients. The proposed gradient approximation shows potential to reduce intensive computation that has been associated with traditional structural optimization.

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)

Solving the Integral of Quadratic Forms of Covariance Matrices for Applications in Polarimetric Radar Imagery

NASA Astrophysics Data System (ADS)

Marino, Armando; Hajnsek, Irena

2015-04-01

In this work, the solution of quadratic forms with special application to polarimetric and interferometric covariance matrices is investigated. An analytical solution for the integral of a single quadratic form is derived. Additionally, the integral of the Pol-InSAR coherence (expressed as combination of quadratic forms) is investigated. An approximation for such integral is proposed and defined as Trace coherence. Such approximation is tested on real data to verify that the error is acceptable. The trace coherence can be used for tackle problems related to change detection. Moreover, the use of the Trace coherence in model inversion (as for the RVoG three stage inversion) will be investigated in the future.

Closed-loop stability of linear quadratic optimal systems in the presence of modeling errors

NASA Technical Reports Server (NTRS)

Toda, M.; Patel, R.; Sridhar, B.

1976-01-01

The well-known stabilizing property of linear quadratic state feedback design is utilized to evaluate the robustness of a linear quadratic feedback design in the presence of modeling errors. Two general conditions are obtained for allowable modeling errors such that the resulting closed-loop system remains stable. One of these conditions is applied to obtain two more particular conditions which are readily applicable to practical situations where a designer has information on the bounds of modeling errors. Relations are established between the allowable parameter uncertainty and the weighting matrices of the quadratic performance index, thereby enabling the designer to select appropriate weighting matrices to attain a robust feedback design.

Investigation of metrics to assess vascular flow modifications for diverter device designs using hydrodynamics and angiographic studies

NASA Astrophysics Data System (ADS)

Ionita, Ciprian N.; Bednarek, Daniel R.; Rudin, Stephen

2012-03-01

Intracranial aneurysm treatment with flow diverters (FD) is a new minimally invasive approach, recently approved for use in human patients. Attempts to correlate the flow reduction observed in angiograms with a parameter related to the FD structure have not been totally successful. To find the proper parameter, we investigated four porous-media flow models. The models describing the relation between the pressure drop and flow velocity that are investigated include the capillary theory linear model (CTLM), the drag force linear model (DFLM), the simple quadratic model (SQM) and the modified quadratic model (MQM). Proportionality parameters are referred to as permeability for the linear models and resistance for the quadratic ones. A two stage experiment was performed. First, we verified flow model validity by placing six different stainless-steel meshes, resembling FD structures, in known flow conditions. The best flow model was used for the second stage, where six different FD's were inserted in aneurysm phantoms and flow modification was estimated using angiographically derived time density curves (TDC). Finally, TDC peak variation was compared with the FD parameter. Model validity experiments indicated errors of: 70% for the linear models, 26% for the SQM and 7% for the MQM. The resistance calculated according to the MQM model correlated well with the contrast flow reduction. Results indicate that resistance calculated according to MQM is appropriate to characterize the FD and could explain the flow modification observed in angiograms.

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

Sequential design of discrete linear quadratic regulators via optimal root-locus techniques

NASA Technical Reports Server (NTRS)

Shieh, Leang S.; Yates, Robert E.; Ganesan, Sekar

1989-01-01

A sequential method employing classical root-locus techniques has been developed in order to determine the quadratic weighting matrices and discrete linear quadratic regulators of multivariable control systems. At each recursive step, an intermediate unity rank state-weighting matrix that contains some invariant eigenvectors of that open-loop matrix is assigned, and an intermediate characteristic equation of the closed-loop system containing the invariant eigenvalues is created.

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.

Test spaces and characterizations of quadratic spaces

NASA Astrophysics Data System (ADS)

Dvurečenskij, Anatolij

1996-10-01

We show that a test space consisting of nonzero vectors of a quadratic space E and of the set all maximal orthogonal systems in E is algebraic iff E is Dacey or, equivalently, iff E is orthomodular. In addition, we present another orthomodularity criteria of quadratic spaces, and using the result of Solèr, we show that they can imply that E is a real, complex, or quaternionic Hilbert space.

A note on the relationship between the quadratic mean stand diameter and harmonic mean basal area under size-biased distribution theory

Treesearch

Jeffrey H. Gove

2003-01-01

This note seeks to extend the utility of size-biased distribution theory as applied to forestry through two relationships regarding the quadratic mean stand diameter. First, the quadratic mean stand diameter's relationship to the harmonic mean basal area for horizontal point sampling, which has been known algebraically from early on, is proved under size-biased...

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.

Exact solutions to quadratic gravity

NASA Astrophysics Data System (ADS)

Pravda, V.; Pravdová, A.; Podolský, J.; Švarc, R.

2017-04-01

Since all Einstein spacetimes are vacuum solutions to quadratic gravity in four dimensions, in this paper we study various aspects of non-Einstein vacuum solutions to this theory. Most such known solutions are of traceless Ricci and Petrov type N with a constant Ricci scalar. Thus we assume the Ricci scalar to be constant which leads to a substantial simplification of the field equations. We prove that a vacuum solution to quadratic gravity with traceless Ricci tensor of type N and aligned Weyl tensor of any Petrov type is necessarily a Kundt spacetime. This will considerably simplify the search for new non-Einstein solutions. Similarly, a vacuum solution to quadratic gravity with traceless Ricci type III and aligned Weyl tensor of Petrov type II or more special is again necessarily a Kundt spacetime. Then we study the general role of conformal transformations in constructing vacuum solutions to quadratic gravity. We find that such solutions can be obtained by solving one nonlinear partial differential equation for a conformal factor on any Einstein spacetime or, more generally, on any background with vanishing Bach tensor. In particular, we show that all geometries conformal to Kundt are either Kundt or Robinson-Trautman, and we provide some explicit Kundt and Robinson-Trautman solutions to quadratic gravity by solving the above mentioned equation on certain Kundt backgrounds.

A Wavelet Bicoherence-Based Quadratic Nonlinearity Feature for Translational Axis Condition Monitoring

PubMed Central

Li, Yong; Wang, Xiufeng; Lin, Jing; Shi, Shengyu

2014-01-01

The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM) has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features. PMID:24473281

Finite Element Simulation of Articular Contact Mechanics with Quadratic Tetrahedral Elements

PubMed Central

Maas, Steve A.; Ellis, Benjamin J.; Rawlins, David S.; Weiss, Jeffrey A.

2016-01-01

Although it is easier to generate finite element discretizations with tetrahedral elements, trilinear hexahedral (HEX8) elements are more often used in simulations of articular contact mechanics. This is due to numerical shortcomings of linear tetrahedral (TET4) elements, limited availability of quadratic tetrahedron elements in combination with effective contact algorithms, and the perceived increased computational expense of quadratic finite elements. In this study we implemented both ten-node (TET10) and fifteen-node (TET15) quadratic tetrahedral elements in FEBio (www.febio.org) and compared their accuracy, robustness in terms of convergence behavior and computational cost for simulations relevant to articular contact mechanics. Suitable volume integration and surface integration rules were determined by comparing the results of several benchmark contact problems. The results demonstrated that the surface integration rule used to evaluate the contact integrals for quadratic elements affected both convergence behavior and accuracy of predicted stresses. The computational expense and robustness of both quadratic tetrahedral formulations compared favorably to the HEX8 models. Of note, the TET15 element demonstrated superior convergence behavior and lower computational cost than both the TET10 and HEX8 elements for meshes with similar numbers of degrees of freedom in the contact problems that we examined. Finally, the excellent accuracy and relative efficiency of these quadratic tetrahedral elements was illustrated by comparing their predictions with those for a HEX8 mesh for simulation of articular contact in a fully validated model of the hip. These results demonstrate that TET10 and TET15 elements provide viable alternatives to HEX8 elements for simulation of articular contact mechanics. PMID:26900037

Development of improved space sampling strategies for ocean chemical properties: Total carbon dioxide and dissolved nitrate

NASA Technical Reports Server (NTRS)

Goyet, Catherine; Davis, Daniel; Peltzer, Edward T.; Brewer, Peter G.

1995-01-01

Large-scale ocean observing programs such as the Joint Global Ocean Flux Study (JGOFS) and the World Ocean Circulation Experiment (WOCE) today, must face the problem of designing an adequate sampling strategy. For ocean chemical variables, the goals and observing technologies are quite different from ocean physical variables (temperature, salinity, pressure). We have recently acquired data on the ocean CO2 properties on WOCE cruises P16c and P17c that are sufficiently dense to test for sampling redundancy. We use linear and quadratic interpolation methods on the sampled field to investigate what is the minimum number of samples required to define the deep ocean total inorganic carbon (TCO2) field within the limits of experimental accuracy (+/- 4 micromol/kg). Within the limits of current measurements, these lines were oversampled in the deep ocean. Should the precision of the measurement be improved, then a denser sampling pattern may be desirable in the future. This approach rationalizes the efficient use of resources for field work and for estimating gridded (TCO2) fields needed to constrain geochemical models.

Topology optimization of embedded piezoelectric actuators considering control spillover effects

NASA Astrophysics Data System (ADS)

Gonçalves, Juliano F.; De Leon, Daniel M.; Perondi, Eduardo A.

2017-02-01

This article addresses the problem of active structural vibration control by means of embedded piezoelectric actuators. The topology optimization method using the solid isotropic material with penalization (SIMP) approach is employed in this work to find the optimum design of actuators taken into account the control spillover effects. A coupled finite element model of the structure is derived assuming a two-phase material and this structural model is written into the state-space representation. The proposed optimization formulation aims to determine the distribution of piezoelectric material which maximizes the controllability for a given vibration mode. The undesirable effects of the feedback control on the residual modes are limited by including a spillover constraint term containing the residual controllability Gramian eigenvalues. The optimization of the shape and placement of the conventionally embedded piezoelectric actuators are performed using a Sequential Linear Programming (SLP) algorithm. Numerical examples are presented considering the control of the bending vibration modes for a cantilever and a fixed beam. A Linear-Quadratic Regulator (LQR) is synthesized for each case of controlled structure in order to compare the influence of the additional constraint.

Proteinortho: detection of (co-)orthologs in large-scale analysis.

PubMed

Lechner, Marcus; Findeiss, Sven; Steiner, Lydia; Marz, Manja; Stadler, Peter F; Prohaska, Sonja J

2011-04-28

Orthology analysis is an important part of data analysis in many areas of bioinformatics such as comparative genomics and molecular phylogenetics. The ever-increasing flood of sequence data, and hence the rapidly increasing number of genomes that can be compared simultaneously, calls for efficient software tools as brute-force approaches with quadratic memory requirements become infeasible in practise. The rapid pace at which new data become available, furthermore, makes it desirable to compute genome-wide orthology relations for a given dataset rather than relying on relations listed in databases. The program Proteinortho described here is a stand-alone tool that is geared towards large datasets and makes use of distributed computing techniques when run on multi-core hardware. It implements an extended version of the reciprocal best alignment heuristic. We apply Proteinortho to compute orthologous proteins in the complete set of all 717 eubacterial genomes available at NCBI at the beginning of 2009. We identified thirty proteins present in 99% of all bacterial proteomes. Proteinortho significantly reduces the required amount of memory for orthology analysis compared to existing tools, allowing such computations to be performed on off-the-shelf hardware.

Numerical study of a matrix-free trust-region SQP method for equality constrained optimization.

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

Heinkenschloss, Matthias; Ridzal, Denis; Aguilo, Miguel Antonio

2011-12-01

This is a companion publication to the paper 'A Matrix-Free Trust-Region SQP Algorithm for Equality Constrained Optimization' [11]. In [11], we develop and analyze a trust-region sequential quadratic programming (SQP) method that supports the matrix-free (iterative, in-exact) solution of linear systems. In this report, we document the numerical behavior of the algorithm applied to a variety of equality constrained optimization problems, with constraints given by partial differential equations (PDEs).

On the structure of nonlinear constitutive equations for fiber reinforced composites

NASA Technical Reports Server (NTRS)

Jansson, Stefan

1992-01-01

The structure of constitutive equations for nonlinear multiaxial behavior of transversely isotropic fiber reinforced metal matrix composites subject to proportional loading was investigated. Results from an experimental program were combined with numerical simulations of the composite behavior for complex stress to reveal the full structure of the equations. It was found that the nonlinear response can be described by a quadratic flow-potential, based on the polynomial stress invariants, together with a hardening rule that is dominated by two different hardening mechanisms.

F100 multivariable control synthesis program: Evaluation of a multivariable control using a real-time engine simulation

NASA Technical Reports Server (NTRS)

Szuch, J. R.; Soeder, J. F.; Seldner, K.; Cwynar, D. S.

1977-01-01

The design, evaluation, and testing of a practical, multivariable, linear quadratic regulator control for the F100 turbofan engine were accomplished. NASA evaluation of the multivariable control logic and implementation are covered. The evaluation utilized a real time, hybrid computer simulation of the engine. Results of the evaluation are presented, and recommendations concerning future engine testing of the control are made. Results indicated that the engine testing of the control should be conducted as planned.

Advanced Energy Storage Management in Distribution Network

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

Liu, Guodong; Ceylan, Oguzhan; Xiao, Bailu

2016-01-01

With increasing penetration of distributed generation (DG) in the distribution networks (DN), the secure and optimal operation of DN has become an important concern. In this paper, an iterative mixed integer quadratic constrained quadratic programming model to optimize the operation of a three phase unbalanced distribution system with high penetration of Photovoltaic (PV) panels, DG and energy storage (ES) is developed. The proposed model minimizes not only the operating cost, including fuel cost and purchasing cost, but also voltage deviations and power loss. The optimization model is based on the linearized sensitivity coefficients between state variables (e.g., node voltages) andmore » control variables (e.g., real and reactive power injections of DG and ES). To avoid slow convergence when close to the optimum, a golden search method is introduced to control the step size and accelerate the convergence. The proposed algorithm is demonstrated on modified IEEE 13 nodes test feeders with multiple PV panels, DG and ES. Numerical simulation results validate the proposed algorithm. Various scenarios of system configuration are studied and some critical findings are concluded.« less

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.

Vehicle dynamics control of four in-wheel motor drive electric vehicle using gain scheduling based on tyre cornering stiffness estimation

NASA Astrophysics Data System (ADS)

Xiong, Lu; Yu, Zhuoping; Wang, Yang; Yang, Chen; Meng, Yufeng

2012-06-01

This paper focuses on the vehicle dynamic control system for a four in-wheel motor drive electric vehicle, aiming at improving vehicle stability under critical driving conditions. The vehicle dynamics controller is composed of three modules, i.e. motion following control, control allocation and vehicle state estimation. Considering the strong nonlinearity of the tyres under critical driving conditions, the yaw motion of the vehicle is regulated by gain scheduling control based on the linear quadratic regulator theory. The feed-forward and feedback gains of the controller are updated in real-time by online estimation of the tyre cornering stiffness, so as to ensure the control robustness against environmental disturbances as well as parameter uncertainty. The control allocation module allocates the calculated generalised force requirements to each in-wheel motor based on quadratic programming theory while taking the tyre longitudinal/lateral force coupling characteristic into consideration. Simulations under a variety of driving conditions are carried out to verify the control algorithm. Simulation results indicate that the proposed vehicle stability controller can effectively stabilise the vehicle motion under critical driving conditions.

DEM interpolation weight calculation modulus based on maximum entropy

NASA Astrophysics Data System (ADS)

Chen, Tian-wei; Yang, Xia

2015-12-01

There is negative-weight in traditional interpolation of gridding DEM, in the article, the principle of Maximum Entropy is utilized to analyze the model system which depends on modulus of space weight. Negative-weight problem of the DEM interpolation is researched via building Maximum Entropy model, and adding nonnegative, first and second order's Moment constraints, the negative-weight problem is solved. The correctness and accuracy of the method was validated with genetic algorithm in matlab program. The method is compared with the method of Yang Chizhong interpolation and quadratic program. Comparison shows that the volume and scaling of Maximum Entropy's weight is fit to relations of space and the accuracy is superior to the latter two.

Digital program for solving the linear stochastic optimal control and estimation problem

NASA Technical Reports Server (NTRS)

Geyser, L. C.; Lehtinen, B.

1975-01-01

A computer program is described which solves the linear stochastic optimal control and estimation (LSOCE) problem by using a time-domain formulation. The LSOCE problem is defined as that of designing controls for a linear time-invariant system which is disturbed by white noise in such a way as to minimize a performance index which is quadratic in state and control variables. The LSOCE problem and solution are outlined; brief descriptions are given of the solution algorithms, and complete descriptions of each subroutine, including usage information and digital listings, are provided. A test case is included, as well as information on the IBM 7090-7094 DCS time and storage requirements.

New verifiable stationarity concepts for a class of mathematical programs with disjunctive constraints.

PubMed

Benko, Matúš; Gfrerer, Helmut

2018-01-01

In this paper, we consider a sufficiently broad class of non-linear mathematical programs with disjunctive constraints, which, e.g. include mathematical programs with complemetarity/vanishing constraints. We present an extension of the concept of [Formula: see text]-stationarity which can be easily combined with the well-known notion of M-stationarity to obtain the stronger property of so-called [Formula: see text]-stationarity. We show how the property of [Formula: see text]-stationarity (and thus also of M-stationarity) can be efficiently verified for the considered problem class by computing [Formula: see text]-stationary solutions of a certain quadratic program. We consider further the situation that the point which is to be tested for [Formula: see text]-stationarity, is not known exactly, but is approximated by some convergent sequence, as it is usually the case when applying some numerical method.

Design of a candidate flutter suppression control law for DAST ARW-2. [Drones for Aerodynamic and Structural Testing Aeroelastic Research Wing

NASA Technical Reports Server (NTRS)

Adams, W. M., Jr.; Tiffany, S. H.

1983-01-01

A control law is developed to suppress symmetric flutter for a mathematical model of an aeroelastic research vehicle. An implementable control law is attained by including modified LQG (linear quadratic Gaussian) design techniques, controller order reduction, and gain scheduling. An alternate (complementary) design approach is illustrated for one flight condition wherein nongradient-based constrained optimization techniques are applied to maximize controller robustness.

Pressure-coupled combustion response model for solid propellants based on Zeldovich-Novozhilov approach

NASA Technical Reports Server (NTRS)

Harstad, K. G.; Strand, L. D.

1987-01-01

An exact analytical solution is given to the problem of long-time propellant thermal response to a specified pressure oscillation. Coupling to the gas phase is made using the quasisteady Zeldovich-Novozhilov approximation. Explicit linear and lowest order (quadratic) nonlinear expressions for propellant response are obtained from the implicit nonlinear solutions. Using these expressions, response curves are presented for an ammonium perchlorate composite propellant and HMX monopropellant.

Two-color walking Peregrine solitary waves.

PubMed

Baronio, Fabio; Chen, Shihua; Mihalache, Dumitru

2017-09-15

We study the extreme localization of light, evolving upon a non-zero background, in two-color parametric wave interaction in nonlinear quadratic media. We report the existence of quadratic Peregrine solitary waves, in the presence of significant group-velocity mismatch between the waves (or Poynting vector beam walk-off), in the regime of cascading second-harmonic generation. This finding opens a novel path for the experimental demonstration of extreme rogue waves in ultrafast quadratic nonlinear optics.

Self-accelerating parabolic beams in quadratic nonlinear media

NASA Astrophysics Data System (ADS)

Dolev, Ido; Libster, Ana; Arie, Ady

2012-09-01

We present experimental observation of self-accelerating parabolic beams in quadratic nonlinear media. We show that the intensity peaks of the first and second harmonics are asynchronous with respect to one another in the two transverse coordinates. In addition, the two coupled harmonics have the same acceleration within and after the nonlinear medium. We also study the evolution of second harmonic accelerating beams inside the quadratic media and their correlation with theoretical beams.

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.

Directional passability and quadratic steering logic for pyramid-type single gimbal control moment gyros

NASA Astrophysics Data System (ADS)

Yamada, Katsuhiko; Jikuya, Ichiro

2014-09-01

Singularity analysis and the steering logic of pyramid-type single gimbal control moment gyros are studied. First, a new concept of directional passability in a specified direction is introduced to investigate the structure of an elliptic singular surface. The differences between passability and directional passability are discussed in detail and are visualized for 0H, 2H, and 4H singular surfaces. Second, quadratic steering logic (QSL), a new steering logic for passing the singular surface, is investigated. The algorithm is based on the quadratic constrained quadratic optimization problem and is reduced to the Newton method by using Gröbner bases. The proposed steering logic is demonstrated through numerical simulations for both constant torque maneuvering examples and attitude control examples.

Retention prediction of highly polar ionizable solutes under gradient conditions on a mixed-mode reversed-phase and weak anion-exchange stationary phase.

PubMed

Balkatzopoulou, P; Fasoula, S; Gika, H; Nikitas, P; Pappa-Louisi, A

2015-05-29

In the present work the retention of three highly polar and ionizable solutes - uric acid, nicotinic acid and ascorbic acid - was investigated on a mixed-mode reversed-phase and weak anion-exchange (RP/WAX) stationary phase in buffered aqueous acetonitrile (ACN) mobile phases. A U-shaped retention behavior was observed for all solutes with respect to the eluent organic modifier content studied in a range of 5-95% (v/v). This retention behavior clearly demonstrates the presence of a HILIC-type retention mechanism at ACN-rich hydro-organic eluents and an RP-like retention at aqueous-rich hydro-organic eluents. Hence, this column should be promising for application under both RP and HILIC gradient elution modes. For this reason, a series of programmed elution runs were carried out with increasing (RP) and decreasing (HILIC) organic solvent concentration in the mobile phase. This dual gradient process was successfully modeled by two retention models exhibiting a quadratic or a cubic dependence of the logarithm of the solute retention factor (lnk) upon the organic modifier volume fraction (φ). It was found that both models produced by gradient retention data allow the prediction of solute retention times for both types of programmed elution on the mixed-mode column. Four, in the case of the quadratic model, or five, in the case of the cubic model, initial HILIC- and RP-type gradient runs gave satisfactory retention predictions of any similar kind elution program, even with different flow rate, with an overall error of only 2.5 or 1.7%, respectively. Copyright © 2015 Elsevier B.V. All rights reserved.

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.

Estimation of the standardized ileal digestible valine to lysine ratio required for 25- to 120-kilogram pigs fed low crude protein diets supplemented with crystalline amino acids.

PubMed

Liu, X T; Ma, W F; Zeng, X F; Xie, C Y; Thacker, P A; Htoo, J K; Qiao, S Y

2015-10-01

Four 28-d experiments were conducted to determine the standardized ileal digestible (SID) valine (Val) to lysine (Lys) ratio required for 26- to 46- (Exp. 1), 49- to 70- (Exp. 2), 71- to 92- (Exp. 3), and 94- to 119-kg (Exp. 4) pigs fed low CP diets supplemented with crystalline AA. The first 3 experiments utilized 150 pigs (Duroc × Landrace × Large White), while Exp. 4 utilized 90 finishing pigs. Pigs in all 4 experiments were randomly allocated to 1 of 5 diets with 6 pens per treatment (3 pens of barrows and 3 pens of gilts) and 5 pigs per pen for the first 3 experiments and 3 pigs per pen for Exp. 4. Diets for all experiments were formulated to contain SID Val to Lys ratios of 0.55, 0.60, 0.65, 0.70, or 0.75. In Exp. 1 (26 to 46 kg), ADG increased (linear, = 0.039; quadratic, = 0.042) with an increasing dietary Val:Lys ratio. The SID Val:Lys ratio to maximize ADG was 0.62 using a linear broken-line model and 0.71 using a quadratic model. In Exp. 2 (49 to 70 kg), ADG increased (linear, = 0.021; quadratic, = 0.042) as the SID Val:Lys ratio increased. G:F improved (linear, = 0.039) and serum urea nitrogen (SUN) decreased (linear, = 0.021; quadratic, = 0.024) with an increased SID Val:Lys ratio. The SID Val:Lys ratios to maximize ADG as well as to minimize SUN levels were 0.67 and 0.65, respectively, using a linear broken-line model and 0.72 and 0.71, respectively, using a quadratic model. In Exp. 3 (71 to 92 kg), ADG increased (linear, = 0.007; quadratic, = 0.022) and SUN decreased (linear, = 0.011; quadratic, = 0.034) as the dietary SID Val:Lys ratio increased. The SID Val:Lys ratios to maximize ADG as well as to minimize SUN levels were 0.67 and 0.67, respectively, using a linear broken-line model and 0.72 and 0.74, respectively, using a quadratic model. In Exp. 4 (94 to 119 kg), ADG increased (linear, = 0.041) and G:F was improved (linear, = 0.004; quadratic, = 0.005) as the dietary SID Val:Lys ratio increased. The SID Val:Lys ratio to maximize G:F was 0.68 using a linear broken-line model and 0.72 using a quadratic model. Carcass traits and muscle quality were not influenced by SID Val:Lys ratio. In conclusion, the dietary SID Val:Lys ratios required for 26- to 46-, 49- to 70-, 71- to 92-, and 94- to 119-kg pigs were estimated to be 0.62, 0.66, 0.67, and 0.68, respectively, using a linear broken-line model and 0.71, 0.72, 0.73, and 0.72, respectively, using a quadratic model.

Behavioral and Neural Adaptation in Approach Behavior.

PubMed

Wang, Shuo; Falvello, Virginia; Porter, Jenny; Said, Christopher P; Todorov, Alexander

2018-06-01

People often make approachability decisions based on perceived facial trustworthiness. However, it remains unclear how people learn trustworthiness from a population of faces and whether this learning influences their approachability decisions. Here we investigated the neural underpinning of approach behavior and tested two important hypotheses: whether the amygdala adapts to different trustworthiness ranges and whether the amygdala is modulated by task instructions and evaluative goals. We showed that participants adapted to the stimulus range of perceived trustworthiness when making approach decisions and that these decisions were further modulated by the social context. The right amygdala showed both linear response and quadratic response to trustworthiness level, as observed in prior studies. Notably, the amygdala's response to trustworthiness was not modulated by stimulus range or social context, a possible neural dynamic adaptation. Together, our data have revealed a robust behavioral adaptation to different trustworthiness ranges as well as a neural substrate underlying approach behavior based on perceived facial trustworthiness.

Geometrical and Graphical Solutions of Quadratic Equations.

ERIC Educational Resources Information Center

Hornsby, E. John, Jr.

1990-01-01

Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)

Finite element simulation of articular contact mechanics with quadratic tetrahedral elements.

PubMed

Maas, Steve A; Ellis, Benjamin J; Rawlins, David S; Weiss, Jeffrey A

2016-03-21

Although it is easier to generate finite element discretizations with tetrahedral elements, trilinear hexahedral (HEX8) elements are more often used in simulations of articular contact mechanics. This is due to numerical shortcomings of linear tetrahedral (TET4) elements, limited availability of quadratic tetrahedron elements in combination with effective contact algorithms, and the perceived increased computational expense of quadratic finite elements. In this study we implemented both ten-node (TET10) and fifteen-node (TET15) quadratic tetrahedral elements in FEBio (www.febio.org) and compared their accuracy, robustness in terms of convergence behavior and computational cost for simulations relevant to articular contact mechanics. Suitable volume integration and surface integration rules were determined by comparing the results of several benchmark contact problems. The results demonstrated that the surface integration rule used to evaluate the contact integrals for quadratic elements affected both convergence behavior and accuracy of predicted stresses. The computational expense and robustness of both quadratic tetrahedral formulations compared favorably to the HEX8 models. Of note, the TET15 element demonstrated superior convergence behavior and lower computational cost than both the TET10 and HEX8 elements for meshes with similar numbers of degrees of freedom in the contact problems that we examined. Finally, the excellent accuracy and relative efficiency of these quadratic tetrahedral elements was illustrated by comparing their predictions with those for a HEX8 mesh for simulation of articular contact in a fully validated model of the hip. These results demonstrate that TET10 and TET15 elements provide viable alternatives to HEX8 elements for simulation of articular contact mechanics. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

Linear quadratic optimization for positive LTI system

NASA Astrophysics Data System (ADS)

Muhafzan, Yenti, Syafrida Wirma; Zulakmal

2017-05-01

Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.

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.

Photon-phonon parametric oscillation induced by quadratic coupling in an optomechanical resonator

NASA Astrophysics Data System (ADS)

Zhang, Lin; Ji, Fengzhou; Zhang, Xu; Zhang, Weiping

2017-07-01

A direct photon-phonon parametric effect of quadratic coupling on the mean-field dynamics of an optomechanical resonator in the large-scale-movement regime is found and investigated. Under a weak pumping power, the mechanical resonator damps to a steady state with a nonlinear static response sensitively modified by the quadratic coupling. When the driving power increases beyond the static energy balance, the steady states lose their stabilities via Hopf bifurcations, and the resonator produces stable self-sustained oscillation (limit-circle behavior) of discrete energies with step-like amplitudes due to the parametric effect of quadratic coupling, which can be understood roughly by the power balance between gain and loss on the resonator. A further increase in the pumping power can induce a chaotic dynamic of the resonator via a typical routine of period-doubling bifurcation, but which can be stabilized by the parametric effect through an inversion-bifurcation process back to the limit-circle states. The bifurcation-to-inverse-bifurcation transitions are numerically verified by the maximal Lyapunov exponents of the dynamics, which indicate an efficient way of suppressing the chaotic behavior of the optomechanical resonator by quadratic coupling. Furthermore, the parametric effect of quadratic coupling on the dynamic transitions of an optomechanical resonator can be conveniently detected or traced by the output power spectrum of the cavity field.

Mapping the absolute magnetic field and evaluating the quadratic Zeeman-effect-induced systematic error in an atom interferometer gravimeter

NASA Astrophysics Data System (ADS)

Hu, Qing-Qing; Freier, Christian; Leykauf, Bastian; Schkolnik, Vladimir; Yang, Jun; Krutzik, Markus; Peters, Achim

2017-09-01

Precisely evaluating the systematic error induced by the quadratic Zeeman effect is important for developing atom interferometer gravimeters aiming at an accuracy in the μ Gal regime (1 μ Gal =10-8m /s2 ≈10-9g ). This paper reports on the experimental investigation of Raman spectroscopy-based magnetic field measurements and the evaluation of the systematic error in the gravimetric atom interferometer (GAIN) due to quadratic Zeeman effect. We discuss Raman duration and frequency step-size-dependent magnetic field measurement uncertainty, present vector light shift and tensor light shift induced magnetic field measurement offset, and map the absolute magnetic field inside the interferometer chamber of GAIN with an uncertainty of 0.72 nT and a spatial resolution of 12.8 mm. We evaluate the quadratic Zeeman-effect-induced gravity measurement error in GAIN as 2.04 μ Gal . The methods shown in this paper are important for precisely mapping the absolute magnetic field in vacuum and reducing the quadratic Zeeman-effect-induced systematic error in Raman transition-based precision measurements, such as atomic interferometer gravimeters.

Adaptive bi-level programming for optimal gene knockouts for targeted overproduction under phenotypic constraints

PubMed Central

2013-01-01

Background Optimization procedures to identify gene knockouts for targeted biochemical overproduction have been widely in use in modern metabolic engineering. Flux balance analysis (FBA) framework has provided conceptual simplifications for genome-scale dynamic analysis at steady states. Based on FBA, many current optimization methods for targeted bio-productions have been developed under the maximum cell growth assumption. The optimization problem to derive gene knockout strategies recently has been formulated as a bi-level programming problem in OptKnock for maximum targeted bio-productions with maximum growth rates. However, it has been shown that knockout mutants in fact reach the steady states with the minimization of metabolic adjustment (MOMA) from the corresponding wild-type strains instead of having maximal growth rates after genetic or metabolic intervention. In this work, we propose a new bi-level computational framework--MOMAKnock--which can derive robust knockout strategies under the MOMA flux distribution approximation. Methods In this new bi-level optimization framework, we aim to maximize the production of targeted chemicals by identifying candidate knockout genes or reactions under phenotypic constraints approximated by the MOMA assumption. Hence, the targeted chemical production is the primary objective of MOMAKnock while the MOMA assumption is formulated as the inner problem of constraining the knockout metabolic flux to be as close as possible to the steady-state phenotypes of wide-type strains. As this new inner problem becomes a quadratic programming problem, a novel adaptive piecewise linearization algorithm is developed in this paper to obtain the exact optimal solution to this new bi-level integer quadratic programming problem for MOMAKnock. Results Our new MOMAKnock model and the adaptive piecewise linearization solution algorithm are tested with a small E. coli core metabolic network and a large-scale iAF1260 E. coli metabolic network. The derived knockout strategies are compared with those from OptKnock. Our preliminary experimental results show that MOMAKnock can provide improved targeted productions with more robust knockout strategies. PMID:23368729

Adaptive bi-level programming for optimal gene knockouts for targeted overproduction under phenotypic constraints.

PubMed

Ren, Shaogang; Zeng, Bo; Qian, Xiaoning

2013-01-01

Optimization procedures to identify gene knockouts for targeted biochemical overproduction have been widely in use in modern metabolic engineering. Flux balance analysis (FBA) framework has provided conceptual simplifications for genome-scale dynamic analysis at steady states. Based on FBA, many current optimization methods for targeted bio-productions have been developed under the maximum cell growth assumption. The optimization problem to derive gene knockout strategies recently has been formulated as a bi-level programming problem in OptKnock for maximum targeted bio-productions with maximum growth rates. However, it has been shown that knockout mutants in fact reach the steady states with the minimization of metabolic adjustment (MOMA) from the corresponding wild-type strains instead of having maximal growth rates after genetic or metabolic intervention. In this work, we propose a new bi-level computational framework--MOMAKnock--which can derive robust knockout strategies under the MOMA flux distribution approximation. In this new bi-level optimization framework, we aim to maximize the production of targeted chemicals by identifying candidate knockout genes or reactions under phenotypic constraints approximated by the MOMA assumption. Hence, the targeted chemical production is the primary objective of MOMAKnock while the MOMA assumption is formulated as the inner problem of constraining the knockout metabolic flux to be as close as possible to the steady-state phenotypes of wide-type strains. As this new inner problem becomes a quadratic programming problem, a novel adaptive piecewise linearization algorithm is developed in this paper to obtain the exact optimal solution to this new bi-level integer quadratic programming problem for MOMAKnock. Our new MOMAKnock model and the adaptive piecewise linearization solution algorithm are tested with a small E. coli core metabolic network and a large-scale iAF1260 E. coli metabolic network. The derived knockout strategies are compared with those from OptKnock. Our preliminary experimental results show that MOMAKnock can provide improved targeted productions with more robust knockout strategies.

A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization

PubMed Central

Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang

2015-01-01

It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence—with at most a linear convergence rate—because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method. PMID:26381742

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.

A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.

PubMed

Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang

2015-01-01

It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.

Numerical optimization techniques for bound circulation distribution for minimum induced drag of Nonplanar wings: Computer program documentation

NASA Technical Reports Server (NTRS)

Kuhlman, J. M.; Ku, T. J.

1981-01-01

A two dimensional advanced panel far-field potential flow model of the undistorted, interacting wakes of multiple lifting surfaces was developed which allows the determination of the spanwise bound circulation distribution required for minimum induced drag. This model was implemented in a FORTRAN computer program, the use of which is documented in this report. The nonplanar wakes are broken up into variable sized, flat panels, as chosen by the user. The wake vortex sheet strength is assumed to vary linearly over each of these panels, resulting in a quadratic variation of bound circulation. Panels are infinite in the streamwise direction. The theory is briefly summarized herein; sample results are given for multiple, nonplanar, lifting surfaces, and the use of the computer program is detailed in the appendixes.

Preliminary demonstration of a robust controller design method

NASA Technical Reports Server (NTRS)

Anderson, L. R.

1980-01-01

Alternative computational procedures for obtaining a feedback control law which yields a control signal based on measurable quantitites are evaluated. The three methods evaluated are: (1) the standard linear quadratic regulator design model; (2) minimization of the norm of the feedback matrix, k via nonlinear programming subject to the constraint that the closed loop eigenvalues be in a specified domain in the complex plane; and (3) maximize the angles between the closed loop eigenvectors in combination with minimizing the norm of K also via the constrained nonlinear programming. The third or robust design method was chosen to yield a closed loop system whose eigenvalues are insensitive to small changes in the A and B matrices. The relationship between orthogonality of closed loop eigenvectors and the sensitivity of closed loop eigenvalues is described. Computer programs are described.

Constraints on geothermal reservoir volume change calculations from InSAR surface displacements and injection and production data

NASA Astrophysics Data System (ADS)

Kaven, J. Ole; Barbour, Andrew J.; Ali, Tabrez

2017-04-01

Continual production of geothermal energy at times leads to significant surface displacement that can be observed in high spatial resolution using InSAR imagery. The surface displacement can be analyzed to resolve volume change within the reservoir revealing the often-complicated patterns of reservoir deformation. Simple point source models of reservoir deformation in a homogeneous elastic or poro-elastic medium can be superimposed to provide spatially varying, kinematic representations of reservoir deformation. In many cases, injection and production data are known in insufficient detail; but, when these are available, the same Green functions can be used to constrain the reservoir deformation. Here we outline how the injection and production data can be used to constrain bounds on the solution by posing the inversion as a quadratic programming with inequality constraints and regularization rather than a conventional least squares solution with regularization. We apply this method to InSAR-derived surface displacements at the Coso and Salton Sea Geothermal Fields in California, using publically available injection and production data. At both geothermal fields the available surface deformation in conjunction with the injection and production data permit robust solutions for the spatially varying reservoir deformation. The reservoir deformation pattern resulting from the constrained quadratic programming solution is more heterogeneous when compared to a conventional least squares solution. The increased heterogeneity is consistent with the known structural controls on heat and fluid transport in each geothermal reservoir.

A neuro approach to solve fuzzy Riccati differential equations

NASA Astrophysics Data System (ADS)

Shahrir, Mohammad Shazri; Kumaresan, N.; Kamali, M. Z. M.; Ratnavelu, Kurunathan

2015-10-01

There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

NASA Technical Reports Server (NTRS)

Burns, John A.; Marrekchi, Hamadi

1993-01-01

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

A neuro approach to solve fuzzy Riccati differential equations

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

Shahrir, Mohammad Shazri, E-mail: mshazri@gmail.com; Telekom Malaysia, R&D TM Innovation Centre, LingkaranTeknokrat Timur, 63000 Cyberjaya, Selangor; Kumaresan, N., E-mail: drnk2008@gmail.com

There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.

Ethanol mediated As(III) adsorption onto Zn-loaded pinecone biochar: Experimental investigation, modeling, and optimization using hybrid artificial neural network-genetic algorithm approach.

PubMed

Zafar, Mohd; Van Vinh, N; Behera, Shishir Kumar; Park, Hung-Suck

2017-04-01

Organic matters (OMs) and their oxidization products often influence the fate and transport of heavy metals in the subsurface aqueous systems through interaction with the mineral surfaces. This study investigates the ethanol (EtOH)-mediated As(III) adsorption onto Zn-loaded pinecone (PC) biochar through batch experiments conducted under Box-Behnken design. The effect of EtOH on As(III) adsorption mechanism was quantitatively elucidated by fitting the experimental data using artificial neural network and quadratic modeling approaches. The quadratic model could describe the limiting nature of EtOH and pH on As(III) adsorption, whereas neural network revealed the stronger influence of EtOH (64.5%) followed by pH (20.75%) and As(III) concentration (14.75%) on the adsorption phenomena. Besides, the interaction among process variables indicated that EtOH enhances As(III) adsorption over a pH range of 2 to 7, possibly due to facilitation of ligand-metal(Zn) binding complexation mechanism. Eventually, hybrid response surface model-genetic algorithm (RSM-GA) approach predicted a better optimal solution than RSM, i.e., the adsorptive removal of As(III) (10.47μg/g) is facilitated at 30.22mg C/L of EtOH with initial As(III) concentration of 196.77μg/L at pH5.8. The implication of this investigation might help in understanding the application of biochar for removal of various As(III) species in the presence of OM. Copyright © 2016. Published by Elsevier B.V.

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

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.

Semiannual Report, April 1, 1989 through September 30, 1989 (Institute for Computer Applications in Science and Engineering)

DTIC Science & Technology

1990-02-01

noise. Tobias B. Orloff Work began on developing a high quality rendering algorithm based on the radiosity method. The algorithm is similar to...previous progressive radiosity algorithms except for the following improvements: 1. At each iteration vertex radiosities are computed using a modified scan...line approach, thus eliminating the quadratic cost associated with a ray tracing computation of vortex radiosities . 2. At each iteration the scene is

Mixed Nash equilibria in Eisert-Lewenstein-Wilkens (ELW) games

NASA Astrophysics Data System (ADS)

Bolonek-Lasoń, Katarzyna; Kosiński, Piotr

2017-01-01

The classification of all mixed Nash equilibria for the original ELW game is presented. It is based on the quaternionic form of the game proposed by Landsburg (Proc. Am. Math. Soc. 139 (2011), 4423; Rochester Working Paper No 524 (2006); Wiley Encyclopedia of Operations Research and Management Science (Wiley and Sons, New York, (2011)). This approach allows to reduce the problem of finding the Nash equilibria to relatively simple analysis of the extrema of certain quadratic forms.

Progress Towards a Cartesian Cut-Cell Method for Viscous Compressible Flow

NASA Technical Reports Server (NTRS)

Berger, Marsha; Aftosmis, Michael J.

2012-01-01

We present preliminary development of an approach for simulating high Reynolds number steady compressible flow in two space dimensions using a Cartesian cut-cell finite volume method. We consider both laminar and turbulent flow with both low and high cell Reynolds numbers near the wall. The approach solves the full Navier-Stokes equations in all cells, and uses a wall model to address the resolution requirements near boundaries and to mitigate mesh irregularities in cut cells. We present a quadratic wall model for low cell Reynolds numbers. At high cell Reynolds numbers, the quadratic is replaced with a newly developed analytic wall model stemming from solution of a limiting form of the Spalart-Allmaras turbulence model which features a forward evaluation for flow velocity and exactly matches characteristics of the SA turbulence model in the field. We develop multigrid operators which attain convergence rates similar to inviscid multigrid. Investigations focus on preliminary verification and validation of the method. Flows over flat plates and compressible airfoils show good agreement with both theoretical results and experimental data. Mesh convergence studies on sub- and transonic airfoil flows show convergence of surface pressures with wall spacings as large as approx.0.1% chord. With the current analytic wall model, one or two additional refinements near the wall are required to obtain mesh converged values of skin friction.

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.

Modelling Ocean Dissipation in Icy Satellites: A Comparison of Linear and Quadratic Friction

NASA Astrophysics Data System (ADS)

Hay, H.; Matsuyama, I.

2015-12-01

Although subsurface oceans are confirmed in Europa, Ganymede, Callisto, and strongly suspected in Enceladus and Titan, the exact mechanism required to heat and maintain these liquid reservoirs over Solar System history remains a mystery. Radiogenic heating can supply enough energy for large satellites whereas tidal dissipation provides the best explanation for the presence of oceans in small icy satellites. The amount of thermal energy actually contributed to the interiors of these icy satellites through oceanic tidal dissipation is largely unquantified. Presented here is a numerical model that builds upon previous work for quantifying tidally dissipated energy in the subsurface oceans of the icy satellites. Recent semi-analytical models (Tyler, 2008 and Matsuyama, 2014) have solved the Laplace Tidal Equations to estimate the time averaged energy flux over an orbital period in icy satellite oceans, neglecting the presence of a solid icy shell. These models are only able to consider linear Rayleigh friction. The numerical model presented here is compared to one of these semi-analytical models, finding excellent agreement between velocity and displacement solutions for all three terms to the tidal potential. Time averaged energy flux is within 2-6% of the analytical values. Quadratic (bottom) friction is then incorporated into the model, replacing linear friction. This approach is commonly applied to terrestrial ocean dissipation studies where dissipation scales nonlinearly with velocity. A suite of simulations are also run for the quadratic friction case which are then compared to and analysed against recent scaling laws developed by Chen and Nimmo (2013).

Breastfeeding and IQ Growth from Toddlerhood through Adolescence.

PubMed

von Stumm, Sophie; Plomin, Robert

2015-01-01

The benefits of breastfeeding for cognitive development continue to be hotly debated but are yet to be supported by conclusive empirical evidence. We used here a latent growth curve modeling approach to test the association of breastfeeding with IQ growth trajectories, which allows differentiating the variance in the IQ starting point in early life from variance in IQ gains that occur later in childhood through adolescence. Breastfeeding (yes/ no) was modeled as a direct predictor of three IQ latent growth factors (i.e. intercept, slope and quadratic term) and adjusted for the covariates socioeconomic status, mother's age at birth and gestational stage. Data came from the Twins Early Development Study (TEDS), a prospective cohort study of twins born between 1996 and 1994 in the United Kingdom, who were assessed 9 times on IQ between age 2 and 16 years (N = 11,582). Having been breastfed was associated with a small yet significant advantage in IQ at age 2 in girls (β = .07, CI 95% from 0.64 to 3.01; N = 3,035) but not in boys (β = .04, CI 95% from -0.14 to 2.41). Having been breastfeeding was neither associated with the other IQ growth factors in girls (slope: β = .02, CI 95% from -0.25 to 0.43; quadratic: β = .01, CI 95% from -0.02 to 0.02) nor in boys (slope: β = .02, CI 95% from -0.30 to 0.47; quadratic: β = -.01, CI 95% from -0.01 to 0.01). Breastfeeding has little benefit for early life intelligence and cognitive growth from toddlerhood through adolescence.

Applying the J-optimal channelized quadratic observer to SPECT myocardial perfusion defect detection

NASA Astrophysics Data System (ADS)

Kupinski, Meredith K.; Clarkson, Eric; Ghaly, Michael; Frey, Eric C.

2016-03-01

To evaluate performance on a perfusion defect detection task from 540 image pairs of myocardial perfusion SPECT image data we apply the J-optimal channelized quadratic observer (J-CQO). We compare AUC values of the linear Hotelling observer and J-CQO when the defect location is fixed and when it occurs in one of two locations. As expected, when the location is fixed a single channels maximizes AUC; location variability requires multiple channels to maximize the AUC. The AUC is estimated from both the projection data and reconstructed images. J-CQO is quadratic since it uses the first- and second- order statistics of the image data from both classes. The linear data reduction by the channels is described by an L x M channel matrix and in prior work we introduced an iterative gradient-based method for calculating the channel matrix. The dimensionality reduction from M measurements to L channels yields better estimates of these sample statistics from smaller sample sizes, and since the channelized covariance matrix is L x L instead of M x M, the matrix inverse is easier to compute. The novelty of our approach is the use of Jeffrey's divergence (J) as the figure of merit (FOM) for optimizing the channel matrix. We previously showed that the J-optimal channels are also the optimum channels for the AUC and the Bhattacharyya distance when the channel outputs are Gaussian distributed with equal means. This work evaluates the use of J as a surrogate FOM (SFOM) for AUC when these statistical conditions are not satisfied.

NLINEAR - NONLINEAR CURVE FITTING PROGRAM

NASA Technical Reports Server (NTRS)

Everhart, J. L.

1994-01-01

A common method for fitting data is a least-squares fit. In the least-squares method, a user-specified fitting function is utilized in such a way as to minimize the sum of the squares of distances between the data points and the fitting curve. The Nonlinear Curve Fitting Program, NLINEAR, is an interactive curve fitting routine based on a description of the quadratic expansion of the chi-squared statistic. NLINEAR utilizes a nonlinear optimization algorithm that calculates the best statistically weighted values of the parameters of the fitting function and the chi-square that is to be minimized. The inputs to the program are the mathematical form of the fitting function and the initial values of the parameters to be estimated. This approach provides the user with statistical information such as goodness of fit and estimated values of parameters that produce the highest degree of correlation between the experimental data and the mathematical model. In the mathematical formulation of the algorithm, the Taylor expansion of chi-square is first introduced, and justification for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations are derived, which are solved by matrix algebra. To achieve convergence, the algorithm requires meaningful initial estimates for the parameters of the fitting function. NLINEAR is written in Fortran 77 for execution on a CDC Cyber 750 under NOS 2.3. It has a central memory requirement of 5K 60 bit words. Optionally, graphical output of the fitting function can be plotted. Tektronix PLOT-10 routines are required for graphics. NLINEAR was developed in 1987.

Schur Stability Regions for Complex Quadratic Polynomials

ERIC Educational Resources Information Center

Cheng, Sui Sun; Huang, Shao Yuan

2010-01-01

Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)

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.

Identification of the key ecological factors influencing vegetation degradation in semi-arid agro-pastoral ecotone considering spatial scales

NASA Astrophysics Data System (ADS)

Peng, Yu; Wang, Qinghui; Fan, Min

2017-11-01

When assessing re-vegetation project performance and optimizing land management, identification of the key ecological factors inducing vegetation degradation has crucial implications. Rainfall, temperature, elevation, slope, aspect, land use type, and human disturbance are ecological factors affecting the status of vegetation index. However, at different spatial scales, the key factors may vary. Using Helin County, Inner-Mongolia, China as the study site and combining remote sensing image interpretation, field surveying, and mathematical methods, this study assesses key ecological factors affecting vegetation degradation under different spatial scales in a semi-arid agro-pastoral ecotone. It indicates that the key factors are different at various spatial scales. Elevation, rainfall, and temperature are identified as crucial for all spatial extents. Elevation, rainfall and human disturbance are key factors for small-scale quadrats of 300 m × 300 m and 600 m × 600 m, temperature and land use type are key factors for a medium-scale quadrat of 1 km × 1 km, and rainfall, temperature, and land use are key factors for large-scale quadrats of 2 km × 2 km and 5 km × 5 km. For this region, human disturbance is not the key factor for vegetation degradation across spatial scales. It is necessary to consider spatial scale for the identification of key factors determining vegetation characteristics. The eco-restoration programs at various spatial scales should identify key influencing factors according their scales so as to take effective measurements. The new understanding obtained in this study may help to explore the forces which driving vegetation degradation in the degraded regions in the world.

Fast parallel DNA-based algorithms for molecular computation: quadratic congruence and factoring integers.

PubMed

Chang, Weng-Long

2012-03-01

Assume that n is a positive integer. If there is an integer such that M (2) ≡ C (mod n), i.e., the congruence has a solution, then C is said to be a quadratic congruence (mod n). If the congruence does not have a solution, then C is said to be a quadratic noncongruence (mod n). The task of solving the problem is central to many important applications, the most obvious being cryptography. In this article, we describe a DNA-based algorithm for solving quadratic congruence and factoring integers. In additional to this novel contribution, we also show the utility of our encoding scheme, and of the algorithm's submodules. We demonstrate how a variety of arithmetic, shifted and comparative operations, namely bitwise and full addition, subtraction, left shifter and comparison perhaps are performed using strands of DNA.

A comparative analysis of predictive models of morbidity in intensive care unit after cardiac surgery - part II: an illustrative example.

PubMed

Cevenini, Gabriele; Barbini, Emanuela; Scolletta, Sabino; Biagioli, Bonizella; Giomarelli, Pierpaolo; Barbini, Paolo

2007-11-22

Popular predictive models for estimating morbidity probability after heart surgery are compared critically in a unitary framework. The study is divided into two parts. In the first part modelling techniques and intrinsic strengths and weaknesses of different approaches were discussed from a theoretical point of view. In this second part the performances of the same models are evaluated in an illustrative example. Eight models were developed: Bayes linear and quadratic models, k-nearest neighbour model, logistic regression model, Higgins and direct scoring systems and two feed-forward artificial neural networks with one and two layers. Cardiovascular, respiratory, neurological, renal, infectious and hemorrhagic complications were defined as morbidity. Training and testing sets each of 545 cases were used. The optimal set of predictors was chosen among a collection of 78 preoperative, intraoperative and postoperative variables by a stepwise procedure. Discrimination and calibration were evaluated by the area under the receiver operating characteristic curve and Hosmer-Lemeshow goodness-of-fit test, respectively. Scoring systems and the logistic regression model required the largest set of predictors, while Bayesian and k-nearest neighbour models were much more parsimonious. In testing data, all models showed acceptable discrimination capacities, however the Bayes quadratic model, using only three predictors, provided the best performance. All models showed satisfactory generalization ability: again the Bayes quadratic model exhibited the best generalization, while artificial neural networks and scoring systems gave the worst results. Finally, poor calibration was obtained when using scoring systems, k-nearest neighbour model and artificial neural networks, while Bayes (after recalibration) and logistic regression models gave adequate results. Although all the predictive models showed acceptable discrimination performance in the example considered, the Bayes and logistic regression models seemed better than the others, because they also had good generalization and calibration. The Bayes quadratic model seemed to be a convincing alternative to the much more usual Bayes linear and logistic regression models. It showed its capacity to identify a minimum core of predictors generally recognized as essential to pragmatically evaluate the risk of developing morbidity after heart surgery.

Application of quadratic optimization to supersonic inlet control.

NASA Technical Reports Server (NTRS)

Lehtinen, B.; Zeller, J. R.

1972-01-01

This paper describes the application of linear stochastic optimal control theory to the design of the control system for the air intake, the inlet, of a supersonic air-breathing propulsion system. The controls must maintain a stable inlet shock position in the presence of random airflow disturbances and prevent inlet unstart. Two different linear time invariant controllers are developed. One is designed to minimize a nonquadratic index, the expected frequency of inlet unstart, and the other is designed to minimize the mean square value of inlet shock motion. The quadratic equivalence principle is used to obtain a linear controller that minimizes the nonquadratic index. The two controllers are compared on the basis of unstart prevention, control effort requirements, and frequency response. It is concluded that while controls designed to minimize unstarts are desirable in that the index minimized is physically meaningful, computation time required is longer than for the minimum mean square shock position approach. The simpler minimum mean square shock position solution produced expected unstart frequency values which were not significantly larger than those of the nonquadratic solution.

Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1985-01-01

In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

The Fresnel Diffraction: A Story of Light and Darkness

NASA Astrophysics Data System (ADS)

Aime, C.; Aristidi, É.; Rabbia, Y.

2013-03-01

In a first part of the paper we give a simple introduction to the free space propagation of light at the level of a Master degree in Physics. The presentation promotes linear filtering aspects at the expense of fundamental physics. Following the Huygens-Fresnel approach, the propagation of the wave writes as a convolution relationship, the impulse response being a quadratic phase factor. We give the corresponding filter in the Fourier plane. As an illustration, we describe the propagation of wave with a spatial sinusoidal amplitude, introduce lenses as quadratic phase transmissions, discuss their Fourier transform properties and give some properties of Soret screens. Classical diffractions of rectangular diaphragms are also given here. In a second part of the paper, the presentation turns into the use of external occulters in coronagraphy for the detection of exoplanets and the study of the solar corona. Making use of Lommel series expansions, we obtain the analytical expression for the diffraction of a circular opaque screen, giving thereby the complete formalism for the Arago-Poisson spot. We include there shaped occulters. The paper ends up with a brief application to incoherent imaging in astronomy.

Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1987-01-01

In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

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

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.

Fabrication of three-dimensional polymer quadratic nonlinear grating structures by layer-by-layer direct laser writing technique

NASA Astrophysics Data System (ADS)

Bich Do, Danh; Lin, Jian Hung; Diep Lai, Ngoc; Kan, Hung-Chih; Hsu, Chia Chen

2011-08-01

We demonstrate the fabrication of a three-dimensional (3D) polymer quadratic nonlinear (χ(2)) grating structure. By performing layer-by-layer direct laser writing (DLW) and spin-coating approaches, desired photobleached grating patterns were embedded in the guest--host dispersed-red-1/poly(methylmethacrylate) (DR1/PMMA) active layers of an active-passive alternative multilayer structure through photobleaching of DR1 molecules. Polyvinyl-alcohol and SU8 thin films were deposited between DR1/PMMA layers serving as a passive layer to separate DR1/PMMA active layers. After applying the corona electric field poling to the multilayer structure, nonbleached DR1 molecules in the active layers formed polar distribution, and a 3D χ(2) grating structure was obtained. The χ(2) grating structures at different DR1/PMMA nonlinear layers were mapped by laser scanning second harmonic (SH) microscopy, and no cross talk was observed between SH images obtained from neighboring nonlinear layers. The layer-by-layer DLW technique is favorable to fabricating hierarchical 3D polymer nonlinear structures for optoelectronic applications with flexible structural design.

Fabrication of three-dimensional polymer quadratic nonlinear grating structures by layer-by-layer direct laser writing technique.

PubMed

Do, Danh Bich; Lin, Jian Hung; Lai, Ngoc Diep; Kan, Hung-Chih; Hsu, Chia Chen

2011-08-10

We demonstrate the fabrication of a three-dimensional (3D) polymer quadratic nonlinear (χ(2)) grating structure. By performing layer-by-layer direct laser writing (DLW) and spin-coating approaches, desired photobleached grating patterns were embedded in the guest-host dispersed-red-1/poly(methylmethacrylate) (DR1/PMMA) active layers of an active-passive alternative multilayer structure through photobleaching of DR1 molecules. Polyvinyl-alcohol and SU8 thin films were deposited between DR1/PMMA layers serving as a passive layer to separate DR1/PMMA active layers. After applying the corona electric field poling to the multilayer structure, nonbleached DR1 molecules in the active layers formed polar distribution, and a 3D χ(2) grating structure was obtained. The χ(2) grating structures at different DR1/PMMA nonlinear layers were mapped by laser scanning second harmonic (SH) microscopy, and no cross talk was observed between SH images obtained from neighboring nonlinear layers. The layer-by-layer DLW technique is favorable to fabricating hierarchical 3D polymer nonlinear structures for optoelectronic applications with flexible structural design.

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.

Flexible resources for quantum metrology

NASA Astrophysics Data System (ADS)

Friis, Nicolai; Orsucci, Davide; Skotiniotis, Michalis; Sekatski, Pavel; Dunjko, Vedran; Briegel, Hans J.; Dür, Wolfgang

2017-06-01

Quantum metrology offers a quadratic advantage over classical approaches to parameter estimation problems by utilising entanglement and nonclassicality. However, the hurdle of actually implementing the necessary quantum probe states and measurements, which vary drastically for different metrological scenarios, is usually not taken into account. We show that for a wide range of tasks in metrology, 2D cluster states (a particular family of states useful for measurement-based quantum computation) can serve as flexible resources that allow one to efficiently prepare any required state for sensing, and perform appropriate (entangled) measurements using only single qubit operations. Crucially, the overhead in the number of qubits is less than quadratic, thus preserving the quantum scaling advantage. This is ensured by using a compression to a logarithmically sized space that contains all relevant information for sensing. We specifically demonstrate how our method can be used to obtain optimal scaling for phase and frequency estimation in local estimation problems, as well as for the Bayesian equivalents with Gaussian priors of varying widths. Furthermore, we show that in the paradigmatic case of local phase estimation 1D cluster states are sufficient for optimal state preparation and measurement.

The Riemannian geometry is not sufficient for the geometrization of the Maxwell's equations

NASA Astrophysics Data System (ADS)

Kulyabov, Dmitry S.; Korolkova, Anna V.; Velieva, Tatyana R.

2018-04-01

The transformation optics uses geometrized Maxwell's constitutive equations to solve the inverse problem of optics, namely to solve the problem of finding the parameters of the medium along the paths of propagation of the electromagnetic field. For the geometrization of Maxwell's constitutive equations, the quadratic Riemannian geometry is usually used. This is due to the use of the approaches of the general relativity. However, there arises the question of the insufficiency of the Riemannian structure for describing the constitutive tensor of the Maxwell's equations. The authors analyze the structure of the constitutive tensor and correlate it with the structure of the metric tensor of Riemannian geometry. It is concluded that the use of the quadratic metric for the geometrization of Maxwell's equations is insufficient, since the number of components of the metric tensor is less than the number of components of the constitutive tensor. A possible solution to this problem may be a transition to Finslerian geometry, in particular, the use of the Berwald-Moor metric to establish the structural correspondence between the field tensors of the electromagnetic field.

Gaussian Mean Field Lattice Gas

NASA Astrophysics Data System (ADS)

Scoppola, Benedetto; Troiani, Alessio

2018-03-01

We study rigorously a lattice gas version of the Sherrington-Kirckpatrick spin glass model. In discrete optimization literature this problem is known as unconstrained binary quadratic programming and it belongs to the class NP-hard. We prove that the fluctuations of the ground state energy tend to vanish in the thermodynamic limit, and we give a lower bound of such ground state energy. Then we present a heuristic algorithm, based on a probabilistic cellular automaton, which seems to be able to find configurations with energy very close to the minimum, even for quite large instances.

Weyl gravity revisited

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

Álvarez, Enrique; González-Martín, Sergio, E-mail: enrique.alvarez@uam.es, E-mail: sergio.gonzalez.martin@csic.es

2017-02-01

The on shell equivalence of first order and second order formalisms for the Einstein-Hilbert action does not hold for those actions quadratic in curvature. It would seem that by considering the connection and the metric as independent dynamical variables, there are no quartic propagators for any dynamical variable. This suggests that it is possible to get both renormalizability and unitarity along these lines. We have studied a particular instance of those theories, namely Weyl gravity. In this first paper we show that it is not possible to implement this program with the Weyl connection alone.

Support Vector Hazards Machine: A Counting Process Framework for Learning Risk Scores for Censored Outcomes.

PubMed

Wang, Yuanjia; Chen, Tianle; Zeng, Donglin

2016-01-01

Learning risk scores to predict dichotomous or continuous outcomes using machine learning approaches has been studied extensively. However, how to learn risk scores for time-to-event outcomes subject to right censoring has received little attention until recently. Existing approaches rely on inverse probability weighting or rank-based regression, which may be inefficient. In this paper, we develop a new support vector hazards machine (SVHM) approach to predict censored outcomes. Our method is based on predicting the counting process associated with the time-to-event outcomes among subjects at risk via a series of support vector machines. Introducing counting processes to represent time-to-event data leads to a connection between support vector machines in supervised learning and hazards regression in standard survival analysis. To account for different at risk populations at observed event times, a time-varying offset is used in estimating risk scores. The resulting optimization is a convex quadratic programming problem that can easily incorporate non-linearity using kernel trick. We demonstrate an interesting link from the profiled empirical risk function of SVHM to the Cox partial likelihood. We then formally show that SVHM is optimal in discriminating covariate-specific hazard function from population average hazard function, and establish the consistency and learning rate of the predicted risk using the estimated risk scores. Simulation studies show improved prediction accuracy of the event times using SVHM compared to existing machine learning methods and standard conventional approaches. Finally, we analyze two real world biomedical study data where we use clinical markers and neuroimaging biomarkers to predict age-at-onset of a disease, and demonstrate superiority of SVHM in distinguishing high risk versus low risk subjects.

Contractions and deformations of quasiclassical Lie algebras preserving a nondegenerate quadratic Casimir operator

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

Campoamor-Stursberg, R., E-mail: rutwig@mat.ucm.e

2008-05-15

By means of contractions of Lie algebras, we obtain new classes of indecomposable quasiclassical Lie algebras that satisfy the Yang-Baxter equations in its reformulation in terms of triple products. These algebras are shown to arise naturally from noncompact real simple algebras with nonsimple complexification, where we impose that a nondegenerate quadratic Casimir operator is preserved by the limiting process. We further consider the converse problem and obtain sufficient conditions on integrable cocycles of quasiclassical Lie algebras in order to preserve nondegenerate quadratic Casimir operators by the associated linear deformations.

Nonadiabatic effects in ultracold molecules via anomalous linear and quadratic Zeeman shifts.

PubMed

McGuyer, B H; Osborn, C B; McDonald, M; Reinaudi, G; Skomorowski, W; Moszynski, R; Zelevinsky, T

2013-12-13

Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound ultracold 88Sr2 molecules near the intercombination-line asymptote. Nonadiabatic Coriolis coupling and the nature of long-range molecular potentials explain how this effect arises and scales roughly cubically with the size of the molecule. The linear shifts yield nonadiabatic mixing angles of the molecular states. The quadratic shifts are sensitive to nearby opposite f-parity states and exhibit fourth-order corrections, providing a stringent test of a state-of-the-art ab initio model.

Exact period-four solutions of a family of n-dimensional quadratic maps via harmonic balance and Gröbner bases.

PubMed

D'Amico, María Belén; Calandrini, Guillermo L

2015-11-01

Analytical solutions of the period-four orbits exhibited by a classical family of n-dimensional quadratic maps are presented. Exact expressions are obtained by applying harmonic balance and Gröbner bases to a single-input single-output representation of the system. A detailed study of a generalized scalar quadratic map and a well-known delayed logistic model is included for illustration. In the former example, conditions for the existence of bistability phenomenon are also introduced.

On orthogonality preserving quadratic stochastic operators

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

Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

2015-05-15

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

Exact period-four solutions of a family of n-dimensional quadratic maps via harmonic balance and Gröbner bases

NASA Astrophysics Data System (ADS)

D'Amico, María Belén; Calandrini, Guillermo L.

2015-11-01

Analytical solutions of the period-four orbits exhibited by a classical family of n-dimensional quadratic maps are presented. Exact expressions are obtained by applying harmonic balance and Gröbner bases to a single-input single-output representation of the system. A detailed study of a generalized scalar quadratic map and a well-known delayed logistic model is included for illustration. In the former example, conditions for the existence of bistability phenomenon are also introduced.

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.

Finite-dimensional linear approximations of solutions to general irregular nonlinear operator equations and equations with quadratic operators

NASA Astrophysics Data System (ADS)

Kokurin, M. Yu.

2010-11-01

A general scheme for improving approximate solutions to irregular nonlinear operator equations in Hilbert spaces is proposed and analyzed in the presence of errors. A modification of this scheme designed for equations with quadratic operators is also examined. The technique of universal linear approximations of irregular equations is combined with the projection onto finite-dimensional subspaces of a special form. It is shown that, for finite-dimensional quadratic problems, the proposed scheme provides information about the global geometric properties of the intersections of quadrics.

Reducing numerical diffusion for incompressible flow calculations

NASA Technical Reports Server (NTRS)

Claus, R. W.; Neely, G. M.; Syed, S. A.

1984-01-01

A number of approaches for improving the accuracy of incompressible, steady-state flow calculations are examined. Two improved differencing schemes, Quadratic Upstream Interpolation for Convective Kinematics (QUICK) and Skew-Upwind Differencing (SUD), are applied to the convective terms in the Navier-Stokes equations and compared with results obtained using hybrid differencing. In a number of test calculations, it is illustrated that no single scheme exhibits superior performance for all flow situations. However, both SUD and QUICK are shown to be generally more accurate than hybrid differencing.

Modular design attitude control system

NASA Technical Reports Server (NTRS)

Chichester, F. D.

1982-01-01

A hybrid multilevel linear quadratic regulator (ML-LQR) approach was developed and applied to the attitude control of models of the rotational dynamics of a prototype flexible spacecraft and of a typical space platform. Three axis rigid body flexible suspension models were developed for both the spacecraft and the space platform utilizing augmented body methods. Models of the spacecraft with hybrid ML-LQR attitude control and with LQR attitude control were simulated and their response with the two different types of control were compared.

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.

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.

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.

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

Calculus students' understanding of the vertex of the quadratic function in relation to the concept of derivative

NASA Astrophysics Data System (ADS)

Burns-Childers, Annie; Vidakovic, Draga

2018-07-01

The purpose of this study was to gain insight into 30, first year calculus students' understanding of the relationship between the concept of vertex of a quadratic function and the concept of the derivative. APOS (action-process-object-schema) theory was applied as a guiding framework of analysis on student written work, think-aloud and follow up group interviews. Students' personal meanings of the vertex, including misconceptions, were explored, along with students' understanding to solve problems pertaining to the derivative of a quadratic function. Results give evidence of students' weak schema of the vertex, lack of connection between different problem types and the importance of linguistics in relation to levels of APOS theory. A preliminary genetic decomposition was developed based on the results. Future research is suggested as a continuation to improve student understanding of the relationship between the vertex of quadratic functions and the derivative.

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

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

An Inviscid Decoupled Method for the Roe FDS Scheme in the Reacting Gas Path of FUN3D

NASA Technical Reports Server (NTRS)

Thompson, Kyle B.; Gnoffo, Peter A.

2016-01-01

An approach is described to decouple the species continuity equations from the mixture continuity, momentum, and total energy equations for the Roe flux difference splitting scheme. This decoupling simplifies the implicit system, so that the flow solver can be made significantly more efficient, with very little penalty on overall scheme robustness. Most importantly, the computational cost of the point implicit relaxation is shown to scale linearly with the number of species for the decoupled system, whereas the fully coupled approach scales quadratically. Also, the decoupled method significantly reduces the cost in wall time and memory in comparison to the fully coupled approach. This work lays the foundation for development of an efficient adjoint solution procedure for high speed reacting flow.

A Gaussian theory for fluctuations in simple liquids.

PubMed

Krüger, Matthias; Dean, David S

2017-04-07

Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point correlation functions (such as the intermediate scattering function) are derived. We show that this correlation function is exact at short times, for any interaction and, in particular, for arbitrary external potentials so that it applies to confined systems. Furthermore, we discuss the relation of this approach to previous ones, such as dynamical density functional theory as well as the formally exact treatment. This approach, inspired by the well known Landau-Ginzburg Hamiltonians, and the corresponding "Model B" equation of motion, may be seen as its microscopic version, containing information about the details on the particle level.

A Gaussian theory for fluctuations in simple liquids

NASA Astrophysics Data System (ADS)

Krüger, Matthias; Dean, David S.

2017-04-01

Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point correlation functions (such as the intermediate scattering function) are derived. We show that this correlation function is exact at short times, for any interaction and, in particular, for arbitrary external potentials so that it applies to confined systems. Furthermore, we discuss the relation of this approach to previous ones, such as dynamical density functional theory as well as the formally exact treatment. This approach, inspired by the well known Landau-Ginzburg Hamiltonians, and the corresponding "Model B" equation of motion, may be seen as its microscopic version, containing information about the details on the particle level.

Integrated structure/control law design by multilevel optimization

NASA Technical Reports Server (NTRS)

Gilbert, Michael G.; Schmidt, David K.

1989-01-01

A new approach to integrated structure/control law design based on multilevel optimization is presented. This new approach is applicable to aircraft and spacecraft and allows for the independent design of the structure and control law. Integration of the designs is achieved through use of an upper level coordination problem formulation within the multilevel optimization framework. The method requires the use of structure and control law design sensitivity information. A general multilevel structure/control law design problem formulation is given, and the use of Linear Quadratic Gaussian (LQG) control law design and design sensitivity methods within the formulation is illustrated. Results of three simple integrated structure/control law design examples are presented. These results show the capability of structure and control law design tradeoffs to improve controlled system performance within the multilevel approach.

Motion control of planar parallel robot using the fuzzy descriptor system approach.

PubMed

Vermeiren, Laurent; Dequidt, Antoine; Afroun, Mohamed; Guerra, Thierry-Marie

2012-09-01

This work presents the control of a two-degree of freedom parallel robot manipulator. A quasi-LPV approach, through the so-called TS fuzzy model and LMI constraints problems is used. Moreover, in this context a way to derive interesting control laws is to keep the descriptor form of the mechanical system. Therefore, new LMI problems have to be defined that helps to reduce the conservatism of the usual results. Some relaxations are also proposed to leave the pure quadratic stability/stabilization framework. A comparison study between the classical control strategies from robotics and the control design using TS fuzzy descriptor models is carried out to show the interest of the proposed approach. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

GLOBAL SOLUTIONS TO FOLDED CONCAVE PENALIZED NONCONVEX LEARNING

PubMed Central

Liu, Hongcheng; Yao, Tao; Li, Runze

2015-01-01

This paper is concerned with solving nonconvex learning problems with folded concave penalty. Despite that their global solutions entail desirable statistical properties, there lack optimization techniques that guarantee global optimality in a general setting. In this paper, we show that a class of nonconvex learning problems are equivalent to general quadratic programs. This equivalence facilitates us in developing mixed integer linear programming reformulations, which admit finite algorithms that find a provably global optimal solution. We refer to this reformulation-based technique as the mixed integer programming-based global optimization (MIPGO). To our knowledge, this is the first global optimization scheme with a theoretical guarantee for folded concave penalized nonconvex learning with the SCAD penalty (Fan and Li, 2001) and the MCP penalty (Zhang, 2010). Numerical results indicate a significant outperformance of MIPGO over the state-of-the-art solution scheme, local linear approximation, and other alternative solution techniques in literature in terms of solution quality. PMID:27141126

User's manual: Subsonic/supersonic advanced panel pilot code

NASA Technical Reports Server (NTRS)

Moran, J.; Tinoco, E. N.; Johnson, F. T.

1978-01-01

Sufficient instructions for running the subsonic/supersonic advanced panel pilot code were developed. This software was developed as a vehicle for numerical experimentation and it should not be construed to represent a finished production program. The pilot code is based on a higher order panel method using linearly varying source and quadratically varying doublet distributions for computing both linearized supersonic and subsonic flow over arbitrary wings and bodies. This user's manual contains complete input and output descriptions. A brief description of the method is given as well as practical instructions for proper configurations modeling. Computed results are also included to demonstrate some of the capabilities of the pilot code. The computer program is written in FORTRAN IV for the SCOPE 3.4.4 operations system of the Ames CDC 7600 computer. The program uses overlay structure and thirteen disk files, and it requires approximately 132000 (Octal) central memory words.

A new performance index for the repetitive motion of mobile manipulators.

PubMed

Xiao, Lin; Zhang, Yunong

2014-02-01

A mobile manipulator is a robotic device composed of a mobile platform and a stationary manipulator fixed to the platform. To achieve the repetitive motion control of mobile manipulators, the mobile platform and the manipulator have to realize the repetitive motion simultaneously. To do so, a novel quadratic performance index is, for the first time, designed and presented in this paper, of which the effectiveness is analyzed by following a neural dynamics method. Then, a repetitive motion scheme is proposed by combining the criterion, physical constraints, and integrated kinematical equations of mobile manipulators, which is further reformulated as a quadratic programming (QP) subject to equality and bound constraints. In addition, two important Bridge theorems are established to prove that such a QP can be converted equivalently into a linear variational inequality, and then equivalently into a piecewise-linear projection equation (PLPE). A real-time numerical algorithm based on PLPE is thus developed and applied for the online solution of the resultant QP. Two tracking-path tasks demonstrate the effectiveness and accuracy of the repetitive motion scheme. In addition, comparisons between the nonrepetitive and repetitive motion further validate the superiority and novelty of the proposed scheme.

Optimal Fermentation Conditions of Hyaluronidase Inhibition Activity on Asparagus cochinchinensis Merrill by Weissella cibaria.

PubMed

Kim, Minji; Kim, Won-Baek; Koo, Kyoung Yoon; Kim, Bo Ram; Kim, Doohyun; Lee, Seoyoun; Son, Hong Joo; Hwang, Dae Youn; Kim, Dong Seob; Lee, Chung Yeoul; Lee, Heeseob

2017-04-28

This study was conducted to evaluate the hyaluronidase (HAase) inhibition activity of Asparagus cochinchinesis (AC) extracts following fermentation by Weissella cibaria through response surface methodology. To optimize the HAase inhibition activity, a central composite design was introduced based on four variables: the concentration of AC extract ( X 1 : 1-5%), amount of starter culture ( X 2 : 1-5%), pH ( X 3 : 4-8), and fermentation time ( X 4 : 0-10 days). The experimental data were fitted to quadratic regression equations, the accuracy of the equations was analyzed by ANOVA, and the regression coefficients for the surface quadratic model of HAase inhibition activity in the fermented AC extract were estimated by the F test and the corresponding p values. The HAase inhibition activity indicated that fermentation time was most significant among the parameters within the conditions tested. To validate the model, two different conditions among those generated by the Design Expert program were selected. Under both conditions, predicted and experimental data agreed well. Moreover, the content of protodioscin (a well-known compound related to anti-inflammation activity) was elevated after fermentation of the AC extract at the optimized fermentation condition.

Theory of Band Warping and its Effects on Thermoelectronic Transport Properties

NASA Astrophysics Data System (ADS)

Mecholsky, Nicholas; Resca, Lorenzo; Pegg, Ian; Fornari, Marco

2015-03-01

Transport properties of materials depend upon features of band structures near extrema in the BZ. Such features are generally described in terms of quadratic expansions and effective masses. Such expansions, however, are permissible only under strict conditions that are sometimes violated by materials. Suggestive terms such as ``band warping'' have been used to refer to such situations and ad hoc methods have been developed to treat them. We develop a generally applicable theory, based on radial expansions, and a corresponding definition of angular effective mass which also accounts for effects of band non-parabolicity and anisotropy. Further, we develop precise procedures to evaluate band warping quantitatively and as an example we analyze the warping features of valence bands in silicon using first-principles calculations and we compare those with semi-empirical models. We use our theory to generalize derivations of transport coefficients for cases of either single or multiple electronic bands, with either quadratically expansible or warped energy surfaces. We introduce the transport-equivalent ellipsoid and illustrate the drastic effects that band warping can induce on thermoelectric properties using multi-band models. Vitreous State Laboratory and Samsung's GRO program.

A CAD Approach to Developing Mass Distribution and Composition Models for Spaceflight Radiation Risk Analyses

NASA Astrophysics Data System (ADS)

Zapp, E.; Shelfer, T.; Semones, E.; Johnson, A.; Weyland, M.; Golightly, M.; Smith, G.; Dardano, C.

For roughly the past three decades, combinatorial geometries have been the predominant mode for the development of mass distribution models associated with the estimation of radiological risk for manned space flight. Examples of these are the MEVDP (Modified Elemental Volume Dose Program) vehicle representation of Liley and Hamilton, and the quadratic functional representation of the CAM/CAF (Computerized Anatomical Male/Female) human body models as modified by Billings and Yucker. These geometries, have the advantageous characteristics of being simple for a familiarized user to maintain, and because of the relative lack of any operating system or run-time library dependence, they are also easy to transfer from one computing platform to another. Unfortunately they are also limited in the amount of modeling detail possible, owing to the abstract geometric representation. In addition, combinatorial representations are also known to be error-prone in practice, since there is no convenient method for error identification (i.e. overlap, etc.), and extensive calculation and/or manual comparison may is often necessary to demonstrate that the geometry is adequately represented. We present an alternate approach linking materials -specific, CAD-based mass models directly to geometric analysis tools requiring no approximation with respect to materials , nor any meshing (i.e. tessellation) of the representative geometry. A new approach to ray tracing is presented which makes use of the fundamentals of the CAD representation to perform geometric analysis directly on the NURBS (Non-Uniform Rational BSpline) surfaces themselves. In this way we achieve a framework for- the rapid, precise development and analysis of materials-specific mass distribution models.

Modeling of polychromatic attenuation using computed tomography reconstructed images

NASA Technical Reports Server (NTRS)

Yan, C. H.; Whalen, R. T.; Beaupre, G. S.; Yen, S. Y.; Napel, S.

1999-01-01

This paper presents a procedure for estimating an accurate model of the CT imaging process including spectral effects. As raw projection data are typically unavailable to the end-user, we adopt a post-processing approach that utilizes the reconstructed images themselves. This approach includes errors from x-ray scatter and the nonidealities of the built-in soft tissue correction into the beam characteristics, which is crucial to beam hardening correction algorithms that are designed to be applied directly to CT reconstructed images. We formulate this approach as a quadratic programming problem and propose two different methods, dimension reduction and regularization, to overcome ill conditioning in the model. For the regularization method we use a statistical procedure, Cross Validation, to select the regularization parameter. We have constructed step-wedge phantoms to estimate the effective beam spectrum of a GE CT-I scanner. Using the derived spectrum, we computed the attenuation ratios for the wedge phantoms and found that the worst case modeling error is less than 3% of the corresponding attenuation ratio. We have also built two test (hybrid) phantoms to evaluate the effective spectrum. Based on these test phantoms, we have shown that the effective beam spectrum provides an accurate model for the CT imaging process. Last, we used a simple beam hardening correction experiment to demonstrate the effectiveness of the estimated beam profile for removing beam hardening artifacts. We hope that this estimation procedure will encourage more independent research on beam hardening corrections and will lead to the development of application-specific beam hardening correction algorithms.