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.

Comparison of optimization algorithms in intensity-modulated radiation therapy planning

NASA Astrophysics Data System (ADS)

Kendrick, Rachel

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

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

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

CAD of control systems: Application of nonlinear programming to a linear quadratic formulation

NASA Technical Reports Server (NTRS)

Fleming, P.

1983-01-01

The familiar suboptimal regulator design approach is recast as a constrained optimization problem and incorporated in a Computer Aided Design (CAD) package where both design objective and constraints are quadratic cost functions. This formulation permits the separate consideration of, for example, model following errors, sensitivity measures and control energy as objectives to be minimized or limits to be observed. Efficient techniques for computing the interrelated cost functions and their gradients are utilized in conjunction with a nonlinear programming algorithm. The effectiveness of the approach and the degree of insight into the problem which it affords is illustrated in a helicopter regulation design example.

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

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.

Determining the Optimal Solution for Quadratically Constrained Quadratic Programming (QCQP) on Energy-Saving Generation Dispatch Problem

NASA Astrophysics Data System (ADS)

Lesmana, E.; Chaerani, D.; Khansa, H. N.

2018-03-01

Energy-Saving Generation Dispatch (ESGD) is a scheme made by Chinese Government in attempt to minimize CO2 emission produced by power plant. This scheme is made related to global warming which is primarily caused by too much CO2 in earth’s atmosphere, and while the need of electricity is something absolute, the power plants producing it are mostly thermal-power plant which produced many CO2. Many approach to fulfill this scheme has been made, one of them came through Minimum Cost Flow in which resulted in a Quadratically Constrained Quadratic Programming (QCQP) form. In this paper, ESGD problem with Minimum Cost Flow in QCQP form will be solved using Lagrange’s Multiplier Method

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.

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.

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

Identify Secretory Protein of Malaria Parasite with Modified Quadratic Discriminant Algorithm and Amino Acid Composition.

PubMed

Feng, Yong-E

2016-06-01

Malaria parasite secretes various proteins in infected red blood cell for its growth and survival. Thus identification of these secretory proteins is important for developing vaccine or drug against malaria. In this study, the modified method of quadratic discriminant analysis is presented for predicting the secretory proteins. Firstly, 20 amino acids are divided into five types according to the physical and chemical characteristics of amino acids. Then, we used five types of amino acids compositions as inputs of the modified quadratic discriminant algorithm. Finally, the best prediction performance is obtained by using 20 amino acid compositions, the sensitivity of 96 %, the specificity of 92 % with 0.88 of Mathew's correlation coefficient in fivefold cross-validation test. The results are also compared with those of existing prediction methods. The compared results shown our method are prominent in the prediction of secretory proteins.

A Comparative Analysis of DBSCAN, K-Means, and Quadratic Variation Algorithms for Automatic Identification of Swallows from Swallowing Accelerometry Signals

PubMed Central

Dudik, Joshua M.; Kurosu, Atsuko; Coyle, James L

2015-01-01

Background Cervical auscultation with high resolution sensors is currently under consideration as a method of automatically screening for specific swallowing abnormalities. To be clinically useful without human involvement, any devices based on cervical auscultation should be able to detect specified swallowing events in an automatic manner. Methods In this paper, we comparatively analyze the density-based spatial clustering of applications with noise algorithm (DBSCAN), a k-means based algorithm, and an algorithm based on quadratic variation as methods of differentiating periods of swallowing activity from periods of time without swallows. These algorithms utilized swallowing vibration data exclusively and compared the results to a gold standard measure of swallowing duration. Data was collected from 23 subjects that were actively suffering from swallowing difficulties. Results Comparing the performance of the DBSCAN algorithm with a proven segmentation algorithm that utilizes k-means clustering demonstrated that the DBSCAN algorithm had a higher sensitivity and correctly segmented more swallows. Comparing its performance with a threshold-based algorithm that utilized the quadratic variation of the signal showed that the DBSCAN algorithm offered no direct increase in performance. However, it offered several other benefits including a faster run time and more consistent performance between patients. All algorithms showed noticeable differen-tiation from the endpoints provided by a videofluoroscopy examination as well as reduced sensitivity. Conclusions In summary, we showed that the DBSCAN algorithm is a viable method for detecting the occurrence of a swallowing event using cervical auscultation signals, but significant work must be done to improve its performance before it can be implemented in an unsupervised manner. PMID:25658505

A Biogeography-Based Optimization Algorithm Hybridized with Tabu Search for the Quadratic Assignment Problem

PubMed Central

Lim, Wee Loon; Wibowo, Antoni; Desa, Mohammad Ishak; Haron, Habibollah

2016-01-01

The quadratic assignment problem (QAP) is an NP-hard combinatorial optimization problem with a wide variety of applications. Biogeography-based optimization (BBO), a relatively new optimization technique based on the biogeography concept, uses the idea of migration strategy of species to derive algorithm for solving optimization problems. It has been shown that BBO provides performance on a par with other optimization methods. A classical BBO algorithm employs the mutation operator as its diversification strategy. However, this process will often ruin the quality of solutions in QAP. In this paper, we propose a hybrid technique to overcome the weakness of classical BBO algorithm to solve QAP, by replacing the mutation operator with a tabu search procedure. Our experiments using the benchmark instances from QAPLIB show that the proposed hybrid method is able to find good solutions for them within reasonable computational times. Out of 61 benchmark instances tested, the proposed method is able to obtain the best known solutions for 57 of them. PMID:26819585

A Biogeography-Based Optimization Algorithm Hybridized with Tabu Search for the Quadratic Assignment Problem.

PubMed

Lim, Wee Loon; Wibowo, Antoni; Desa, Mohammad Ishak; Haron, Habibollah

2016-01-01

The quadratic assignment problem (QAP) is an NP-hard combinatorial optimization problem with a wide variety of applications. Biogeography-based optimization (BBO), a relatively new optimization technique based on the biogeography concept, uses the idea of migration strategy of species to derive algorithm for solving optimization problems. It has been shown that BBO provides performance on a par with other optimization methods. A classical BBO algorithm employs the mutation operator as its diversification strategy. However, this process will often ruin the quality of solutions in QAP. In this paper, we propose a hybrid technique to overcome the weakness of classical BBO algorithm to solve QAP, by replacing the mutation operator with a tabu search procedure. Our experiments using the benchmark instances from QAPLIB show that the proposed hybrid method is able to find good solutions for them within reasonable computational times. Out of 61 benchmark instances tested, the proposed method is able to obtain the best known solutions for 57 of them.

A comparative analysis of DBSCAN, K-means, and quadratic variation algorithms for automatic identification of swallows from swallowing accelerometry signals.

PubMed

Dudik, Joshua M; Kurosu, Atsuko; Coyle, James L; Sejdić, Ervin

2015-04-01

Cervical auscultation with high resolution sensors is currently under consideration as a method of automatically screening for specific swallowing abnormalities. To be clinically useful without human involvement, any devices based on cervical auscultation should be able to detect specified swallowing events in an automatic manner. In this paper, we comparatively analyze the density-based spatial clustering of applications with noise algorithm (DBSCAN), a k-means based algorithm, and an algorithm based on quadratic variation as methods of differentiating periods of swallowing activity from periods of time without swallows. These algorithms utilized swallowing vibration data exclusively and compared the results to a gold standard measure of swallowing duration. Data was collected from 23 subjects that were actively suffering from swallowing difficulties. Comparing the performance of the DBSCAN algorithm with a proven segmentation algorithm that utilizes k-means clustering demonstrated that the DBSCAN algorithm had a higher sensitivity and correctly segmented more swallows. Comparing its performance with a threshold-based algorithm that utilized the quadratic variation of the signal showed that the DBSCAN algorithm offered no direct increase in performance. However, it offered several other benefits including a faster run time and more consistent performance between patients. All algorithms showed noticeable differentiation from the endpoints provided by a videofluoroscopy examination as well as reduced sensitivity. In summary, we showed that the DBSCAN algorithm is a viable method for detecting the occurrence of a swallowing event using cervical auscultation signals, but significant work must be done to improve its performance before it can be implemented in an unsupervised manner. Copyright © 2015 Elsevier Ltd. All rights reserved.

An efficient inverse radiotherapy planning method for VMAT using quadratic programming optimization.

PubMed

Hoegele, W; Loeschel, R; Merkle, N; Zygmanski, P

2012-01-01

The purpose of this study is to investigate the feasibility of an inverse planning optimization approach for the Volumetric Modulated Arc Therapy (VMAT) based on quadratic programming and the projection method. The performance of this method is evaluated against a reference commercial planning system (eclipse(TM) for rapidarc(TM)) for clinically relevant cases. The inverse problem is posed in terms of a linear combination of basis functions representing arclet dose contributions and their respective linear coefficients as degrees of freedom. MLC motion is decomposed into basic motion patterns in an intuitive manner leading to a system of equations with a relatively small number of equations and unknowns. These equations are solved using quadratic programming under certain limiting physical conditions for the solution, such as the avoidance of negative dose during optimization and Monitor Unit reduction. The modeling by the projection method assures a unique treatment plan with beneficial properties, such as the explicit relation between organ weightings and the final dose distribution. Clinical cases studied include prostate and spine treatments. The optimized plans are evaluated by comparing isodose lines, DVH profiles for target and normal organs, and Monitor Units to those obtained by the clinical treatment planning system eclipse(TM). The resulting dose distributions for a prostate (with rectum and bladder as organs at risk), and for a spine case (with kidneys, liver, lung and heart as organs at risk) are presented. Overall, the results indicate that similar plan qualities for quadratic programming (QP) and rapidarc(TM) could be achieved at significantly more efficient computational and planning effort using QP. Additionally, results for the quasimodo phantom [Bohsung et al., "IMRT treatment planning: A comparative inter-system and inter-centre planning exercise of the estro quasimodo group," Radiother. Oncol. 76(3), 354-361 (2005)] are presented as an example

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.

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

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

Liu, X; Belcher, AH; Wiersma, R

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

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.

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.

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…

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.

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.

A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.

1991-01-01

A hybrid method for computing the feedback gains in linear quadratic regulator problem is proposed. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite-dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed, and numerical evidence of the efficacy of these ideas is presented.

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…

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)

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.

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.

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.

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.

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.

A class of stochastic optimization problems with one quadratic & several linear objective functions and extended portfolio selection model

NASA Astrophysics Data System (ADS)

Xu, Jiuping; Li, Jun

2002-09-01

In this paper a class of stochastic multiple-objective programming problems with one quadratic, several linear objective functions and linear constraints has been introduced. The former model is transformed into a deterministic multiple-objective nonlinear programming model by means of the introduction of random variables' expectation. The reference direction approach is used to deal with linear objectives and results in a linear parametric optimization formula with a single linear objective function. This objective function is combined with the quadratic function using the weighted sums. The quadratic problem is transformed into a linear (parametric) complementary problem, the basic formula for the proposed approach. The sufficient and necessary conditions for (properly, weakly) efficient solutions and some construction characteristics of (weakly) efficient solution sets are obtained. An interactive algorithm is proposed based on reference direction and weighted sums. Varying the parameter vector on the right-hand side of the model, the DM can freely search the efficient frontier with the model. An extended portfolio selection model is formed when liquidity is considered as another objective to be optimized besides expectation and risk. The interactive approach is illustrated with a practical example.

Smoothing optimization of supporting quadratic surfaces with Zernike polynomials

NASA Astrophysics Data System (ADS)

Zhang, Hang; Lu, Jiandong; Liu, Rui; Ma, Peifu

2018-03-01

A new optimization method to get a smooth freeform optical surface from an initial surface generated by the supporting quadratic method (SQM) is proposed. To smooth the initial surface, a 9-vertex system from the neighbor quadratic surface and the Zernike polynomials are employed to establish a linear equation system. A local optimized surface to the 9-vertex system can be build by solving the equations. Finally, a continuous smooth optimization surface is constructed by stitching the above algorithm on the whole initial surface. The spot corresponding to the optimized surface is no longer discrete pixels but a continuous distribution.

The Type-2 Fuzzy Logic Controller-Based Maximum Power Point Tracking Algorithm and the Quadratic Boost Converter for Pv System

NASA Astrophysics Data System (ADS)

Altin, Necmi

2018-05-01

An interval type-2 fuzzy logic controller-based maximum power point tracking algorithm and direct current-direct current (DC-DC) converter topology are proposed for photovoltaic (PV) systems. The proposed maximum power point tracking algorithm is designed based on an interval type-2 fuzzy logic controller that has an ability to handle uncertainties. The change in PV power and the change in PV voltage are determined as inputs of the proposed controller, while the change in duty cycle is determined as the output of the controller. Seven interval type-2 fuzzy sets are determined and used as membership functions for input and output variables. The quadratic boost converter provides high voltage step-up ability without any reduction in performance and stability of the system. The performance of the proposed system is validated through MATLAB/Simulink simulations. It is seen that the proposed system provides high maximum power point tracking speed and accuracy even for fast changing atmospheric conditions and high voltage step-up requirements.

Design a software real-time operation platform for wave piercing catamarans motion control using linear quadratic regulator based genetic algorithm.

PubMed

Liang, Lihua; Yuan, Jia; Zhang, Songtao; Zhao, Peng

2018-01-01

This work presents optimal linear quadratic regulator (LQR) based on genetic algorithm (GA) to solve the two degrees of freedom (2 DoF) motion control problem in head seas for wave piercing catamarans (WPC). The proposed LQR based GA control strategy is to select optimal weighting matrices (Q and R). The seakeeping performance of WPC based on proposed algorithm is challenged because of multi-input multi-output (MIMO) system of uncertain coefficient problems. Besides the kinematical constraint problems of WPC, the external conditions must be considered, like the sea disturbance and the actuators (a T-foil and two flaps) control. Moreover, this paper describes the MATLAB and LabVIEW software plats to simulate the reduction effects of WPC. Finally, the real-time (RT) NI CompactRIO embedded controller is selected to test the effectiveness of the actuators based on proposed techniques. In conclusion, simulation and experimental results prove the correctness of the proposed algorithm. The percentage of heave and pitch reductions are more than 18% in different high speeds and bad sea conditions. And the results also verify the feasibility of NI CompactRIO embedded controller.

Design a software real-time operation platform for wave piercing catamarans motion control using linear quadratic regulator based genetic algorithm

PubMed Central

Liang, Lihua; Zhang, Songtao; Zhao, Peng

2018-01-01

This work presents optimal linear quadratic regulator (LQR) based on genetic algorithm (GA) to solve the two degrees of freedom (2 DoF) motion control problem in head seas for wave piercing catamarans (WPC). The proposed LQR based GA control strategy is to select optimal weighting matrices (Q and R). The seakeeping performance of WPC based on proposed algorithm is challenged because of multi-input multi-output (MIMO) system of uncertain coefficient problems. Besides the kinematical constraint problems of WPC, the external conditions must be considered, like the sea disturbance and the actuators (a T-foil and two flaps) control. Moreover, this paper describes the MATLAB and LabVIEW software plats to simulate the reduction effects of WPC. Finally, the real-time (RT) NI CompactRIO embedded controller is selected to test the effectiveness of the actuators based on proposed techniques. In conclusion, simulation and experimental results prove the correctness of the proposed algorithm. The percentage of heave and pitch reductions are more than 18% in different high speeds and bad sea conditions. And the results also verify the feasibility of NI CompactRIO embedded controller. PMID:29709008

An analysis of spectral envelope-reduction via quadratic assignment problems

NASA Technical Reports Server (NTRS)

George, Alan; Pothen, Alex

1994-01-01

A new spectral algorithm for reordering a sparse symmetric matrix to reduce its envelope size was described. The ordering is computed by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. In this paper, we provide an analysis of the spectral envelope reduction algorithm. We described related 1- and 2-sum problems; the former is related to the envelope size, while the latter is related to an upper bound on the work involved in an envelope Cholesky factorization scheme. We formulate the latter two problems as quadratic assignment problems, and then study the 2-sum problem in more detail. We obtain lower bounds on the 2-sum by considering a projected quadratic assignment problem, and then show that finding a permutation matrix closest to an orthogonal matrix attaining one of the lower bounds justifies the spectral envelope reduction algorithm. The lower bound on the 2-sum is seen to be tight for reasonably 'uniform' finite element meshes. We also obtain asymptotically tight lower bounds for the envelope size for certain classes of meshes.

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.

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…

Weight Vector Fluctuations in Adaptive Antenna Arrays Tuned Using the Least-Mean-Square Error Algorithm with Quadratic Constraint

NASA Astrophysics Data System (ADS)

Zimina, S. V.

2015-06-01

We present the results of statistical analysis of an adaptive antenna array tuned using the least-mean-square error algorithm with quadratic constraint on the useful-signal amplification with allowance for the weight-coefficient fluctuations. Using the perturbation theory, the expressions for the correlation function and power of the output signal of the adaptive antenna array, as well as the formula for the weight-vector covariance matrix are obtained in the first approximation. The fluctuations are shown to lead to the signal distortions at the antenna-array output. The weight-coefficient fluctuations result in the appearance of additional terms in the statistical characteristics of the antenna array. It is also shown that the weight-vector fluctuations are isotropic, i.e., identical in all directions of the weight-coefficient space.

A parallel algorithm for the eigenvalues and eigenvectors for a general complex matrix

NASA Technical Reports Server (NTRS)

Shroff, Gautam

1989-01-01

A new parallel Jacobi-like algorithm is developed for computing the eigenvalues of a general complex matrix. Most parallel methods for this parallel typically display only linear convergence. Sequential norm-reducing algorithms also exit and they display quadratic convergence in most cases. The new algorithm is a parallel form of the norm-reducing algorithm due to Eberlein. It is proven that the asymptotic convergence rate of this algorithm is quadratic. Numerical experiments are presented which demonstrate the quadratic convergence of the algorithm and certain situations where the convergence is slow are also identified. The algorithm promises to be very competitive on a variety of parallel architectures.

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…

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.

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 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

Genetic algorithms using SISAL parallel programming language

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

Tejada, S.

1994-05-06

Genetic algorithms are a mathematical optimization technique developed by John Holland at the University of Michigan [1]. The SISAL programming language possesses many of the characteristics desired to implement genetic algorithms. SISAL is a deterministic, functional programming language which is inherently parallel. Because SISAL is functional and based on mathematical concepts, genetic algorithms can be efficiently translated into the language. Several of the steps involved in genetic algorithms, such as mutation, crossover, and fitness evaluation, can be parallelized using SISAL. In this paper I will l discuss the implementation and performance of parallel genetic algorithms in SISAL.

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.

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

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.

Quadratic Finite Element Method for 1D Deterministic Transport

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

Tolar, Jr., D R; Ferguson, J M

2004-01-06

In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ({und r}) and angular ({und {Omega}}) dependences on the angular flux {psi}{und r},{und {Omega}}are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of {psi}{und r},{und {Omega}}. Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable ({mu}) in developing the one-dimensional (1D) spherical geometry S{sub N} equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S{sub N} algorithms.

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

NASA Astrophysics Data System (ADS)

Tangpatiphan, Kritsana; Yokoyama, Akihiko

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

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

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.

The generalized quadratic knapsack problem. A neuronal network approach.

PubMed

Talaván, Pedro M; Yáñez, Javier

2006-05-01

The solution of an optimization problem through the continuous Hopfield network (CHN) is based on some energy or Lyapunov function, which decreases as the system evolves until a local minimum value is attained. A new energy function is proposed in this paper so that any 0-1 linear constrains programming with quadratic objective function can be solved. This problem, denoted as the generalized quadratic knapsack problem (GQKP), includes as particular cases well-known problems such as the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). This new energy function generalizes those proposed by other authors. Through this energy function, any GQKP can be solved with an appropriate parameter setting procedure, which is detailed in this paper. As a particular case, and in order to test this generalized energy function, some computational experiments solving the traveling salesman problem are also included.

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 (0algorithms (k-means, principal components, principal manifolds and graphs, regularized and sparse regression), based on piece-wise quadratic error potentials of subquadratic growth (PQSQ potentials). We develop a new and universal framework to minimize arbitrary sub-quadratic error potentials using an algorithm with guaranteed fast convergence to the local or global error minimum. The theory of PQSQ potentials is based on the notion of the cone of minorant functions, and represents a natural approximation formalism based on the application of min-plus algebra. The approach can be applied in most of existing machine learning methods, including methods of data approximation and regularized and sparse regression, leading to the improvement in the computational cost/accuracy trade-off. We demonstrate that on synthetic and real-life datasets PQSQ-based machine learning methods achieve orders of magnitude faster computational performance than the corresponding state-of-the-art methods, having similar or better approximation accuracy. Copyright © 2016 Elsevier Ltd. All rights reserved.

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

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.

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.

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.

Quadratic Polynomial Regression using Serial Observation Processing:Implementation within DART

NASA Astrophysics Data System (ADS)

Hodyss, D.; Anderson, J. L.; Collins, N.; Campbell, W. F.; Reinecke, P. A.

2017-12-01

Many Ensemble-Based Kalman ltering (EBKF) algorithms process the observations serially. Serial observation processing views the data assimilation process as an iterative sequence of scalar update equations. What is useful about this data assimilation algorithm is that it has very low memory requirements and does not need complex methods to perform the typical high-dimensional inverse calculation of many other algorithms. Recently, the push has been towards the prediction, and therefore the assimilation of observations, for regions and phenomena for which high-resolution is required and/or highly nonlinear physical processes are operating. For these situations, a basic hypothesis is that the use of the EBKF is sub-optimal and performance gains could be achieved by accounting for aspects of the non-Gaussianty. To this end, we develop here a new component of the Data Assimilation Research Testbed [DART] to allow for a wide-variety of users to test this hypothesis. This new version of DART allows one to run several variants of the EBKF as well as several variants of the quadratic polynomial lter using the same forecast model and observations. Dierences between the results of the two systems will then highlight the degree of non-Gaussianity in the system being examined. We will illustrate in this work the differences between the performance of linear versus quadratic polynomial regression in a hierarchy of models from Lorenz-63 to a simple general circulation model.

Algorithm improvement program nuclide identification algorithm scoring criteria and scoring application.

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

Enghauser, Michael

2016-02-01

The goal of the Domestic Nuclear Detection Office (DNDO) Algorithm Improvement Program (AIP) is to facilitate gamma-radiation detector nuclide identification algorithm development, improvement, and validation. Accordingly, scoring criteria have been developed to objectively assess the performance of nuclide identification algorithms. In addition, a Microsoft Excel spreadsheet application for automated nuclide identification scoring has been developed. This report provides an overview of the equations, nuclide weighting factors, nuclide equivalencies, and configuration weighting factors used by the application for scoring nuclide identification algorithm performance. Furthermore, this report presents a general overview of the nuclide identification algorithm scoring application including illustrative examples.

US-VISIT Identity Matching Algorithm Evaluation Program: ADIS Algorithm Evaluation Project Plan Update

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

Grant, C W; Lenderman, J S; Gansemer, J D

This document is an update to the 'ADIS Algorithm Evaluation Project Plan' specified in the Statement of Work for the US-VISIT Identity Matching Algorithm Evaluation Program, as deliverable II.D.1. The original plan was delivered in August 2010. This document modifies the plan to reflect modified deliverables reflecting delays in obtaining a database refresh. This document describes the revised schedule of the program deliverables. The detailed description of the processes used, the statistical analysis processes and the results of the statistical analysis will be described fully in the program deliverables. The US-VISIT Identity Matching Algorithm Evaluation Program is work performed bymore » Lawrence Livermore National Laboratory (LLNL) under IAA HSHQVT-07-X-00002 P00004 from the Department of Homeland Security (DHS).« less

Synthesis of concentric circular antenna arrays using dragonfly algorithm

NASA Astrophysics Data System (ADS)

Babayigit, B.

2018-05-01

Due to the strong non-linear relationship between the array factor and the array elements, concentric circular antenna array (CCAA) synthesis problem is challenging. Nature-inspired optimisation techniques have been playing an important role in solving array synthesis problems. Dragonfly algorithm (DA) is a novel nature-inspired optimisation technique which is based on the static and dynamic swarming behaviours of dragonflies in nature. This paper presents the design of CCAAs to get low sidelobes using DA. The effectiveness of the proposed DA is investigated in two different (with and without centre element) cases of two three-ring (having 4-, 6-, 8-element or 8-, 10-, 12-element) CCAA design. The radiation pattern of each design cases is obtained by finding optimal excitation weights of the array elements using DA. Simulation results show that the proposed algorithm outperforms the other state-of-the-art techniques (symbiotic organisms search, biogeography-based optimisation, sequential quadratic programming, opposition-based gravitational search algorithm, cat swarm optimisation, firefly algorithm, evolutionary programming) for all design cases. DA can be a promising technique for electromagnetic problems.

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.

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.

Dynamic programming algorithms for biological sequence comparison.

PubMed

Pearson, W R; Miller, W

1992-01-01

Efficient dynamic programming algorithms are available for a broad class of protein and DNA sequence comparison problems. These algorithms require computer time proportional to the product of the lengths of the two sequences being compared [O(N2)] but require memory space proportional only to the sum of these lengths [O(N)]. Although the requirement for O(N2) time limits use of the algorithms to the largest computers when searching protein and DNA sequence databases, many other applications of these algorithms, such as calculation of distances for evolutionary trees and comparison of a new sequence to a library of sequence profiles, are well within the capabilities of desktop computers. In particular, the results of library searches with rapid searching programs, such as FASTA or BLAST, should be confirmed by performing a rigorous optimal alignment. Whereas rapid methods do not overlook significant sequence similarities, FASTA limits the number of gaps that can be inserted into an alignment, so that a rigorous alignment may extend the alignment substantially in some cases. BLAST does not allow gaps in the local regions that it reports; a calculation that allows gaps is very likely to extend the alignment substantially. Although a Monte Carlo evaluation of the statistical significance of a similarity score with a rigorous algorithm is much slower than the heuristic approach used by the RDF2 program, the dynamic programming approach should take less than 1 hr on a 386-based PC or desktop Unix workstation. For descriptive purposes, we have limited our discussion to methods for calculating similarity scores and distances that use gap penalties of the form g = rk. Nevertheless, programs for the more general case (g = q+rk) are readily available. Versions of these programs that run either on Unix workstations, IBM-PC class computers, or the Macintosh can be obtained from either of the authors.

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.

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.

Algorithm Improvement Program Nuclide Identification Algorithm Scoring Criteria And Scoring Application - DNDO.

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

Enghauser, Michael

2015-02-01

The goal of the Domestic Nuclear Detection Office (DNDO) Algorithm Improvement Program (AIP) is to facilitate gamma-radiation detector nuclide identification algorithm development, improvement, and validation. Accordingly, scoring criteria have been developed to objectively assess the performance of nuclide identification algorithms. In addition, a Microsoft Excel spreadsheet application for automated nuclide identification scoring has been developed. This report provides an overview of the equations, nuclide weighting factors, nuclide equivalencies, and configuration weighting factors used by the application for scoring nuclide identification algorithm performance. Furthermore, this report presents a general overview of the nuclide identification algorithm scoring application including illustrative examples.

Quadratic constrained mixed discrete optimization with an adiabatic quantum optimizer

NASA Astrophysics Data System (ADS)

Chandra, Rishabh; Jacobson, N. Tobias; Moussa, Jonathan E.; Frankel, Steven H.; Kais, Sabre

2014-07-01

We extend the family of problems that may be implemented on an adiabatic quantum optimizer (AQO). When a quadratic optimization problem has at least one set of discrete controls and the constraints are linear, we call this a quadratic constrained mixed discrete optimization (QCMDO) problem. QCMDO problems are NP-hard, and no efficient classical algorithm for their solution is known. Included in the class of QCMDO problems are combinatorial optimization problems constrained by a linear partial differential equation (PDE) or system of linear PDEs. An essential complication commonly encountered in solving this type of problem is that the linear constraint may introduce many intermediate continuous variables into the optimization while the computational cost grows exponentially with problem size. We resolve this difficulty by developing a constructive mapping from QCMDO to quadratic unconstrained binary optimization (QUBO) such that the size of the QUBO problem depends only on the number of discrete control variables. With a suitable embedding, taking into account the physical constraints of the realizable coupling graph, the resulting QUBO problem can be implemented on an existing AQO. The mapping itself is efficient, scaling cubically with the number of continuous variables in the general case and linearly in the PDE case if an efficient preconditioner is available.

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

Motion Cueing Algorithm Development: New Motion Cueing Program Implementation and Tuning

NASA Technical Reports Server (NTRS)

Houck, Jacob A. (Technical Monitor); Telban, Robert J.; Cardullo, Frank M.; Kelly, Lon C.

2005-01-01

A computer program has been developed for the purpose of driving the NASA Langley Research Center Visual Motion Simulator (VMS). This program includes two new motion cueing algorithms, the optimal algorithm and the nonlinear algorithm. A general description of the program is given along with a description and flowcharts for each cueing algorithm, and also descriptions and flowcharts for subroutines used with the algorithms. Common block variable listings and a program listing are also provided. The new cueing algorithms have a nonlinear gain algorithm implemented that scales each aircraft degree-of-freedom input with a third-order polynomial. A description of the nonlinear gain algorithm is given along with past tuning experience and procedures for tuning the gain coefficient sets for each degree-of-freedom to produce the desired piloted performance. This algorithm tuning will be needed when the nonlinear motion cueing algorithm is implemented on a new motion system in the Cockpit Motion Facility (CMF) at the NASA Langley Research Center.

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.

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

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)

Synthesizing Dynamic Programming Algorithms from Linear Temporal Logic Formulae

NASA Technical Reports Server (NTRS)

Rosu, Grigore; Havelund, Klaus

2001-01-01

The problem of testing a linear temporal logic (LTL) formula on a finite execution trace of events, generated by an executing program, occurs naturally in runtime analysis of software. We present an algorithm which takes an LTL formula and generates an efficient dynamic programming algorithm. The generated algorithm tests whether the LTL formula is satisfied by a finite trace of events given as input. The generated algorithm runs in linear time, its constant depending on the size of the LTL formula. The memory needed is constant, also depending on the size of the formula.

DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers

NASA Astrophysics Data System (ADS)

Mokhtari, Aryan; Shi, Wei; Ling, Qing; Ribeiro, Alejandro

2016-10-01

This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with neighbors only. A decentralized version of the alternating directions method of multipliers (DADMM) is a common method for solving this category of problems. DADMM exhibits linear convergence rate to the optimal objective but its implementation requires solving a convex optimization problem at each iteration. This can be computationally costly and may result in large overall convergence times. The decentralized quadratically approximated ADMM algorithm (DQM), which minimizes a quadratic approximation of the objective function that DADMM minimizes at each iteration, is proposed here. The consequent reduction in computational time is shown to have minimal effect on convergence properties. Convergence still proceeds at a linear rate with a guaranteed constant that is asymptotically equivalent to the DADMM linear convergence rate constant. Numerical results demonstrate advantages of DQM relative to DADMM and other alternatives in a logistic regression problem.

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.

Portfolio optimization by using linear programing models based on genetic algorithm

NASA Astrophysics Data System (ADS)

Sukono; Hidayat, Y.; Lesmana, E.; Putra, A. S.; Napitupulu, H.; Supian, S.

2018-01-01

In this paper, we discussed the investment portfolio optimization using linear programming model based on genetic algorithms. It is assumed that the portfolio risk is measured by absolute standard deviation, and each investor has a risk tolerance on the investment portfolio. To complete the investment portfolio optimization problem, the issue is arranged into a linear programming model. Furthermore, determination of the optimum solution for linear programming is done by using a genetic algorithm. As a numerical illustration, we analyze some of the stocks traded on the capital market in Indonesia. Based on the analysis, it is shown that the portfolio optimization performed by genetic algorithm approach produces more optimal efficient portfolio, compared to the portfolio optimization performed by a linear programming algorithm approach. Therefore, genetic algorithms can be considered as an alternative on determining the investment portfolio optimization, particularly using linear programming models.

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

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.

Some insights on hard quadratic assignment problem instances

NASA Astrophysics Data System (ADS)

Hussin, Mohamed Saifullah

2017-11-01

Since the formal introduction of metaheuristics, a huge number Quadratic Assignment Problem (QAP) instances have been introduced. Those instances however are loosely-structured, and therefore made it difficult to perform any systematic analysis. The QAPLIB for example, is a library that contains a huge number of QAP benchmark instances that consists of instances with different size and structure, but with a very limited availability for every instance type. This prevents researchers from performing organized study on those instances, such as parameter tuning and testing. In this paper, we will discuss several hard instances that have been introduced over the years, and algorithms that have been used for solving them.

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,…

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…

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.

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.

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.

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.

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.

Enhanced algorithms for stochastic programming

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

Krishna, Alamuru S.

1993-09-01

In this dissertation, we present some of the recent advances made in solving two-stage stochastic linear programming problems of large size and complexity. Decomposition and sampling are two fundamental components of techniques to solve stochastic optimization problems. We describe improvements to the current techniques in both these areas. We studied different ways of using importance sampling techniques in the context of Stochastic programming, by varying the choice of approximation functions used in this method. We have concluded that approximating the recourse function by a computationally inexpensive piecewise-linear function is highly efficient. This reduced the problem from finding the mean ofmore » a computationally expensive functions to finding that of a computationally inexpensive function. Then we implemented various variance reduction techniques to estimate the mean of a piecewise-linear function. This method achieved similar variance reductions in orders of magnitude less time than, when we directly applied variance-reduction techniques directly on the given problem. In solving a stochastic linear program, the expected value problem is usually solved before a stochastic solution and also to speed-up the algorithm by making use of the information obtained from the solution of the expected value problem. We have devised a new decomposition scheme to improve the convergence of this algorithm.« less

Quantum algorithms for Gibbs sampling and hitting-time estimation

DOE PAGES

Chowdhury, Anirban Narayan; Somma, Rolando D.

2017-02-01

In this paper, we present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in √Nβ/Ζ and polynomial in log(1/ϵ), where N is the Hilbert space dimension, β is the inverse temperature, Ζ is the partition function, and ϵ is the desired precision of the output state. Our quantum algorithm exponentially improves the dependence on 1/ϵ and quadratically improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. Formore » a sparse stochastic matrix Ρ, it runs in time almost linear in 1/(ϵΔ 3/2), where ϵ is the absolute precision in the estimation and Δ is a parameter determined by Ρ, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the dependence on 1/ϵ and 1/Δ of the analog classical algorithm for hitting-time estimation. Finally, both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.« less

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.

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.

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)

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.

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.

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.

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

PubMed

Skariah, Deepak G; Arigovindan, Muthuvel

2017-06-19

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

Basis for a neuronal version of Grover's quantum algorithm

PubMed Central

Clark, Kevin B.

2014-01-01

Grover's quantum (search) algorithm exploits principles of quantum information theory and computation to surpass the strong Church–Turing limit governing classical computers. The algorithm initializes a search field into superposed N (eigen)states to later execute nonclassical “subroutines” involving unitary phase shifts of measured states and to produce root-rate or quadratic gain in the algorithmic time (O(N1/2)) needed to find some “target” solution m. Akin to this fast technological search algorithm, single eukaryotic cells, such as differentiated neurons, perform natural quadratic speed-up in the search for appropriate store-operated Ca2+ response regulation of, among other processes, protein and lipid biosynthesis, cell energetics, stress responses, cell fate and death, synaptic plasticity, and immunoprotection. Such speed-up in cellular decision making results from spatiotemporal dynamics of networked intracellular Ca2+-induced Ca2+ release and the search (or signaling) velocity of Ca2+ wave propagation. As chemical processes, such as the duration of Ca2+ mobilization, become rate-limiting over interstore distances, Ca2+ waves quadratically decrease interstore-travel time from slow saltatory to fast continuous gradients proportional to the square-root of the classical Ca2+ diffusion coefficient, D1/2, matching the computing efficiency of Grover's quantum algorithm. In this Hypothesis and Theory article, I elaborate on these traits using a fire-diffuse-fire model of store-operated cytosolic Ca2+ signaling valid for glutamatergic neurons. Salient model features corresponding to Grover's quantum algorithm are parameterized to meet requirements for the Oracle Hadamard transform and Grover's iteration. A neuronal version of Grover's quantum algorithm figures to benefit signal coincidence detection and integration, bidirectional synaptic plasticity, and other vital cell functions by rapidly selecting, ordering, and/or counting optional response

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

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…

Performance Trend of Different Algorithms for Structural Design Optimization

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Coroneos, Rula M.; Guptill, James D.; Hopkins, Dale A.

1996-01-01

Nonlinear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Center, a project was initiated to assess performance of different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with the sequential unconstrained minimizations technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.

A review on quantum search algorithms

NASA Astrophysics Data System (ADS)

Giri, Pulak Ranjan; Korepin, Vladimir E.

2017-12-01

The use of superposition of states in quantum computation, known as quantum parallelism, has significant advantage in terms of speed over the classical computation. It is evident from the early invented quantum algorithms such as Deutsch's algorithm, Deutsch-Jozsa algorithm and its variation as Bernstein-Vazirani algorithm, Simon algorithm, Shor's algorithms, etc. Quantum parallelism also significantly speeds up the database search algorithm, which is important in computer science because it comes as a subroutine in many important algorithms. Quantum database search of Grover achieves the task of finding the target element in an unsorted database in a time quadratically faster than the classical computer. We review Grover's quantum search algorithms for a singe and multiple target elements in a database. The partial search algorithm of Grover and Radhakrishnan and its optimization by Korepin called GRK algorithm are also discussed.

Algorithmic Trading with Developmental and Linear Genetic Programming

NASA Astrophysics Data System (ADS)

Wilson, Garnett; Banzhaf, Wolfgang

A developmental co-evolutionary genetic programming approach (PAM DGP) and a standard linear genetic programming (LGP) stock trading systemare applied to a number of stocks across market sectors. Both GP techniques were found to be robust to market fluctuations and reactive to opportunities associated with stock price rise and fall, with PAMDGP generating notably greater profit in some stock trend scenarios. Both algorithms were very accurate at buying to achieve profit and selling to protect assets, while exhibiting bothmoderate trading activity and the ability to maximize or minimize investment as appropriate. The content of the trading rules produced by both algorithms are also examined in relation to stock price trend scenarios.

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...

A scalable parallel algorithm for multiple objective linear programs

NASA Technical Reports Server (NTRS)

Wiecek, Malgorzata M.; Zhang, Hong

1994-01-01

This paper presents an ADBASE-based parallel algorithm for solving multiple objective linear programs (MOLP's). Job balance, speedup and scalability are of primary interest in evaluating efficiency of the new algorithm. Implementation results on Intel iPSC/2 and Paragon multiprocessors show that the algorithm significantly speeds up the process of solving MOLP's, which is understood as generating all or some efficient extreme points and unbounded efficient edges. The algorithm gives specially good results for large and very large problems. Motivation and justification for solving such large MOLP's are also included.

Optimized programming algorithm for cylindrical and directional deep brain stimulation electrodes.

PubMed

Anderson, Daria Nesterovich; Osting, Braxton; Vorwerk, Johannes; Dorval, Alan D; Butson, Christopher R

2018-04-01

Deep brain stimulation (DBS) is a growing treatment option for movement and psychiatric disorders. As DBS technology moves toward directional leads with increased numbers of smaller electrode contacts, trial-and-error methods of manual DBS programming are becoming too time-consuming for clinical feasibility. We propose an algorithm to automate DBS programming in near real-time for a wide range of DBS lead designs. Magnetic resonance imaging and diffusion tensor imaging are used to build finite element models that include anisotropic conductivity. The algorithm maximizes activation of target tissue and utilizes the Hessian matrix of the electric potential to approximate activation of neurons in all directions. We demonstrate our algorithm's ability in an example programming case that targets the subthalamic nucleus (STN) for the treatment of Parkinson's disease for three lead designs: the Medtronic 3389 (four cylindrical contacts), the direct STNAcute (two cylindrical contacts, six directional contacts), and the Medtronic-Sapiens lead (40 directional contacts). The optimization algorithm returns patient-specific contact configurations in near real-time-less than 10 s for even the most complex leads. When the lead was placed centrally in the target STN, the directional leads were able to activate over 50% of the region, whereas the Medtronic 3389 could activate only 40%. When the lead was placed 2 mm lateral to the target, the directional leads performed as well as they did in the central position, but the Medtronic 3389 activated only 2.9% of the STN. This DBS programming algorithm can be applied to cylindrical electrodes as well as novel directional leads that are too complex with modern technology to be manually programmed. This algorithm may reduce clinical programming time and encourage the use of directional leads, since they activate a larger volume of the target area than cylindrical electrodes in central and off-target lead placements.

Algorithm and program for information processing with the filin apparatus

NASA Technical Reports Server (NTRS)

Gurin, L. S.; Morkrov, V. S.; Moskalenko, Y. I.; Tsoy, K. A.

1979-01-01

The reduction of spectral radiation data from space sources is described. The algorithm and program for identifying segments of information obtained from the Film telescope-spectrometer on the Salyut-4 are presented. The information segments represent suspected X-ray sources. The proposed algorithm is an algorithm of the lowest level. Following evaluation, information free of uninformative segments is subject to further processing with algorithms of a higher level. The language used is FORTRAN 4.

A Stereo Dual-Channel Dynamic Programming Algorithm for UAV Image Stitching.

PubMed

Li, Ming; Chen, Ruizhi; Zhang, Weilong; Li, Deren; Liao, Xuan; Wang, Lei; Pan, Yuanjin; Zhang, Peng

2017-09-08

Dislocation is one of the major challenges in unmanned aerial vehicle (UAV) image stitching. In this paper, we propose a new algorithm for seamlessly stitching UAV images based on a dynamic programming approach. Our solution consists of two steps: Firstly, an image matching algorithm is used to correct the images so that they are in the same coordinate system. Secondly, a new dynamic programming algorithm is developed based on the concept of a stereo dual-channel energy accumulation. A new energy aggregation and traversal strategy is adopted in our solution, which can find a more optimal seam line for image stitching. Our algorithm overcomes the theoretical limitation of the classical Duplaquet algorithm. Experiments show that the algorithm can effectively solve the dislocation problem in UAV image stitching, especially for the cases in dense urban areas. Our solution is also direction-independent, which has better adaptability and robustness for stitching images.

Security analysis of quadratic phase based cryptography

NASA Astrophysics Data System (ADS)

Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Healy, John J.; Sheridan, John T.

2016-09-01

The linear canonical transform (LCT) is essential in modeling a coherent light field propagation through first-order optical systems. Recently, a generic optical system, known as a Quadratic Phase Encoding System (QPES), for encrypting a two-dimensional (2D) image has been reported. It has been reported together with two phase keys the individual LCT parameters serve as keys of the cryptosystem. However, it is important that such the encryption systems also satisfies some dynamic security properties. Therefore, in this work, we examine some cryptographic evaluation methods, such as Avalanche Criterion and Bit Independence, which indicates the degree of security of the cryptographic algorithms on QPES. We compare our simulation results with the conventional Fourier and the Fresnel transform based DRPE systems. The results show that the LCT based DRPE has an excellent avalanche and bit independence characteristics than that of using the conventional Fourier and Fresnel based encryption systems.

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.

Programming Deep Brain Stimulation for Parkinson's Disease: The Toronto Western Hospital Algorithms.

PubMed

Picillo, Marina; Lozano, Andres M; Kou, Nancy; Puppi Munhoz, Renato; Fasano, Alfonso

2016-01-01

Deep brain stimulation (DBS) is an established and effective treatment for Parkinson's disease (PD). After surgery, a number of extensive programming sessions are performed to define the most optimal stimulation parameters. Programming sessions mainly rely only on neurologist's experience. As a result, patients often undergo inconsistent and inefficient stimulation changes, as well as unnecessary visits. We reviewed the literature on initial and follow-up DBS programming procedures and integrated our current practice at Toronto Western Hospital (TWH) to develop standardized DBS programming protocols. We propose four algorithms including the initial programming and specific algorithms tailored to symptoms experienced by patients following DBS: speech disturbances, stimulation-induced dyskinesia and gait impairment. We conducted a literature search of PubMed from inception to July 2014 with the keywords "deep brain stimulation", "festination", "freezing", "initial programming", "Parkinson's disease", "postural instability", "speech disturbances", and "stimulation induced dyskinesia". Seventy papers were considered for this review. Based on the literature review and our experience at TWH, we refined four algorithms for: (1) the initial programming stage, and management of symptoms following DBS, particularly addressing (2) speech disturbances, (3) stimulation-induced dyskinesia, and (4) gait impairment. We propose four algorithms tailored to an individualized approach to managing symptoms associated with DBS and disease progression in patients with PD. We encourage established as well as new DBS centers to test the clinical usefulness of these algorithms in supplementing the current standards of care. Copyright © 2016 Elsevier Inc. All rights reserved.

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.

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

A Stereo Dual-Channel Dynamic Programming Algorithm for UAV Image Stitching

PubMed Central

Chen, Ruizhi; Zhang, Weilong; Li, Deren; Liao, Xuan; Zhang, Peng

2017-01-01

Dislocation is one of the major challenges in unmanned aerial vehicle (UAV) image stitching. In this paper, we propose a new algorithm for seamlessly stitching UAV images based on a dynamic programming approach. Our solution consists of two steps: Firstly, an image matching algorithm is used to correct the images so that they are in the same coordinate system. Secondly, a new dynamic programming algorithm is developed based on the concept of a stereo dual-channel energy accumulation. A new energy aggregation and traversal strategy is adopted in our solution, which can find a more optimal seam line for image stitching. Our algorithm overcomes the theoretical limitation of the classical Duplaquet algorithm. Experiments show that the algorithm can effectively solve the dislocation problem in UAV image stitching, especially for the cases in dense urban areas. Our solution is also direction-independent, which has better adaptability and robustness for stitching images. PMID:28885547

A Partitioning and Bounded Variable Algorithm for Linear Programming

ERIC Educational Resources Information Center

Sheskin, Theodore J.

2006-01-01

An interesting new partitioning and bounded variable algorithm (PBVA) is proposed for solving linear programming problems. The PBVA is a variant of the simplex algorithm which uses a modified form of the simplex method followed by the dual simplex method for bounded variables. In contrast to the two-phase method and the big M method, the PBVA does…

Block clustering based on difference of convex functions (DC) programming and DC algorithms.

PubMed

Le, Hoai Minh; Le Thi, Hoai An; Dinh, Tao Pham; Huynh, Van Ngai

2013-10-01

We investigate difference of convex functions (DC) programming and the DC algorithm (DCA) to solve the block clustering problem in the continuous framework, which traditionally requires solving a hard combinatorial optimization problem. DC reformulation techniques and exact penalty in DC programming are developed to build an appropriate equivalent DC program of the block clustering problem. They lead to an elegant and explicit DCA scheme for the resulting DC program. Computational experiments show the robustness and efficiency of the proposed algorithm and its superiority over standard algorithms such as two-mode K-means, two-mode fuzzy clustering, and block classification EM.

Linear Quadratic Gaussian Controller Design Using a Graphical User Interface: Application to the Beam-Waveguide Antennas

NASA Astrophysics Data System (ADS)

Maneri, E.; Gawronski, W.

1999-10-01

The linear quadratic Gaussian (LQG) design algorithms described in [2] and [5] have been used in the controller design of JPL's beam-waveguide [5] and 70-m [6] antennas. This algorithm significantly improves tracking precision in a windy environment. This article describes the graphical user interface (GUI) software for the design LQG controllers. It consists of two parts: the basic LQG design and the fine-tuning of the basic design using a constrained optimization algorithm. The presented GUI was developed to simplify the design process, to make the design process user-friendly, and to enable design of an LQG controller for one with a limited control engineering background. The user is asked to manipulate the GUI sliders and radio buttons to watch the antenna performance. Simple rules are given at the GUI display.

The spectral positioning algorithm of new spectrum vehicle based on convex programming in wireless sensor network

NASA Astrophysics Data System (ADS)

Zhang, Yongjun; Lu, Zhixin

2017-10-01

Spectrum resources are very precious, so it is increasingly important to locate interference signals rapidly. Convex programming algorithms in wireless sensor networks are often used as localization algorithms. But in view of the traditional convex programming algorithm is too much overlap of wireless sensor nodes that bring low positioning accuracy, the paper proposed a new algorithm. Which is mainly based on the traditional convex programming algorithm, the spectrum car sends unmanned aerial vehicles (uses) that can be used to record data periodically along different trajectories. According to the probability density distribution, the positioning area is segmented to further reduce the location area. Because the algorithm only increases the communication process of the power value of the unknown node and the sensor node, the advantages of the convex programming algorithm are basically preserved to realize the simple and real-time performance. The experimental results show that the improved algorithm has a better positioning accuracy than the original convex programming algorithm.

Parametric Quantum Search Algorithm as Quantum Walk: A Quantum Simulation

NASA Astrophysics Data System (ADS)

Ellinas, Demosthenes; Konstandakis, Christos

2016-02-01

Parametric quantum search algorithm (PQSA) is a form of quantum search that results by relaxing the unitarity of the original algorithm. PQSA can naturally be cast in the form of quantum walk, by means of the formalism of oracle algebra. This is due to the fact that the completely positive trace preserving search map used by PQSA, admits a unitarization (unitary dilation) a la quantum walk, at the expense of introducing auxiliary quantum coin-qubit space. The ensuing QW describes a process of spiral motion, chosen to be driven by two unitary Kraus generators, generating planar rotations of Bloch vector around an axis. The quadratic acceleration of quantum search translates into an equivalent quadratic saving of the number of coin qubits in the QW analogue. The associated to QW model Hamiltonian operator is obtained and is shown to represent a multi-particle long-range interacting quantum system that simulates parametric search. Finally, the relation of PQSA-QW simulator to the QW search algorithm is elucidated.

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

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

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…

ORACLS: A system for linear-quadratic-Gaussian control law design

NASA Technical Reports Server (NTRS)

Armstrong, E. S.

1978-01-01

A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

Quadratic adaptive algorithm for solving cardiac action potential models.

PubMed

Chen, Min-Hung; Chen, Po-Yuan; Luo, Ching-Hsing

2016-10-01

An adaptive integration method is proposed for computing cardiac action potential models accurately and efficiently. Time steps are adaptively chosen by solving a quadratic formula involving the first and second derivatives of the membrane action potential. To improve the numerical accuracy, we devise an extremum-locator (el) function to predict the local extremum when approaching the peak amplitude of the action potential. In addition, the time step restriction (tsr) technique is designed to limit the increase in time steps, and thus prevent the membrane potential from changing abruptly. The performance of the proposed method is tested using the Luo-Rudy phase 1 (LR1), dynamic (LR2), and human O'Hara-Rudy dynamic (ORd) ventricular action potential models, and the Courtemanche atrial model incorporating a Markov sodium channel model. Numerical experiments demonstrate that the action potential generated using the proposed method is more accurate than that using the traditional Hybrid method, especially near the peak region. The traditional Hybrid method may choose large time steps near to the peak region, and sometimes causes the action potential to become distorted. In contrast, the proposed new method chooses very fine time steps in the peak region, but large time steps in the smooth region, and the profiles are smoother and closer to the reference solution. In the test on the stiff Markov ionic channel model, the Hybrid blows up if the allowable time step is set to be greater than 0.1ms. In contrast, our method can adjust the time step size automatically, and is stable. Overall, the proposed method is more accurate than and as efficient as the traditional Hybrid method, especially for the human ORd model. The proposed method shows improvement for action potentials with a non-smooth morphology, and it needs further investigation to determine whether the method is helpful during propagation of the action potential. Copyright © 2016 Elsevier Ltd. All rights

Testing Algorithmic Skills in Traditional and Non-Traditional Programming Environments

ERIC Educational Resources Information Center

Csernoch, Mária; Biró, Piroska; Máth, János; Abari, Kálmán

2015-01-01

The Testing Algorithmic and Application Skills (TAaAS) project was launched in the 2011/2012 academic year to test first year students of Informatics, focusing on their algorithmic skills in traditional and non-traditional programming environments, and on the transference of their knowledge of Informatics from secondary to tertiary education. The…

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

NASA Astrophysics Data System (ADS)

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

2006-01-01

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

Algorithm Building and Learning Programming Languages Using a New Educational Paradigm

NASA Astrophysics Data System (ADS)

Jain, Anshul K.; Singhal, Manik; Gupta, Manu Sheel

2011-08-01

This research paper presents a new concept of using a single tool to associate syntax of various programming languages, algorithms and basic coding techniques. A simple framework has been programmed in Python that helps students learn skills to develop algorithms, and implement them in various programming languages. The tool provides an innovative and a unified graphical user interface for development of multimedia objects, educational games and applications. It also aids collaborative learning amongst students and teachers through an integrated mechanism based on Remote Procedure Calls. The paper also elucidates an innovative method for code generation to enable students to learn the basics of programming languages using drag-n-drop methods for image objects.

Quadratic Blind Linear Unmixing: A Graphical User Interface for Tissue Characterization

PubMed Central

Gutierrez-Navarro, O.; Campos-Delgado, D.U.; Arce-Santana, E. R.; Jo, Javier A.

2016-01-01

Spectral unmixing is the process of breaking down data from a sample into its basic components and their abundances. Previous work has been focused on blind unmixing of multi-spectral fluorescence lifetime imaging microscopy (m-FLIM) datasets under a linear mixture model and quadratic approximations. This method provides a fast linear decomposition and can work without a limitation in the maximum number of components or end-members. Hence this work presents an interactive software which implements our blind end-member and abundance extraction (BEAE) and quadratic blind linear unmixing (QBLU) algorithms in Matlab. The options and capabilities of our proposed software are described in detail. When the number of components is known, our software can estimate the constitutive end-members and their abundances. When no prior knowledge is available, the software can provide a completely blind solution to estimate the number of components, the end-members and their abundances. The characterization of three case studies validates the performance of the new software: ex-vivo human coronary arteries, human breast cancer cell samples, and in-vivo hamster oral mucosa. The software is freely available in a hosted webpage by one of the developing institutions, and allows the user a quick, easy-to-use and efficient tool for multi/hyper-spectral data decomposition. PMID:26589467

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.

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.

Comparative Evaluation of Different Optimization Algorithms for Structural Design Applications

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Coroneos, Rula M.; Guptill, James D.; Hopkins, Dale A.

1996-01-01

Non-linear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Centre, a project was initiated to assess the performance of eight different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using the eight different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems, however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with Sequential Unconstrained Minimizations Technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.

Image Processing Algorithms in the Secondary School Programming Education

ERIC Educational Resources Information Center

Gerják, István

2017-01-01

Learning computer programming for students of the age of 14-18 is difficult and requires endurance and engagement. Being familiar with the syntax of a computer language and writing programs in it are challenges for youngsters, not to mention that understanding algorithms is also a big challenge. To help students in the learning process, teachers…

Development and validation of an online interactive, multimedia wound care algorithms program.

PubMed

Beitz, Janice M; van Rijswijk, Lia

2012-01-01

To provide education based on evidence-based and validated wound care algorithms we designed and implemented an interactive, Web-based learning program for teaching wound care. A mixed methods quantitative pilot study design with qualitative components was used to test and ascertain the ease of use, validity, and reliability of the online program. A convenience sample of 56 RN wound experts (formally educated, certified in wound care, or both) participated. The interactive, online program consists of a user introduction, interactive assessment of 15 acute and chronic wound photos, user feedback about the percentage correct, partially correct, or incorrect algorithm and dressing choices and a user survey. After giving consent, participants accessed the online program, provided answers to the demographic survey, and completed the assessment module and photographic test, along with a posttest survey. The construct validity of the online interactive program was strong. Eighty-five percent (85%) of algorithm and 87% of dressing choices were fully correct even though some programming design issues were identified. Online study results were consistently better than previously conducted comparable paper-pencil study results. Using a 5-point Likert-type scale, participants rated the program's value and ease of use as 3.88 (valuable to very valuable) and 3.97 (easy to very easy), respectively. Similarly the research process was described qualitatively as "enjoyable" and "exciting." This digital program was well received indicating its "perceived benefits" for nonexpert users, which may help reduce barriers to implementing safe, evidence-based care. Ongoing research using larger sample sizes may help refine the program or algorithms while identifying clinician educational needs. Initial design imperfections and programming problems identified also underscored the importance of testing all paper and Web-based programs designed to educate health care professionals or guide

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…

Algorithms and programming tools for image processing on the MPP:3

NASA Technical Reports Server (NTRS)

Reeves, Anthony P.

1987-01-01

This is the third and final report on the work done for NASA Grant 5-403 on Algorithms and Programming Tools for Image Processing on the MPP:3. All the work done for this grant is summarized in the introduction. Work done since August 1986 is reported in detail. Research for this grant falls under the following headings: (1) fundamental algorithms for the MPP; (2) programming utilities for the MPP; (3) the Parallel Pascal Development System; and (4) performance analysis. In this report, the results of two efforts are reported: region growing, and performance analysis of important characteristic algorithms. In each case, timing results from MPP implementations are included. A paper is included in which parallel algorithms for region growing on the MPP is discussed. These algorithms permit different sized regions to be merged in parallel. Details on the implementation and peformance of several important MPP algorithms are given. These include a number of standard permutations, the FFT, convolution, arbitrary data mappings, image warping, and pyramid operations, all of which have been implemented on the MPP. The permutation and image warping functions have been included in the standard development system library.

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.

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.

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.

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

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

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 quantum heuristic algorithm for the traveling salesman problem

NASA Astrophysics Data System (ADS)

Bang, Jeongho; Ryu, Junghee; Lee, Changhyoup; Yoo, Seokwon; Lim, James; Lee, Jinhyoung

2012-12-01

We propose a quantum heuristic algorithm to solve the traveling salesman problem by generalizing the Grover search. Sufficient conditions are derived to greatly enhance the probability of finding the tours with the cheapest costs reaching almost to unity. These conditions are characterized by the statistical properties of tour costs and are shown to be automatically satisfied in the large-number limit of cities. In particular for a continuous distribution of the tours along the cost, we show that the quantum heuristic algorithm exhibits a quadratic speedup compared to its classical heuristic algorithm.

A Comparison of One Time Pad Random Key Generation using Linear Congruential Generator and Quadratic Congruential Generator

NASA Astrophysics Data System (ADS)

Apdilah, D.; Harahap, M. K.; Khairina, N.; Husein, A. M.; Harahap, M.

2018-04-01

One Time Pad algorithm always requires a pairing of the key for plaintext. If the length of keys less than a length of the plaintext, the key will be repeated until the length of the plaintext same with the length of the key. In this research, we use Linear Congruential Generator and Quadratic Congruential Generator for generating a random number. One Time Pad use a random number as a key for encryption and decryption process. Key will generate the first letter from the plaintext, we compare these two algorithms in terms of time speed encryption, and the result is a combination of OTP with LCG faster than the combination of OTP with QCG.

Programming Deep Brain Stimulation for Tremor and Dystonia: The Toronto Western Hospital Algorithms.

PubMed

Picillo, Marina; Lozano, Andres M; Kou, Nancy; Munhoz, Renato Puppi; Fasano, Alfonso

2016-01-01

Deep brain stimulation (DBS) is an effective treatment for essential tremor (ET) and dystonia. After surgery, a number of extensive programming sessions are performed, mainly relying on neurologist's personal experience as no programming guidelines have been provided so far, with the exception of recommendations provided by groups of experts. Finally, fewer information is available for the management of DBS in ET and dystonia compared with Parkinson's disease. Our aim is to review the literature on initial and follow-up DBS programming procedures for ET and dystonia and integrate the results with our current practice at Toronto Western Hospital (TWH) to develop standardized DBS programming protocols. We conducted a literature search of PubMed from inception to July 2014 with the keywords "balance", "bradykinesia", "deep brain stimulation", "dysarthria", "dystonia", "gait disturbances", "initial programming", "loss of benefit", "micrographia", "speech", "speech difficulties" and "tremor". Seventy-six papers were considered for this review. Based on the literature review and our experience at TWH, we refined three algorithms for management of ET, including: (1) initial programming, (2) management of balance and speech issues and (3) loss of stimulation benefit. We also depicted algorithms for the management of dystonia, including: (1) initial programming and (2) management of stimulation-induced hypokinesia (shuffling gait, micrographia and speech impairment). We propose five algorithms tailored to an individualized approach to managing ET and dystonia patients with DBS. We encourage the application of these algorithms to supplement current standards of care in established as well as new DBS centers to test the clinical usefulness of these algorithms in supplementing the current standards of care. Copyright © 2016 Elsevier Inc. All rights reserved.

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…

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.

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.

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.

A Quadratic Spring Equation

ERIC Educational Resources Information Center

Fay, Temple H.

2010-01-01

Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…

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.

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.

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.

A GPU-Accelerated 3-D Coupled Subsample Estimation Algorithm for Volumetric Breast Strain Elastography.

PubMed

Peng, Bo; Wang, Yuqi; Hall, Timothy J; Jiang, Jingfeng

2017-04-01

Our primary objective of this paper was to extend a previously published 2-D coupled subsample tracking algorithm for 3-D speckle tracking in the framework of ultrasound breast strain elastography. In order to overcome heavy computational cost, we investigated the use of a graphic processing unit (GPU) to accelerate the 3-D coupled subsample speckle tracking method. The performance of the proposed GPU implementation was tested using a tissue-mimicking phantom and in vivo breast ultrasound data. The performance of this 3-D subsample tracking algorithm was compared with the conventional 3-D quadratic subsample estimation algorithm. On the basis of these evaluations, we concluded that the GPU implementation of this 3-D subsample estimation algorithm can provide high-quality strain data (i.e., high correlation between the predeformation and the motion-compensated postdeformation radio frequency echo data and high contrast-to-noise ratio strain images), as compared with the conventional 3-D quadratic subsample algorithm. Using the GPU implementation of the 3-D speckle tracking algorithm, volumetric strain data can be achieved relatively fast (approximately 20 s per volume [2.5 cm ×2.5 cm ×2.5 cm]).

Quadratic blind linear unmixing: A graphical user interface for tissue characterization.

PubMed

Gutierrez-Navarro, O; Campos-Delgado, D U; Arce-Santana, E R; Jo, Javier A

2016-02-01

Spectral unmixing is the process of breaking down data from a sample into its basic components and their abundances. Previous work has been focused on blind unmixing of multi-spectral fluorescence lifetime imaging microscopy (m-FLIM) datasets under a linear mixture model and quadratic approximations. This method provides a fast linear decomposition and can work without a limitation in the maximum number of components or end-members. Hence this work presents an interactive software which implements our blind end-member and abundance extraction (BEAE) and quadratic blind linear unmixing (QBLU) algorithms in Matlab. The options and capabilities of our proposed software are described in detail. When the number of components is known, our software can estimate the constitutive end-members and their abundances. When no prior knowledge is available, the software can provide a completely blind solution to estimate the number of components, the end-members and their abundances. The characterization of three case studies validates the performance of the new software: ex-vivo human coronary arteries, human breast cancer cell samples, and in-vivo hamster oral mucosa. The software is freely available in a hosted webpage by one of the developing institutions, and allows the user a quick, easy-to-use and efficient tool for multi/hyper-spectral data decomposition. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Integration of a Decentralized Linear-Quadratic-Gaussian Control into GSFC's Universal 3-D Autonomous Formation Flying Algorithm

NASA Technical Reports Server (NTRS)

Folta, David C.; Carpenter, J. Russell

1999-01-01

A decentralized control is investigated for applicability to the autonomous formation flying control algorithm developed by GSFC for the New Millenium Program Earth Observer-1 (EO-1) mission. This decentralized framework has the following characteristics: The approach is non-hierarchical, and coordination by a central supervisor is not required; Detected failures degrade the system performance gracefully; Each node in the decentralized network processes only its own measurement data, in parallel with the other nodes; Although the total computational burden over the entire network is greater than it would be for a single, centralized controller, fewer computations are required locally at each node; Requirements for data transmission between nodes are limited to only the dimension of the control vector, at the cost of maintaining a local additional data vector. The data vector compresses all past measurement history from all the nodes into a single vector of the dimension of the state; and The approach is optimal with respect to standard cost functions. The current approach is valid for linear time-invariant systems only. Similar to the GSFC formation flying algorithm, the extension to linear LQG time-varying systems requires that each node propagate its filter covariance forward (navigation) and controller Riccati matrix backward (guidance) at each time step. Extension of the GSFC algorithm to non-linear systems can also be accomplished via linearization about a reference trajectory in the standard fashion, or linearization about the current state estimate as with the extended Kalman filter. To investigate the feasibility of the decentralized integration with the GSFC algorithm, an existing centralized LQG design for a single spacecraft orbit control problem is adapted to the decentralized framework while using the GSFC algorithm's state transition matrices and framework. The existing GSFC design uses both reference trajectories of each spacecraft in formation and

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

NASA Technical Reports Server (NTRS)

Cooper, D. B.; Yalabik, N.

1975-01-01

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

The Mystical "Quadratic Formula."

ERIC Educational Resources Information Center

March, Robert H.

1993-01-01

Uses projectile motion to explain the two roots found when using the quadratic formula. An example is provided for finding the time of flight for a projectile which has a negative root implying a negative time of flight. This negative time of flight also has a useful physical meaning. (MVL)

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.

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…

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.

Algorithms and programming tools for image processing on the MPP, part 2

NASA Technical Reports Server (NTRS)

Reeves, Anthony P.

1986-01-01

A number of algorithms were developed for image warping and pyramid image filtering. Techniques were investigated for the parallel processing of a large number of independent irregular shaped regions on the MPP. In addition some utilities for dealing with very long vectors and for sorting were developed. Documentation pages for the algorithms which are available for distribution are given. The performance of the MPP for a number of basic data manipulations was determined. From these results it is possible to predict the efficiency of the MPP for a number of algorithms and applications. The Parallel Pascal development system, which is a portable programming environment for the MPP, was improved and better documentation including a tutorial was written. This environment allows programs for the MPP to be developed on any conventional computer system; it consists of a set of system programs and a library of general purpose Parallel Pascal functions. The algorithms were tested on the MPP and a presentation on the development system was made to the MPP users group. The UNIX version of the Parallel Pascal System was distributed to a number of new sites.

A computational algorithm for spacecraft control and momentum management

NASA Technical Reports Server (NTRS)

Dzielski, John; Bergmann, Edward; Paradiso, Joseph

1990-01-01

Developments in the area of nonlinear control theory have shown how coordinate changes in the state and input spaces of a dynamical system can be used to transform certain nonlinear differential equations into equivalent linear equations. These techniques are applied to the control of a spacecraft equipped with momentum exchange devices. An optimal control problem is formulated that incorporates a nonlinear spacecraft model. An algorithm is developed for solving the optimization problem using feedback linearization to transform to an equivalent problem involving a linear dynamical constraint and a functional approximation technique to solve for the linear dynamics in terms of the control. The original problem is transformed into an unconstrained nonlinear quadratic program that yields an approximate solution to the original problem. Two examples are presented to illustrate the results.

Fast algorithms for transforming back and forth between a signed permutation and its equivalent simple permutation.

PubMed

Gog, Simon; Bader, Martin

2008-10-01

The problem of sorting signed permutations by reversals is a well-studied problem in computational biology. The first polynomial time algorithm was presented by Hannenhalli and Pevzner in 1995. The algorithm was improved several times, and nowadays the most efficient algorithm has a subquadratic running time. Simple permutations played an important role in the development of these algorithms. Although the latest result of Tannier et al. does not require simple permutations, the preliminary version of their algorithm as well as the first polynomial time algorithm of Hannenhalli and Pevzner use the structure of simple permutations. More precisely, the latter algorithms require a precomputation that transforms a permutation into an equivalent simple permutation. To the best of our knowledge, all published algorithms for this transformation have at least a quadratic running time. For further investigations on genome rearrangement problems, the existence of a fast algorithm for the transformation could be crucial. Another important task is the back transformation, i.e. if we have a sorting on the simple permutation, transform it into a sorting on the original permutation. Again, the naive approach results in an algorithm with quadratic running time. In this paper, we present a linear time algorithm for transforming a permutation into an equivalent simple permutation, and an O(n log n) algorithm for the back transformation of the sorting sequence.

Analysis of Maneuvering Targets with Complex Motions by Two-Dimensional Product Modified Lv's Distribution for Quadratic Frequency Modulation Signals.

PubMed

Jing, Fulong; Jiao, Shuhong; Hou, Changbo; Si, Weijian; Wang, Yu

2017-06-21

For targets with complex motion, such as ships fluctuating with oceanic waves and high maneuvering airplanes, azimuth echo signals can be modeled as multicomponent quadratic frequency modulation (QFM) signals after migration compensation and phase adjustment. For the QFM signal model, the chirp rate (CR) and the quadratic chirp rate (QCR) are two important physical quantities, which need to be estimated. For multicomponent QFM signals, the cross terms create a challenge for detection, which needs to be addressed. In this paper, by employing a novel multi-scale parametric symmetric self-correlation function (PSSF) and modified scaled Fourier transform (mSFT), an effective parameter estimation algorithm is proposed-referred to as the Two-Dimensional product modified Lv's distribution (2D-PMLVD)-for QFM signals. The 2D-PMLVD is simple and can be easily implemented by using fast Fourier transform (FFT) and complex multiplication. These measures are analyzed in the paper, including the principle, the cross term, anti-noise performance, and computational complexity. Compared to the other three representative methods, the 2D-PMLVD can achieve better anti-noise performance. The 2D-PMLVD, which is free of searching and has no identifiability problems, is more suitable for multicomponent situations. Through several simulations and analyses, the effectiveness of the proposed estimation algorithm is verified.

Local multiplicative Schwarz algorithms for convection-diffusion equations

NASA Technical Reports Server (NTRS)

Cai, Xiao-Chuan; Sarkis, Marcus

1995-01-01

We develop a new class of overlapping Schwarz type algorithms for solving scalar convection-diffusion equations discretized by finite element or finite difference methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. The ordering of the subdomain preconditioners is determined by considering the direction of the flow. We prove that the algorithms are optimal in the sense that the convergence rates are independent of the mesh size, as well as the number of subdomains. We show by numerical examples that the new algorithms are less sensitive to the direction of the flow than either the classical multiplicative Schwarz algorithms, and converge faster than the additive Schwarz algorithms. Thus, the new algorithms are more suitable for fluid flow applications than the classical additive or multiplicative Schwarz algorithms.

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)

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.

Optimally stopped variational quantum algorithms

NASA Astrophysics Data System (ADS)

Vinci, Walter; Shabani, Alireza

2018-04-01

Quantum processors promise a paradigm shift in high-performance computing which needs to be assessed by accurate benchmarking measures. In this article, we introduce a benchmark for the variational quantum algorithm (VQA), recently proposed as a heuristic algorithm for small-scale quantum processors. In VQA, a classical optimization algorithm guides the processor's quantum dynamics to yield the best solution for a given problem. A complete assessment of the scalability and competitiveness of VQA should take into account both the quality and the time of dynamics optimization. The method of optimal stopping, employed here, provides such an assessment by explicitly including time as a cost factor. Here, we showcase this measure for benchmarking VQA as a solver for some quadratic unconstrained binary optimization. Moreover, we show that a better choice for the cost function of the classical routine can significantly improve the performance of the VQA algorithm and even improve its scaling properties.

AI-BL1.0: a program for automatic on-line beamline optimization using the evolutionary algorithm.

PubMed

Xi, Shibo; Borgna, Lucas Santiago; Zheng, Lirong; Du, Yonghua; Hu, Tiandou

2017-01-01

In this report, AI-BL1.0, an open-source Labview-based program for automatic on-line beamline optimization, is presented. The optimization algorithms used in the program are Genetic Algorithm and Differential Evolution. Efficiency was improved by use of a strategy known as Observer Mode for Evolutionary Algorithm. The program was constructed and validated at the XAFCA beamline of the Singapore Synchrotron Light Source and 1W1B beamline of the Beijing Synchrotron Radiation Facility.

An Atmospheric Guidance Algorithm Testbed for the Mars Surveyor Program 2001 Orbiter and Lander

NASA Technical Reports Server (NTRS)

Striepe, Scott A.; Queen, Eric M.; Powell, Richard W.; Braun, Robert D.; Cheatwood, F. McNeil; Aguirre, John T.; Sachi, Laura A.; Lyons, Daniel T.

1998-01-01

An Atmospheric Flight Team was formed by the Mars Surveyor Program '01 mission office to develop aerocapture and precision landing testbed simulations and candidate guidance algorithms. Three- and six-degree-of-freedom Mars atmospheric flight simulations have been developed for testing, evaluation, and analysis of candidate guidance algorithms for the Mars Surveyor Program 2001 Orbiter and Lander. These simulations are built around the Program to Optimize Simulated Trajectories. Subroutines were supplied by Atmospheric Flight Team members for modeling the Mars atmosphere, spacecraft control system, aeroshell aerodynamic characteristics, and other Mars 2001 mission specific models. This paper describes these models and their perturbations applied during Monte Carlo analyses to develop, test, and characterize candidate guidance algorithms.

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…

Performance comparison of genetic algorithms and particle swarm optimization for model integer programming bus timetabling problem

NASA Astrophysics Data System (ADS)

Wihartiko, F. D.; Wijayanti, H.; Virgantari, F.

2018-03-01

Genetic Algorithm (GA) is a common algorithm used to solve optimization problems with artificial intelligence approach. Similarly, the Particle Swarm Optimization (PSO) algorithm. Both algorithms have different advantages and disadvantages when applied to the case of optimization of the Model Integer Programming for Bus Timetabling Problem (MIPBTP), where in the case of MIPBTP will be found the optimal number of trips confronted with various constraints. The comparison results show that the PSO algorithm is superior in terms of complexity, accuracy, iteration and program simplicity in finding the optimal solution.

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

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.

A parallel variable metric optimization algorithm

NASA Technical Reports Server (NTRS)

Straeter, T. A.

1973-01-01

An algorithm, designed to exploit the parallel computing or vector streaming (pipeline) capabilities of computers is presented. When p is the degree of parallelism, then one cycle of the parallel variable metric algorithm is defined as follows: first, the function and its gradient are computed in parallel at p different values of the independent variable; then the metric is modified by p rank-one corrections; and finally, a single univariant minimization is carried out in the Newton-like direction. Several properties of this algorithm are established. The convergence of the iterates to the solution is proved for a quadratic functional on a real separable Hilbert space. For a finite-dimensional space the convergence is in one cycle when p equals the dimension of the space. Results of numerical experiments indicate that the new algorithm will exploit parallel or pipeline computing capabilities to effect faster convergence than serial techniques.

Binary Inspiral in Quadratic Gravity

NASA Astrophysics Data System (ADS)

Yagi, Kent

2015-01-01

Quadratic gravity is a general class of quantum-gravity-inspired theories, where the Einstein-Hilbert action is extended through the addition of all terms quadratic in the curvature tensor coupled to a scalar field. In this article, we focus on the scalar Gauss- Bonnet (sGB) theory and consider the black hole binary inspiral in this theory. By applying the post-Newtonian (PN) formalism, we found that there is a scalar dipole radiation which leads to -1PN correction in the energy flux relative to gravitational radiation in general relativity. From the orbital decay rate of a low-mass X-ray binary A0600-20, we obtain the bound that is six orders of magnitude stronger than the current solar system bound. Furthermore, we show that the excess in the orbital decay rate of XTE J1118+480 can be explained by the scalar radiation in sGB theory.

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.)

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…

Artificial intelligence programming with LabVIEW: genetic algorithms for instrumentation control and optimization.

PubMed

Moore, J H

1995-06-01

A genetic algorithm for instrumentation control and optimization was developed using the LabVIEW graphical programming environment. The usefulness of this methodology for the optimization of a closed loop control instrument is demonstrated with minimal complexity and the programming is presented in detail to facilitate its adaptation to other LabVIEW applications. Closed loop control instruments have variety of applications in the biomedical sciences including the regulation of physiological processes such as blood pressure. The program presented here should provide a useful starting point for those wishing to incorporate genetic algorithm approaches to LabVIEW mediated optimization of closed loop control instruments.

An O({radical}nL) primal-dual affine scaling algorithm for linear programming

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

Huang, Siming

1994-12-31

We present a new primal-dual affine scaling algorithm for linear programming. The search direction of the algorithm is a combination of classical affine scaling direction of Dikin and a recent new affine scaling direction of Jansen, Roos and Terlaky. The algorithm has an iteration complexity of O({radical}nL), comparing to O(nL) complexity of Jansen, Roos and Terlaky.

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

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.

The Impact of Online Algorithm Visualization on ICT Students' Achievements in Introduction to Programming Course

ERIC Educational Resources Information Center

Saltan, Fatih

2017-01-01

Online Algorithm Visualization (OAV) is one of the recent developments in the instructional technology field that aims to help students handle difficulties faced when they begin to learn programming. This study aims to investigate the effect of online algorithm visualization on students' achievement in the introduction to programming course. To…

Algorithm for constructing the programmed motion of a bounding vehicle for the flight phase

NASA Technical Reports Server (NTRS)

Lapshin, V. V.

1979-01-01

The construction of the programmed motion of a multileg bounding vehicle in the flight was studied. An algorithm is given for solving the boundary value problem for constructing this programmed motion. If the motion is shown to be symmetrical, a simplified use of the algorithm can be applied. A method is proposed for nonimpact of the legs during lift-off of the vehicle, and for softness at touchdown. Tables are utilized to construct this programmed motion over a broad set of standard motion conditions.

A GPU-accelerated 3D Coupled Sub-sample Estimation Algorithm for Volumetric Breast Strain Elastography

PubMed Central

Peng, Bo; Wang, Yuqi; Hall, Timothy J; Jiang, Jingfeng

2017-01-01

Our primary objective of this work was to extend a previously published 2D coupled sub-sample tracking algorithm for 3D speckle tracking in the framework of ultrasound breast strain elastography. In order to overcome heavy computational cost, we investigated the use of a graphic processing unit (GPU) to accelerate the 3D coupled sub-sample speckle tracking method. The performance of the proposed GPU implementation was tested using a tissue-mimicking (TM) phantom and in vivo breast ultrasound data. The performance of this 3D sub-sample tracking algorithm was compared with the conventional 3D quadratic sub-sample estimation algorithm. On the basis of these evaluations, we concluded that the GPU implementation of this 3D sub-sample estimation algorithm can provide high-quality strain data (i.e. high correlation between the pre- and the motion-compensated post-deformation RF echo data and high contrast-to-noise ratio strain images), as compared to the conventional 3D quadratic sub-sample algorithm. Using the GPU implementation of the 3D speckle tracking algorithm, volumetric strain data can be achieved relatively fast (approximately 20 seconds per volume [2.5 cm × 2.5 cm × 2.5 cm]). PMID:28166493

A Program Complexity Metric Based on Variable Usage for Algorithmic Thinking Education of Novice Learners

ERIC Educational Resources Information Center

Fuwa, Minori; Kayama, Mizue; Kunimune, Hisayoshi; Hashimoto, Masami; Asano, David K.

2015-01-01

We have explored educational methods for algorithmic thinking for novices and implemented a block programming editor and a simple learning management system. In this paper, we propose a program/algorithm complexity metric specified for novice learners. This metric is based on the variable usage in arithmetic and relational formulas in learner's…

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.

Online Quadrat Study - Site Index

Science.gov Websites

Study Project - Prairie Advocates Project ) Background Information - Data Collection and Entry - Data Data Entry Data Summaries and Graphs Quadrat Study Poster for your classroom. Directions for Looking at by Prairie Study Prairie Experts For Non-Fermilab Prairie researchers: Complete step-by-step

A Circuit-Based Quantum Algorithm Driven by Transverse Fields for Grover's Problem

NASA Technical Reports Server (NTRS)

Jiang, Zhang; Rieffel, Eleanor G.; Wang, Zhihui

2017-01-01

We designed a quantum search algorithm, giving the same quadratic speedup achieved by Grover's original algorithm; we replace Grover's diffusion operator (hard to implement) with a product diffusion operator generated by transverse fields (easy to implement). In our algorithm, the problem Hamiltonian (oracle) and the transverse fields are applied to the system alternatively. We construct such a sequence that the corresponding unitary generates a closed transition between the initial state (even superposition of all states) and a modified target state, which has a high degree of overlap with the original target state.

The Psychopharmacology Algorithm Project at the Harvard South Shore Program: An Algorithm for Generalized Anxiety Disorder.

PubMed

Abejuela, Harmony Raylen; Osser, David N

2016-01-01

This revision of previous algorithms for the pharmacotherapy of generalized anxiety disorder was developed by the Psychopharmacology Algorithm Project at the Harvard South Shore Program. Algorithms from 1999 and 2010 and associated references were reevaluated. Newer studies and reviews published from 2008-14 were obtained from PubMed and analyzed with a focus on their potential to justify changes in the recommendations. Exceptions to the main algorithm for special patient populations, such as women of childbearing potential, pregnant women, the elderly, and those with common medical and psychiatric comorbidities, were considered. Selective serotonin reuptake inhibitors (SSRIs) are still the basic first-line medication. Early alternatives include duloxetine, buspirone, hydroxyzine, pregabalin, or bupropion, in that order. If response is inadequate, then the second recommendation is to try a different SSRI. Additional alternatives now include benzodiazepines, venlafaxine, kava, and agomelatine. If the response to the second SSRI is unsatisfactory, then the recommendation is to try a serotonin-norepinephrine reuptake inhibitor (SNRI). Other alternatives to SSRIs and SNRIs for treatment-resistant or treatment-intolerant patients include tricyclic antidepressants, second-generation antipsychotics, and valproate. This revision of the GAD algorithm responds to issues raised by new treatments under development (such as pregabalin) and organizes the evidence systematically for practical clinical application.

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.

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.

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…

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.

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.

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…

A wavelet-based adaptive fusion algorithm of infrared polarization imaging

NASA Astrophysics Data System (ADS)

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

2011-08-01

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

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)

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

Dose algorithm for EXTRAD 4100S extremity dosimeter for use at Sandia National Laboratories.

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

Potter, Charles Augustus

An updated algorithm for the EXTRAD 4100S extremity dosimeter has been derived. This algorithm optimizes the binning of dosimeter element ratios and uses a quadratic function to determine the response factors for low response ratios. This results in lower systematic bias across all test categories and eliminates the need for the 'red strap' algorithm that was used for high energy beta/gamma emitting radionuclides. The Radiation Protection Dosimetry Program (RPDP) at Sandia National Laboratories uses the Thermo Fisher EXTRAD 4100S extremity dosimeter, shown in Fig 1.1 to determine shallow dose to the extremities of potentially exposed individuals. This dosimeter consists ofmore » two LiF TLD elements or 'chipstrates', one of TLD-700 ({sup 7}Li) and one of TLD-100 (natural Li) separated by a tin filter. Following readout and background subtraction, the ratio of the responses of the two elements is determined defining the penetrability of the incident radiation. While this penetrability approximates the incident energy of the radiation, X-rays and beta particles exist in energy distributions that make determination of dose conversion factors less straightforward in their determination.« less

A ’Multiple Pivoting’ Algorithm for Goal-Interval Programming Formulations.

DTIC Science & Technology

1980-03-01

jotso _P- ,- Research Report CCS 355 A "MULTIPLE PIVOTING" ALGORITHM FOR GOAL-INTERVAL PROGRAMMING FORMULATIONS by R. Armstrong* A. Charnes*W. Cook...J. Godfrey*** March 1980 *The University of Texas at Austin **York University, Downsview, Ontario, Canada ***Washington, DC This research was partly...areas. However, the main direction of goal programing research has been in formulating models instead of seeking procedures that would provide

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.

Universal algorithms and programs for calculating the motion parameters in the two-body problem

NASA Technical Reports Server (NTRS)

Bakhshiyan, B. T.; Sukhanov, A. A.

1979-01-01

The algorithms and FORTRAN programs for computing positions and velocities, orbital elements and first and second partial derivatives in the two-body problem are presented. The algorithms are applicable for any value of eccentricity and are convenient for computing various navigation parameters.

Optimization and experimental realization of the quantum permutation algorithm

NASA Astrophysics Data System (ADS)

Yalçınkaya, I.; Gedik, Z.

2017-12-01

The quantum permutation algorithm provides computational speed-up over classical algorithms for determining the parity of a given cyclic permutation. For its n -qubit implementations, the number of required quantum gates scales quadratically with n due to the quantum Fourier transforms included. We show here for the n -qubit case that the algorithm can be simplified so that it requires only O (n ) quantum gates, which theoretically reduces the complexity of the implementation. To test our results experimentally, we utilize IBM's 5-qubit quantum processor to realize the algorithm by using the original and simplified recipes for the 2-qubit case. It turns out that the latter results in a significantly higher success probability which allows us to verify the algorithm more precisely than the previous experimental realizations. We also verify the algorithm for the first time for the 3-qubit case with a considerable success probability by taking the advantage of our simplified scheme.

Quadratic spatial soliton interactions

NASA Astrophysics Data System (ADS)

Jankovic, Ladislav

Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30

Fixed-point image orthorectification algorithms for reduced computational cost

NASA Astrophysics Data System (ADS)

French, Joseph Clinton

Imaging systems have been applied to many new applications in recent years. With the advent of low-cost, low-power focal planes and more powerful, lower cost computers, remote sensing applications have become more wide spread. Many of these applications require some form of geolocation, especially when relative distances are desired. However, when greater global positional accuracy is needed, orthorectification becomes necessary. Orthorectification is the process of projecting an image onto a Digital Elevation Map (DEM), which removes terrain distortions and corrects the perspective distortion by changing the viewing angle to be perpendicular to the projection plane. Orthorectification is used in disaster tracking, landscape management, wildlife monitoring and many other applications. However, orthorectification is a computationally expensive process due to floating point operations and divisions in the algorithm. To reduce the computational cost of on-board processing, two novel algorithm modifications are proposed. One modification is projection utilizing fixed-point arithmetic. Fixed point arithmetic removes the floating point operations and reduces the processing time by operating only on integers. The second modification is replacement of the division inherent in projection with a multiplication of the inverse. The inverse must operate iteratively. Therefore, the inverse is replaced with a linear approximation. As a result of these modifications, the processing time of projection is reduced by a factor of 1.3x with an average pixel position error of 0.2% of a pixel size for 128-bit integer processing and over 4x with an average pixel position error of less than 13% of a pixel size for a 64-bit integer processing. A secondary inverse function approximation is also developed that replaces the linear approximation with a quadratic. The quadratic approximation produces a more accurate approximation of the inverse, allowing for an integer multiplication calculation

A reliable algorithm for optimal control synthesis

NASA Technical Reports Server (NTRS)

Vansteenwyk, Brett; Ly, Uy-Loi

1992-01-01

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

A compressed sensing based 3D resistivity inversion algorithm for hydrogeological applications

NASA Astrophysics Data System (ADS)

Ranjan, Shashi; Kambhammettu, B. V. N. P.; Peddinti, Srinivasa Rao; Adinarayana, J.

2018-04-01

Image reconstruction from discrete electrical responses pose a number of computational and mathematical challenges. Application of smoothness constrained regularized inversion from limited measurements may fail to detect resistivity anomalies and sharp interfaces separated by hydro stratigraphic units. Under favourable conditions, compressed sensing (CS) can be thought of an alternative to reconstruct the image features by finding sparse solutions to highly underdetermined linear systems. This paper deals with the development of a CS assisted, 3-D resistivity inversion algorithm for use with hydrogeologists and groundwater scientists. CS based l1-regularized least square algorithm was applied to solve the resistivity inversion problem. Sparseness in the model update vector is introduced through block oriented discrete cosine transformation, with recovery of the signal achieved through convex optimization. The equivalent quadratic program was solved using primal-dual interior point method. Applicability of the proposed algorithm was demonstrated using synthetic and field examples drawn from hydrogeology. The proposed algorithm has outperformed the conventional (smoothness constrained) least square method in recovering the model parameters with much fewer data, yet preserving the sharp resistivity fronts separated by geologic layers. Resistivity anomalies represented by discrete homogeneous blocks embedded in contrasting geologic layers were better imaged using the proposed algorithm. In comparison to conventional algorithm, CS has resulted in an efficient (an increase in R2 from 0.62 to 0.78; a decrease in RMSE from 125.14 Ω-m to 72.46 Ω-m), reliable, and fast converging (run time decreased by about 25%) solution.

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

NASA Astrophysics Data System (ADS)

Li, Yongzhe; Vorobyov, Sergiy A.

2018-03-01

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

Concurrent extensions to the FORTRAN language for parallel programming of computational fluid dynamics algorithms

NASA Technical Reports Server (NTRS)

Weeks, Cindy Lou

1986-01-01

Experiments were conducted at NASA Ames Research Center to define multi-tasking software requirements for multiple-instruction, multiple-data stream (MIMD) computer architectures. The focus was on specifying solutions for algorithms in the field of computational fluid dynamics (CFD). The program objectives were to allow researchers to produce usable parallel application software as soon as possible after acquiring MIMD computer equipment, to provide researchers with an easy-to-learn and easy-to-use parallel software language which could be implemented on several different MIMD machines, and to enable researchers to list preferred design specifications for future MIMD computer architectures. Analysis of CFD algorithms indicated that extensions of an existing programming language, adaptable to new computer architectures, provided the best solution to meeting program objectives. The CoFORTRAN Language was written in response to these objectives and to provide researchers a means to experiment with parallel software solutions to CFD algorithms on machines with parallel architectures.

The psychopharmacology algorithm project at the Harvard South Shore Program: an algorithm for acute mania.

PubMed

Mohammad, Othman; Osser, David N

2014-01-01

This new algorithm for the pharmacotherapy of acute mania was developed by the Psychopharmacology Algorithm Project at the Harvard South Shore Program. The authors conducted a literature search in PubMed and reviewed key studies, other algorithms and guidelines, and their references. Treatments were prioritized considering three main considerations: (1) effectiveness in treating the current episode, (2) preventing potential relapses to depression, and (3) minimizing side effects over the short and long term. The algorithm presupposes that clinicians have made an accurate diagnosis, decided how to manage contributing medical causes (including substance misuse), discontinued antidepressants, and considered the patient's childbearing potential. We propose different algorithms for mixed and nonmixed mania. Patients with mixed mania may be treated first with a second-generation antipsychotic, of which the first choice is quetiapine because of its greater efficacy for depressive symptoms and episodes in bipolar disorder. Valproate and then either lithium or carbamazepine may be added. For nonmixed mania, lithium is the first-line recommendation. A second-generation antipsychotic can be added. Again, quetiapine is favored, but if quetiapine is unacceptable, risperidone is the next choice. Olanzapine is not considered a first-line treatment due to its long-term side effects, but it could be second-line. If the patient, whether mixed or nonmixed, is still refractory to the above medications, then depending on what has already been tried, consider carbamazepine, haloperidol, olanzapine, risperidone, and valproate first tier; aripiprazole, asenapine, and ziprasidone second tier; and clozapine third tier (because of its weaker evidence base and greater side effects). Electroconvulsive therapy may be considered at any point in the algorithm if the patient has a history of positive response or is intolerant of medications.

Enhancements on the Convex Programming Based Powered Descent Guidance Algorithm for Mars Landing

NASA Technical Reports Server (NTRS)

Acikmese, Behcet; Blackmore, Lars; Scharf, Daniel P.; Wolf, Aron

2008-01-01

In this paper, we present enhancements on the powered descent guidance algorithm developed for Mars pinpoint landing. The guidance algorithm solves the powered descent minimum fuel trajectory optimization problem via a direct numerical method. Our main contribution is to formulate the trajectory optimization problem, which has nonconvex control constraints, as a finite dimensional convex optimization problem, specifically as a finite dimensional second order cone programming (SOCP) problem. SOCP is a subclass of convex programming, and there are efficient SOCP solvers with deterministic convergence properties. Hence, the resulting guidance algorithm can potentially be implemented onboard a spacecraft for real-time applications. Particularly, this paper discusses the algorithmic improvements obtained by: (i) Using an efficient approach to choose the optimal time-of-flight; (ii) Using a computationally inexpensive way to detect the feasibility/ infeasibility of the problem due to the thrust-to-weight constraint; (iii) Incorporating the rotation rate of the planet into the problem formulation; (iv) Developing additional constraints on the position and velocity to guarantee no-subsurface flight between the time samples of the temporal discretization; (v) Developing a fuel-limited targeting algorithm; (vi) Initial result on developing an onboard table lookup method to obtain almost fuel optimal solutions in real-time.

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

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.)

Facial Affect Recognition Using Regularized Discriminant Analysis-Based Algorithms

NASA Astrophysics Data System (ADS)

Lee, Chien-Cheng; Huang, Shin-Sheng; Shih, Cheng-Yuan

2010-12-01

This paper presents a novel and effective method for facial expression recognition including happiness, disgust, fear, anger, sadness, surprise, and neutral state. The proposed method utilizes a regularized discriminant analysis-based boosting algorithm (RDAB) with effective Gabor features to recognize the facial expressions. Entropy criterion is applied to select the effective Gabor feature which is a subset of informative and nonredundant Gabor features. The proposed RDAB algorithm uses RDA as a learner in the boosting algorithm. The RDA combines strengths of linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA). It solves the small sample size and ill-posed problems suffered from QDA and LDA through a regularization technique. Additionally, this study uses the particle swarm optimization (PSO) algorithm to estimate optimal parameters in RDA. Experiment results demonstrate that our approach can accurately and robustly recognize facial expressions.

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.

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.

Fast intersection detection algorithm for PC-based robot off-line programming

NASA Astrophysics Data System (ADS)

Fedrowitz, Christian H.

1994-11-01

This paper presents a method for fast and reliable collision detection in complex production cells. The algorithm is part of the PC-based robot off-line programming system of the University of Siegen (Ropsus). The method is based on a solid model which is managed by a simplified constructive solid geometry model (CSG-model). The collision detection problem is divided in two steps. In the first step the complexity of the problem is reduced in linear time. In the second step the remaining solids are tested for intersection. For this the Simplex algorithm, which is known from linear optimization, is used. It computes a point which is common to two convex polyhedra. The polyhedra intersect, if such a point exists. Regarding the simplified geometrical model of Ropsus the algorithm runs also in linear time. In conjunction with the first step a resultant collision detection algorithm is found which requires linear time in all. Moreover it computes the resultant intersection polyhedron using the dual transformation.

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

Geometrical Solutions of Quadratic Equations.

ERIC Educational Resources Information Center

Grewal, A. S.; Godloza, L.

1999-01-01

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

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.

Phase retrieval via incremental truncated amplitude flow algorithm

NASA Astrophysics Data System (ADS)

Zhang, Quanbing; Wang, Zhifa; Wang, Linjie; Cheng, Shichao

2017-10-01

This paper considers the phase retrieval problem of recovering the unknown signal from the given quadratic measurements. A phase retrieval algorithm based on Incremental Truncated Amplitude Flow (ITAF) which combines the ITWF algorithm and the TAF algorithm is proposed. The proposed ITAF algorithm enhances the initialization by performing both of the truncation methods used in ITWF and TAF respectively, and improves the performance in the gradient stage by applying the incremental method proposed in ITWF to the loop stage of TAF. Moreover, the original sampling vector and measurements are preprocessed before initialization according to the variance of the sensing matrix. Simulation experiments verified the feasibility and validity of the proposed ITAF algorithm. The experimental results show that it can obtain higher success rate and faster convergence speed compared with other algorithms. Especially, for the noiseless random Gaussian signals, ITAF can recover any real-valued signal accurately from the magnitude measurements whose number is about 2.5 times of the signal length, which is close to the theoretic limit (about 2 times of the signal length). And it usually converges to the optimal solution within 20 iterations which is much less than the state-of-the-art algorithms.

A pruning algorithm for Meta-blocking based on cumulative weight

NASA Astrophysics Data System (ADS)

Zhang, Fulin; Gao, Zhipeng; Niu, Kun

2017-08-01

Entity Resolution is an important process in data cleaning and data integration. It usually employs a blocking method to avoid the quadratic complexity work when scales to large data sets. Meta-blocking can perform better in the context of highly heterogeneous information spaces. Yet, its precision and efficiency still have room to improve. In this paper, we present a new pruning algorithm for Meta-Blocking. It can achieve a higher precision than the existing WEP algorithm at a small cost of recall. In addition, can reduce the runtime of the blocking process. We evaluate our proposed method over five real-world data sets.

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

Application of a Dynamic Programming Algorithm for Weapon Target Assignment

DTIC Science & Technology

2016-02-01

25] A . Turan , “Techniques for the Allocation of Resources Under Uncertainty,” Middle Eastern Technical University, Ankara, Turkey, 2012. [26] K...UNCLASSIFIED UNCLASSIFIED Application of a Dynamic Programming Algorithm for Weapon Target Assignment Lloyd Hammond Weapons and...optimisation techniques to support the decision making process. This report documents the methodology used to identify, develop and assess a

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

Generation of Non-Homogeneous Poisson Processes by Thinning: Programming Considerations and Comparision with Competing Algorithms.

DTIC Science & Technology

1978-12-01

Poisson processes . The method is valid for Poisson processes with any given intensity function. The basic thinning algorithm is modified to exploit several refinements which reduce computer execution time by approximately one-third. The basic and modified thinning programs are compared with the Poisson decomposition and gap-statistics algorithm, which is easily implemented for Poisson processes with intensity functions of the form exp(a sub 0 + a sub 1t + a sub 2 t-squared. The thinning programs are competitive in both execution

Quadratic canonical transformation theory and higher order density matrices.

PubMed

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

2009-03-28

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

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.

Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

DOE PAGES

Gade, Dinakar; Hackebeil, Gabriel; Ryan, Sarah M.; ...

2016-04-02

We present a method for computing lower bounds in the progressive hedging algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using dual prices that are calculated during execution of the standard PHA. In conclusion, we report computational results on stochastic unit commitment and stochastic server location problem instances, and explore the relationship between key PHA parameters and the quality of the resulting lower bounds.

A split finite element algorithm for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1979-01-01

An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.

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.

Towards robust algorithms for current deposition and dynamic load-balancing in a GPU particle in cell code

NASA Astrophysics Data System (ADS)

Rossi, Francesco; Londrillo, Pasquale; Sgattoni, Andrea; Sinigardi, Stefano; Turchetti, Giorgio

2012-12-01

We present `jasmine', an implementation of a fully relativistic, 3D, electromagnetic Particle-In-Cell (PIC) code, capable of running simulations in various laser plasma acceleration regimes on Graphics-Processing-Units (GPUs) HPC clusters. Standard energy/charge preserving FDTD-based algorithms have been implemented using double precision and quadratic (or arbitrary sized) shape functions for the particle weighting. When porting a PIC scheme to the GPU architecture (or, in general, a shared memory environment), the particle-to-grid operations (e.g. the evaluation of the current density) require special care to avoid memory inconsistencies and conflicts. Here we present a robust implementation of this operation that is efficient for any number of particles per cell and particle shape function order. Our algorithm exploits the exposed GPU memory hierarchy and avoids the use of atomic operations, which can hurt performance especially when many particles lay on the same cell. We show the code multi-GPU scalability results and present a dynamic load-balancing algorithm. The code is written using a python-based C++ meta-programming technique which translates in a high level of modularity and allows for easy performance tuning and simple extension of the core algorithms to various simulation schemes.

CALIBRATION, OPTIMIZATION, AND SENSITIVITY AND UNCERTAINTY ALGORITHMS APPLICATION PROGRAMMING INTERFACE (COSU-API)

EPA Science Inventory

The Application Programming Interface (API) for Uncertainty Analysis, Sensitivity Analysis, and Parameter Estimation (UA/SA/PE API) tool development, here fore referred to as the Calibration, Optimization, and Sensitivity and Uncertainty Algorithms API (COSU-API), was initially d...

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.

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.

Curious Consequences of a Miscopied Quadratic

ERIC Educational Resources Information Center

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

2005-01-01

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

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.

Recursive algorithms for phylogenetic tree counting.

PubMed

Gavryushkina, Alexandra; Welch, David; Drummond, Alexei J

2013-10-28

In Bayesian phylogenetic inference we are interested in distributions over a space of trees. The number of trees in a tree space is an important characteristic of the space and is useful for specifying prior distributions. When all samples come from the same time point and no prior information available on divergence times, the tree counting problem is easy. However, when fossil evidence is used in the inference to constrain the tree or data are sampled serially, new tree spaces arise and counting the number of trees is more difficult. We describe an algorithm that is polynomial in the number of sampled individuals for counting of resolutions of a constraint tree assuming that the number of constraints is fixed. We generalise this algorithm to counting resolutions of a fully ranked constraint tree. We describe a quadratic algorithm for counting the number of possible fully ranked trees on n sampled individuals. We introduce a new type of tree, called a fully ranked tree with sampled ancestors, and describe a cubic time algorithm for counting the number of such trees on n sampled individuals. These algorithms should be employed for Bayesian Markov chain Monte Carlo inference when fossil data are included or data are serially sampled.

Correlation signatures of wet soils and snows. [algorithm development and computer programming

NASA Technical Reports Server (NTRS)

Phillips, M. R.

1972-01-01

Interpretation, analysis, and development of algorithms have provided the necessary computational programming tools for soil data processing, data handling and analysis. Algorithms that have been developed thus far, are adequate and have been proven successful for several preliminary and fundamental applications such as software interfacing capabilities, probability distributions, grey level print plotting, contour plotting, isometric data displays, joint probability distributions, boundary mapping, channel registration and ground scene classification. A description of an Earth Resources Flight Data Processor, (ERFDP), which handles and processes earth resources data under a users control is provided.

Dynamic programming and graph algorithms in computer vision.

PubMed

Felzenszwalb, Pedro F; Zabih, Ramin

2011-04-01

Optimization is a powerful paradigm for expressing and solving problems in a wide range of areas, and has been successfully applied to many vision problems. Discrete optimization techniques are especially interesting since, by carefully exploiting problem structure, they often provide nontrivial guarantees concerning solution quality. In this paper, we review dynamic programming and graph algorithms, and discuss representative examples of how these discrete optimization techniques have been applied to some classical vision problems. We focus on the low-level vision problem of stereo, the mid-level problem of interactive object segmentation, and the high-level problem of model-based recognition.

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…

Filtered gradient reconstruction algorithm for compressive spectral imaging

NASA Astrophysics Data System (ADS)

Mejia, Yuri; Arguello, Henry

2017-04-01

Compressive sensing matrices are traditionally based on random Gaussian and Bernoulli entries. Nevertheless, they are subject to physical constraints, and their structure unusually follows a dense matrix distribution, such as the case of the matrix related to compressive spectral imaging (CSI). The CSI matrix represents the integration of coded and shifted versions of the spectral bands. A spectral image can be recovered from CSI measurements by using iterative algorithms for linear inverse problems that minimize an objective function including a quadratic error term combined with a sparsity regularization term. However, current algorithms are slow because they do not exploit the structure and sparse characteristics of the CSI matrices. A gradient-based CSI reconstruction algorithm, which introduces a filtering step in each iteration of a conventional CSI reconstruction algorithm that yields improved image quality, is proposed. Motivated by the structure of the CSI matrix, Φ, this algorithm modifies the iterative solution such that it is forced to converge to a filtered version of the residual ΦTy, where y is the compressive measurement vector. We show that the filtered-based algorithm converges to better quality performance results than the unfiltered version. Simulation results highlight the relative performance gain over the existing iterative algorithms.

Approximate Algorithms for Computing Spatial Distance Histograms with Accuracy Guarantees

PubMed Central

Grupcev, Vladimir; Yuan, Yongke; Tu, Yi-Cheng; Huang, Jin; Chen, Shaoping; Pandit, Sagar; Weng, Michael

2014-01-01

Particle simulation has become an important research tool in many scientific and engineering fields. Data generated by such simulations impose great challenges to database storage and query processing. One of the queries against particle simulation data, the spatial distance histogram (SDH) query, is the building block of many high-level analytics, and requires quadratic time to compute using a straightforward algorithm. Previous work has developed efficient algorithms that compute exact SDHs. While beating the naive solution, such algorithms are still not practical in processing SDH queries against large-scale simulation data. In this paper, we take a different path to tackle this problem by focusing on approximate algorithms with provable error bounds. We first present a solution derived from the aforementioned exact SDH algorithm, and this solution has running time that is unrelated to the system size N. We also develop a mathematical model to analyze the mechanism that leads to errors in the basic approximate algorithm. Our model provides insights on how the algorithm can be improved to achieve higher accuracy and efficiency. Such insights give rise to a new approximate algorithm with improved time/accuracy tradeoff. Experimental results confirm our analysis. PMID:24693210

SPARSE: quadratic time simultaneous alignment and folding of RNAs without sequence-based heuristics.

PubMed

Will, Sebastian; Otto, Christina; Miladi, Milad; Möhl, Mathias; Backofen, Rolf

2015-08-01

RNA-Seq experiments have revealed a multitude of novel ncRNAs. The gold standard for their analysis based on simultaneous alignment and folding suffers from extreme time complexity of [Formula: see text]. Subsequently, numerous faster 'Sankoff-style' approaches have been suggested. Commonly, the performance of such methods relies on sequence-based heuristics that restrict the search space to optimal or near-optimal sequence alignments; however, the accuracy of sequence-based methods breaks down for RNAs with sequence identities below 60%. Alignment approaches like LocARNA that do not require sequence-based heuristics, have been limited to high complexity ([Formula: see text] quartic time). Breaking this barrier, we introduce the novel Sankoff-style algorithm 'sparsified prediction and alignment of RNAs based on their structure ensembles (SPARSE)', which runs in quadratic time without sequence-based heuristics. To achieve this low complexity, on par with sequence alignment algorithms, SPARSE features strong sparsification based on structural properties of the RNA ensembles. Following PMcomp, SPARSE gains further speed-up from lightweight energy computation. Although all existing lightweight Sankoff-style methods restrict Sankoff's original model by disallowing loop deletions and insertions, SPARSE transfers the Sankoff algorithm to the lightweight energy model completely for the first time. Compared with LocARNA, SPARSE achieves similar alignment and better folding quality in significantly less time (speedup: 3.7). At similar run-time, it aligns low sequence identity instances substantially more accurate than RAF, which uses sequence-based heuristics. © The Author 2015. Published by Oxford University Press.

Exponential Thurston maps and limits of quadratic differentials

NASA Astrophysics Data System (ADS)

Hubbard, John; Schleicher, Dierk; Shishikura, Mitsuhiro

2009-01-01

We give a topological characterization of postsingularly finite topological exponential maps, i.e., universal covers g\\colon{C}to{C}setminus\\{0\\} such that 0 has a finite orbit. Such a map either is Thurston equivalent to a unique holomorphic exponential map λ e^z or it has a topological obstruction called a degenerate Levy cycle. This is the first analog of Thurston's topological characterization theorem of rational maps, as published by Douady and Hubbard, for the case of infinite degree. One main tool is a theorem about the distribution of mass of an integrable quadratic differential with a given number of poles, providing an almost compact space of models for the entire mass of quadratic differentials. This theorem is given for arbitrary Riemann surfaces of finite type in a uniform way.

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.

Minimum time acceleration of aircraft turbofan engines by using an algorithm based on nonlinear programming

NASA Technical Reports Server (NTRS)

Teren, F.

1977-01-01

Minimum time accelerations of aircraft turbofan engines are presented. The calculation of these accelerations was made by using a piecewise linear engine model, and an algorithm based on nonlinear programming. Use of this model and algorithm allows such trajectories to be readily calculated on a digital computer with a minimal expenditure of computer time.

A tight upper bound for quadratic knapsack problems in grid-based wind farm layout optimization

NASA Astrophysics Data System (ADS)

Quan, Ning; Kim, Harrison M.

2018-03-01

The 0-1 quadratic knapsack problem (QKP) in wind farm layout optimization models possible turbine locations as nodes, and power loss due to wake effects between pairs of turbines as edges in a complete graph. The goal is to select up to a certain number of turbine locations such that the sum of selected node and edge coefficients is maximized. Finding the optimal solution to the QKP is difficult in general, but it is possible to obtain a tight upper bound on the QKP's optimal value which facilitates the use of heuristics to solve QKPs by giving a good estimate of the optimality gap of any feasible solution. This article applies an upper bound method that is especially well-suited to QKPs in wind farm layout optimization due to certain features of the formulation that reduce the computational complexity of calculating the upper bound. The usefulness of the upper bound was demonstrated by assessing the performance of the greedy algorithm for solving QKPs in wind farm layout optimization. The results show that the greedy algorithm produces good solutions within 4% of the optimal value for small to medium sized problems considered in this article.

Penalty dynamic programming algorithm for dim targets detection in sensor systems.

PubMed

Huang, Dayu; Xue, Anke; Guo, Yunfei

2012-01-01

In order to detect and track multiple maneuvering dim targets in sensor systems, an improved dynamic programming track-before-detect algorithm (DP-TBD) called penalty DP-TBD (PDP-TBD) is proposed. The performances of tracking techniques are used as a feedback to the detection part. The feedback is constructed by a penalty term in the merit function, and the penalty term is a function of the possible target state estimation, which can be obtained by the tracking methods. With this feedback, the algorithm combines traditional tracking techniques with DP-TBD and it can be applied to simultaneously detect and track maneuvering dim targets. Meanwhile, a reasonable constraint that a sensor measurement can originate from one target or clutter is proposed to minimize track separation. Thus, the algorithm can be used in the multi-target situation with unknown target numbers. The efficiency and advantages of PDP-TBD compared with two existing methods are demonstrated by several simulations.

Penalty Dynamic Programming Algorithm for Dim Targets Detection in Sensor Systems

PubMed Central

Huang, Dayu; Xue, Anke; Guo, Yunfei

2012-01-01

In order to detect and track multiple maneuvering dim targets in sensor systems, an improved dynamic programming track-before-detect algorithm (DP-TBD) called penalty DP-TBD (PDP-TBD) is proposed. The performances of tracking techniques are used as a feedback to the detection part. The feedback is constructed by a penalty term in the merit function, and the penalty term is a function of the possible target state estimation, which can be obtained by the tracking methods. With this feedback, the algorithm combines traditional tracking techniques with DP-TBD and it can be applied to simultaneously detect and track maneuvering dim targets. Meanwhile, a reasonable constraint that a sensor measurement can originate from one target or clutter is proposed to minimize track separation. Thus, the algorithm can be used in the multi-target situation with unknown target numbers. The efficiency and advantages of PDP-TBD compared with two existing methods are demonstrated by several simulations. PMID:22666074

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

NASA Astrophysics Data System (ADS)

Dobeck, Gerald J.; Cobb, J. Tory

2002-08-01

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

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.

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.

Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Extended Decentralized Linear-Quadratic-Gaussian Control

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2000-01-01

A straightforward extension of a solution to the decentralized linear-Quadratic-Gaussian problem is proposed that allows its use for commonly encountered classes of problems that are currently solved with the extended Kalman filter. This extension allows the system to be partitioned in such a way as to exclude the nonlinearities from the essential algebraic relationships that allow the estimation and control to be optimally decentralized.

Quadratic grating apodized photon sieves for simultaneous multiplane microscopy

NASA Astrophysics Data System (ADS)

Cheng, Yiguang; Zhu, Jiangping; He, Yu; Tang, Yan; Hu, Song; Zhao, Lixin

2017-10-01

We present a new type of imaging device, named quadratic grating apodized photon sieve (QGPS), used as the objective for simultaneous multiplane imaging in X-rays. The proposed QGPS is structured based on the combination of two concepts: photon sieves and quadratic gratings. Its design principles are also expounded in detail. Analysis of imaging properties of QGPS in terms of point-spread function shows that QGPS can image multiple layers within an object field onto a single image plane. Simulated and experimental results in visible light both demonstrate the feasibility of QGPS for simultaneous multiplane imaging, which is extremely promising to detect dynamic specimens by X-ray microscopy in the physical and life sciences.

Investigating Students' Mathematical Difficulties with Quadratic Equations

ERIC Educational Resources Information Center

O'Connor, Bronwyn Reid; Norton, Stephen

2016-01-01

This paper examines the factors that hinder students' success in working with and understanding the mathematics of quadratic equations using a case study analysis of student error patterns. Twenty-five Year 11 students were administered a written test to examine their understanding of concepts and procedures associated with this topic. The…

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.

Dynamic Programming and Graph Algorithms in Computer Vision*

PubMed Central

Felzenszwalb, Pedro F.; Zabih, Ramin

2013-01-01

Optimization is a powerful paradigm for expressing and solving problems in a wide range of areas, and has been successfully applied to many vision problems. Discrete optimization techniques are especially interesting, since by carefully exploiting problem structure they often provide non-trivial guarantees concerning solution quality. In this paper we briefly review dynamic programming and graph algorithms, and discuss representative examples of how these discrete optimization techniques have been applied to some classical vision problems. We focus on the low-level vision problem of stereo; the mid-level problem of interactive object segmentation; and the high-level problem of model-based recognition. PMID:20660950

Error bounds of adaptive dynamic programming algorithms for solving undiscounted optimal control problems.

PubMed

Liu, Derong; Li, Hongliang; Wang, Ding

2015-06-01

In this paper, we establish error bounds of adaptive dynamic programming algorithms for solving undiscounted infinite-horizon optimal control problems of discrete-time deterministic nonlinear systems. We consider approximation errors in the update equations of both value function and control policy. We utilize a new assumption instead of the contraction assumption in discounted optimal control problems. We establish the error bounds for approximate value iteration based on a new error condition. Furthermore, we also establish the error bounds for approximate policy iteration and approximate optimistic policy iteration algorithms. It is shown that the iterative approximate value function can converge to a finite neighborhood of the optimal value function under some conditions. To implement the developed algorithms, critic and action neural networks are used to approximate the value function and control policy, respectively. Finally, a simulation example is given to demonstrate the effectiveness of the developed algorithms.

Optimal reservoir operation policies using novel nested algorithms

NASA Astrophysics Data System (ADS)

Delipetrev, Blagoj; Jonoski, Andreja; Solomatine, Dimitri

2015-04-01

Historically, the two most widely practiced methods for optimal reservoir operation have been dynamic programming (DP) and stochastic dynamic programming (SDP). These two methods suffer from the so called "dual curse" which prevents them to be used in reasonably complex water systems. The first one is the "curse of dimensionality" that denotes an exponential growth of the computational complexity with the state - decision space dimension. The second one is the "curse of modelling" that requires an explicit model of each component of the water system to anticipate the effect of each system's transition. We address the problem of optimal reservoir operation concerning multiple objectives that are related to 1) reservoir releases to satisfy several downstream users competing for water with dynamically varying demands, 2) deviations from the target minimum and maximum reservoir water levels and 3) hydropower production that is a combination of the reservoir water level and the reservoir releases. Addressing such a problem with classical methods (DP and SDP) requires a reasonably high level of discretization of the reservoir storage volume, which in combination with the required releases discretization for meeting the demands of downstream users leads to computationally expensive formulations and causes the curse of dimensionality. We present a novel approach, named "nested" that is implemented in DP, SDP and reinforcement learning (RL) and correspondingly three new algorithms are developed named nested DP (nDP), nested SDP (nSDP) and nested RL (nRL). The nested algorithms are composed from two algorithms: 1) DP, SDP or RL and 2) nested optimization algorithm. Depending on the way we formulate the objective function related to deficits in the allocation problem in the nested optimization, two methods are implemented: 1) Simplex for linear allocation problems, and 2) quadratic Knapsack method in the case of nonlinear problems. The novel idea is to include the nested

Quadratic forms involving Green's and Robin functions

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

Dubinin, Vladimir N

2009-10-31

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

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.

Systematic search for wide periodic windows and bounds for the set of regular parameters for the quadratic map.

PubMed

Galias, Zbigniew

2017-05-01

An efficient method to find positions of periodic windows for the quadratic map f(x)=ax(1-x) and a heuristic algorithm to locate the majority of wide periodic windows are proposed. Accurate rigorous bounds of positions of all periodic windows with periods below 37 and the majority of wide periodic windows with longer periods are found. Based on these results, we prove that the measure of the set of regular parameters in the interval [3,4] is above 0.613960137. The properties of periodic windows are studied numerically. The results of the analysis are used to estimate that the true value of the measure of the set of regular parameters is close to 0.6139603.

Quantum algorithm for association rules mining

NASA Astrophysics Data System (ADS)

Yu, Chao-Hua; Gao, Fei; Wang, Qing-Le; Wen, Qiao-Yan

2016-10-01

Association rules mining (ARM) is one of the most important problems in knowledge discovery and data mining. Given a transaction database that has a large number of transactions and items, the task of ARM is to acquire consumption habits of customers by discovering the relationships between itemsets (sets of items). In this paper, we address ARM in the quantum settings and propose a quantum algorithm for the key part of ARM, finding frequent itemsets from the candidate itemsets and acquiring their supports. Specifically, for the case in which there are Mf(k ) frequent k -itemsets in the Mc(k ) candidate k -itemsets (Mf(k )≤Mc(k ) ), our algorithm can efficiently mine these frequent k -itemsets and estimate their supports by using parallel amplitude estimation and amplitude amplification with complexity O (k/√{Mc(k )Mf(k ) } ɛ ) , where ɛ is the error for estimating the supports. Compared with the classical counterpart, i.e., the classical sampling-based algorithm, whose complexity is O (k/Mc(k ) ɛ2) , our quantum algorithm quadratically improves the dependence on both ɛ and Mc(k ) in the best case when Mf(k )≪Mc(k ) and on ɛ alone in the worst case when Mf(k )≈Mc(k ) .

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

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

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.

The PlusCal Algorithm Language

NASA Astrophysics Data System (ADS)

Lamport, Leslie

Algorithms are different from programs and should not be described with programming languages. The only simple alternative to programming languages has been pseudo-code. PlusCal is an algorithm language that can be used right now to replace pseudo-code, for both sequential and concurrent algorithms. It is based on the TLA + specification language, and a PlusCal algorithm is automatically translated to a TLA + specification that can be checked with the TLC model checker and reasoned about formally.

Software For Genetic Algorithms

NASA Technical Reports Server (NTRS)

Wang, Lui; Bayer, Steve E.

1992-01-01

SPLICER computer program is genetic-algorithm software tool used to solve search and optimization problems. Provides underlying framework and structure for building genetic-algorithm application program. Written in Think C.

SPARSE: quadratic time simultaneous alignment and folding of RNAs without sequence-based heuristics

PubMed Central

Will, Sebastian; Otto, Christina; Miladi, Milad; Möhl, Mathias; Backofen, Rolf

2015-01-01

Motivation: RNA-Seq experiments have revealed a multitude of novel ncRNAs. The gold standard for their analysis based on simultaneous alignment and folding suffers from extreme time complexity of O(n6). Subsequently, numerous faster ‘Sankoff-style’ approaches have been suggested. Commonly, the performance of such methods relies on sequence-based heuristics that restrict the search space to optimal or near-optimal sequence alignments; however, the accuracy of sequence-based methods breaks down for RNAs with sequence identities below 60%. Alignment approaches like LocARNA that do not require sequence-based heuristics, have been limited to high complexity (≥ quartic time). Results: Breaking this barrier, we introduce the novel Sankoff-style algorithm ‘sparsified prediction and alignment of RNAs based on their structure ensembles (SPARSE)’, which runs in quadratic time without sequence-based heuristics. To achieve this low complexity, on par with sequence alignment algorithms, SPARSE features strong sparsification based on structural properties of the RNA ensembles. Following PMcomp, SPARSE gains further speed-up from lightweight energy computation. Although all existing lightweight Sankoff-style methods restrict Sankoff’s original model by disallowing loop deletions and insertions, SPARSE transfers the Sankoff algorithm to the lightweight energy model completely for the first time. Compared with LocARNA, SPARSE achieves similar alignment and better folding quality in significantly less time (speedup: 3.7). At similar run-time, it aligns low sequence identity instances substantially more accurate than RAF, which uses sequence-based heuristics. Availability and implementation: SPARSE is freely available at http://www.bioinf.uni-freiburg.de/Software/SPARSE. Contact: backofen@informatik.uni-freiburg.de Supplementary information: Supplementary data are available at Bioinformatics online. PMID:25838465

Quadratic electroabsorption studies of molecular motion in dye-doped polymers

NASA Astrophysics Data System (ADS)

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

1993-02-01

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

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.

Integration of the Quadratic Function and Generalization

ERIC Educational Resources Information Center

Mitsuma, Kunio

2011-01-01

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

A dynamic programming-based particle swarm optimization algorithm for an inventory management problem under uncertainty

NASA Astrophysics Data System (ADS)

Xu, Jiuping; Zeng, Ziqiang; Han, Bernard; Lei, Xiao

2013-07-01

This article presents a dynamic programming-based particle swarm optimization (DP-based PSO) algorithm for solving an inventory management problem for large-scale construction projects under a fuzzy random environment. By taking into account the purchasing behaviour and strategy under rules of international bidding, a multi-objective fuzzy random dynamic programming model is constructed. To deal with the uncertainties, a hybrid crisp approach is used to transform fuzzy random parameters into fuzzy variables that are subsequently defuzzified by using an expected value operator with optimistic-pessimistic index. The iterative nature of the authors' model motivates them to develop a DP-based PSO algorithm. More specifically, their approach treats the state variables as hidden parameters. This in turn eliminates many redundant feasibility checks during initialization and particle updates at each iteration. Results and sensitivity analysis are presented to highlight the performance of the authors' optimization method, which is very effective as compared to the standard PSO algorithm.

Linear quadratic regulators with eigenvalue placement in a specified region

NASA Technical Reports Server (NTRS)

Shieh, Leang S.; Dib, Hani M.; Ganesan, Sekar

1988-01-01

A linear optimal quadratic regulator is developed for optimally placing the closed-loop poles of multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at + or - pi/2k (k = 2 or 3) from the negative real axis with a sector angle of pi/2 or less, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane. The design method is mainly based on the solution of a linear matrix Liapunov equation, and the resultant closed-loop system with its eigenvalues in the desired region is optimal with respect to a quadratic performance index.

Tuning a fuzzy controller using quadratic response surfaces

NASA Technical Reports Server (NTRS)

Schott, Brian; Whalen, Thomas

1992-01-01

Response surface methodology, an alternative method to traditional tuning of a fuzzy controller, is described. An example based on a simulated inverted pendulum 'plant' shows that with (only) 15 trial runs, the controller can be calibrated using a quadratic form to approximate the response surface.

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.

ALGORITHMS AND PROGRAMS FOR STRONG GRAVITATIONAL LENSING IN KERR SPACE-TIME INCLUDING POLARIZATION

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

Chen, Bin; Maddumage, Prasad; Kantowski, Ronald

2015-05-15

Active galactic nuclei (AGNs) and quasars are important astrophysical objects to understand. Recently, microlensing observations have constrained the size of the quasar X-ray emission region to be of the order of 10 gravitational radii of the central supermassive black hole. For distances within a few gravitational radii, light paths are strongly bent by the strong gravity field of the central black hole. If the central black hole has nonzero angular momentum (spin), then a photon’s polarization plane will be rotated by the gravitational Faraday effect. The observed X-ray flux and polarization will then be influenced significantly by the strong gravitymore » field near the source. Consequently, linear gravitational lensing theory is inadequate for such extreme circumstances. We present simple algorithms computing the strong lensing effects of Kerr black holes, including the effects on polarization. Our algorithms are realized in a program “KERTAP” in two versions: MATLAB and Python. The key ingredients of KERTAP are a graphic user interface, a backward ray-tracing algorithm, a polarization propagator dealing with gravitational Faraday rotation, and algorithms computing observables such as flux magnification and polarization angles. Our algorithms can be easily realized in other programming languages such as FORTRAN, C, and C++. The MATLAB version of KERTAP is parallelized using the MATLAB Parallel Computing Toolbox and the Distributed Computing Server. The Python code was sped up using Cython and supports full implementation of MPI using the “mpi4py” package. As an example, we investigate the inclination angle dependence of the observed polarization and the strong lensing magnification of AGN X-ray emission. We conclude that it is possible to perform complex numerical-relativity related computations using interpreted languages such as MATLAB and Python.« less

Algorithms and Programs for Strong Gravitational Lensing In Kerr Space-time Including Polarization

NASA Astrophysics Data System (ADS)

Chen, Bin; Kantowski, Ronald; Dai, Xinyu; Baron, Eddie; Maddumage, Prasad

2015-05-01

Active galactic nuclei (AGNs) and quasars are important astrophysical objects to understand. Recently, microlensing observations have constrained the size of the quasar X-ray emission region to be of the order of 10 gravitational radii of the central supermassive black hole. For distances within a few gravitational radii, light paths are strongly bent by the strong gravity field of the central black hole. If the central black hole has nonzero angular momentum (spin), then a photon’s polarization plane will be rotated by the gravitational Faraday effect. The observed X-ray flux and polarization will then be influenced significantly by the strong gravity field near the source. Consequently, linear gravitational lensing theory is inadequate for such extreme circumstances. We present simple algorithms computing the strong lensing effects of Kerr black holes, including the effects on polarization. Our algorithms are realized in a program “KERTAP” in two versions: MATLAB and Python. The key ingredients of KERTAP are a graphic user interface, a backward ray-tracing algorithm, a polarization propagator dealing with gravitational Faraday rotation, and algorithms computing observables such as flux magnification and polarization angles. Our algorithms can be easily realized in other programming languages such as FORTRAN, C, and C++. The MATLAB version of KERTAP is parallelized using the MATLAB Parallel Computing Toolbox and the Distributed Computing Server. The Python code was sped up using Cython and supports full implementation of MPI using the “mpi4py” package. As an example, we investigate the inclination angle dependence of the observed polarization and the strong lensing magnification of AGN X-ray emission. We conclude that it is possible to perform complex numerical-relativity related computations using interpreted languages such as MATLAB and Python.

Verifying a Computer Algorithm Mathematically.

ERIC Educational Resources Information Center

Olson, Alton T.

1986-01-01

Presents an example of mathematics from an algorithmic point of view, with emphasis on the design and verification of this algorithm. The program involves finding roots for algebraic equations using the half-interval search algorithm. The program listing is included. (JN)

A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations.

PubMed

Li, Yong; Yuan, Gonglin; Wei, Zengxin

2015-01-01

In this paper, a trust-region algorithm is proposed for large-scale nonlinear equations, where the limited-memory BFGS (L-M-BFGS) update matrix is used in the trust-region subproblem to improve the effectiveness of the algorithm for large-scale problems. The global convergence of the presented method is established under suitable conditions. The numerical results of the test problems show that the method is competitive with the norm method.

Numerical Solution of the Electron Heat Transport Equation and Physics-Constrained Modeling of the Thermal Conductivity via Sequential Quadratic Programming Optimization in Nuclear Fusion Plasmas

NASA Astrophysics Data System (ADS)

Paloma, Cynthia S.

The plasma electron temperature (Te) plays a critical role in a tokamak nu- clear fusion reactor since temperatures on the order of 108K are required to achieve fusion conditions. Many plasma properties in a tokamak nuclear fusion reactor are modeled by partial differential equations (PDE's) because they depend not only on time but also on space. In particular, the dynamics of the electron temperature is governed by a PDE referred to as the Electron Heat Transport Equation (EHTE). In this work, a numerical method is developed to solve the EHTE based on a custom finite-difference technique. The solution of the EHTE is compared to temperature profiles obtained by using TRANSP, a sophisticated plasma transport code, for specific discharges from the DIII-D tokamak, located at the DIII-D National Fusion Facility in San Diego, CA. The thermal conductivity (also called thermal diffusivity) of the electrons (Xe) is a plasma parameter that plays a critical role in the EHTE since it indicates how the electron temperature diffusion varies across the minor effective radius of the tokamak. TRANSP approximates Xe through a curve-fitting technique to match experimentally measured electron temperature profiles. While complex physics-based model have been proposed for Xe, there is a lack of a simple mathematical model for the thermal diffusivity that could be used for control design. In this work, a model for Xe is proposed based on a scaling law involving key plasma variables such as the electron temperature (Te), the electron density (ne), and the safety factor (q). An optimization algorithm is developed based on the Sequential Quadratic Programming (SQP) technique to optimize the scaling factors appearing in the proposed model so that the predicted electron temperature and magnetic flux profiles match predefined target profiles in the best possible way. A simulation study summarizing the outcomes of the optimization procedure is presented to illustrate the potential of the

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.

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.

Insulin algorithms in the self-management of insulin-dependent diabetes: the interactive 'Apple Juice' program.

PubMed

Williams, A G

1996-01-01

The 'Apple Juice' program is an interactive diabetes self-management program which runs on a lap-top Macintosh Powerbook 100 computer. The dose-by-dose insulin advisory program was initially designed for children with insulin-dependent (type 1) diabetes mellitus. It utilizes several different insulin algorithms, measurement formulae, and compensation factors for meals, activity, medication and the dawn phenomenon. It was developed to assist the individual with diabetes and/or care providers, in determining specific insulin dosage recommendations throughout a 24 h period. Information technology functions include, but are not limited to automated record keeping, data recall, event reminders, data trend/pattern analyses and education. This paper highlights issues, observations and recommendations surrounding the use of the current version of the software, along with a detailed description of the insulin algorithms and measurement formulae applied successfully with the author's daughter over a six year period.

Characterization of a Quadratic Function in Rn

ERIC Educational Resources Information Center

Xu, Conway

2010-01-01

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

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

PubMed

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

2015-09-01

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

Emotion suppression moderates the quadratic association between RSA and executive function

PubMed Central

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

2016-01-01

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

The Joint Polar Satellite System (JPSS) Program's Algorithm Change Process (ACP): Past, Present and Future

NASA Technical Reports Server (NTRS)

Griffin, Ashley

2017-01-01

The Joint Polar Satellite System (JPSS) Program Office is the supporting organization for the Suomi National Polar Orbiting Partnership (S-NPP) and JPSS-1 satellites. S-NPP carries the following sensors: VIIRS, CrIS, ATMS, OMPS, and CERES with instruments that ultimately produce over 25 data products that cover the Earths weather, oceans, and atmosphere. A team of scientists and engineers from all over the United States document, monitor and fix errors in operational software code or documentation with the algorithm change process (ACP) to ensure the success of the S-NPP and JPSS 1 missions by maintaining quality and accuracy of the data products the scientific community relies on. This poster will outline the programs algorithm change process (ACP), identify the various users and scientific applications of our operational data products and highlight changes that have been made to the ACP to accommodate operating system upgrades to the JPSS programs Interface Data Processing Segment (IDPS), so that the program is ready for the transition to the 2017 JPSS-1 satellite mission and beyond.

Approximate Dynamic Programming Algorithms for United States Air Force Officer Sustainment

DTIC Science & Technology

2015-03-26

level of correction needed. While paying bonuses has an easily calculable cost, RIFs have more subtle costs. Mone (1994) discovered that in a steady...a regression is performed utilizing instrumental variables to minimize Bellman error. This algorithm uses a set of basis functions to approximate the...transitioned to an all-volunteer force. Charnes et al. (1972) utilize a goal programming model for General Schedule civilian manpower management in the

STAR adaptation of QR algorithm. [program for solving over-determined systems of linear equations

NASA Technical Reports Server (NTRS)

Shah, S. N.

1981-01-01

The QR algorithm used on a serial computer and executed on the Control Data Corporation 6000 Computer was adapted to execute efficiently on the Control Data STAR-100 computer. How the scalar program was adapted for the STAR-100 and why these adaptations yielded an efficient STAR program is described. Program listings of the old scalar version and the vectorized SL/1 version are presented in the appendices. Execution times for the two versions applied to the same system of linear equations, are compared.

Finding Optimal Gains In Linear-Quadratic Control Problems

NASA Technical Reports Server (NTRS)

Milman, Mark H.; Scheid, Robert E., Jr.

1990-01-01

Analytical method based on Volterra factorization leads to new approximations for optimal control gains in finite-time linear-quadratic control problem of system having infinite number of dimensions. Circumvents need to analyze and solve Riccati equations and provides more transparent connection between dynamics of system and optimal gain.

Method for optimizing channelized quadratic observers for binary classification of large-dimensional image datasets

PubMed Central

Kupinski, M. K.; Clarkson, E.

2015-01-01

We present a new method for computing optimized channels for channelized quadratic observers (CQO) that is feasible for high-dimensional image data. The method for calculating channels is applicable in general and optimal for Gaussian distributed image data. Gradient-based algorithms for determining the channels are presented for five different information-based figures of merit (FOMs). Analytic solutions for the optimum channels for each of the five FOMs are derived for the case of equal mean data for both classes. The optimum channels for three of the FOMs under the equal mean condition are shown to be the same. This result is critical since some of the FOMs are much easier to compute. Implementing the CQO requires a set of channels and the first- and second-order statistics of channelized image data from both classes. The dimensionality reduction from M measurements to L channels is a critical advantage of CQO since estimating image statistics from channelized data requires smaller sample sizes and inverting a smaller covariance matrix is easier. In a simulation study we compare the performance of ideal and Hotelling observers to CQO. The optimal CQO channels are calculated using both eigenanalysis and a new gradient-based algorithm for maximizing Jeffrey's divergence (J). Optimal channel selection without eigenanalysis makes the J-CQO on large-dimensional image data feasible. PMID:26366764

An Optimal Algorithm towards Successive Location Privacy in Sensor Networks with Dynamic Programming

NASA Astrophysics Data System (ADS)

Zhao, Baokang; Wang, Dan; Shao, Zili; Cao, Jiannong; Chan, Keith C. C.; Su, Jinshu

In wireless sensor networks, preserving location privacy under successive inference attacks is extremely critical. Although this problem is NP-complete in general cases, we propose a dynamic programming based algorithm and prove it is optimal in special cases where the correlation only exists between p immediate adjacent observations.

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…

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.

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.

Communications circuit including a linear quadratic estimator

DOEpatents

Ferguson, Dennis D.

2015-07-07

A circuit includes a linear quadratic estimator (LQE) configured to receive a plurality of measurements a signal. The LQE is configured to weight the measurements based on their respective uncertainties to produce weighted averages. The circuit further includes a controller coupled to the LQE and configured to selectively adjust at least one data link parameter associated with a communication channel in response to receiving the weighted averages.

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

PubMed

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

2010-04-01

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

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.

Simulating first order optical systems—algorithms for and composition of discrete linear canonical transforms

NASA Astrophysics Data System (ADS)

Healy, John J.

2018-01-01

The linear canonical transforms (LCTs) are a parameterised group of linear integral transforms. The LCTs encompass a number of well-known transformations as special cases, including the Fourier transform, fractional Fourier transform, and the Fresnel integral. They relate the scalar wave fields at the input and output of systems composed of thin lenses and free space, along with other quadratic phase systems. In this paper, we perform a systematic search of all algorithms based on up to five stages of magnification, chirp multiplication and Fourier transforms. Based on that search, we propose a novel algorithm, for which we present numerical results. We compare the sampling requirements of three algorithms. Finally, we discuss some issues surrounding the composition of discrete LCTs.

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)

Retrieval Accuracy Assessment with Gap Detection for Case 2 Waters Chla Algorithms

NASA Astrophysics Data System (ADS)

Salem, S. I.; Higa, H.; Kim, H.; Oki, K.; Oki, T.

2016-12-01

Inland lakes and coastal regions types of Case 2 Waters should be continuously and accurately monitored as the former contain 90% of the global liquid freshwater storage, while the latter provide most of the dissolved organic carbon (DOC) which is an important link in the global carbon cycle. The optical properties of Case 2 Waters are dominated by three optically active components: phytoplankton, non-algal particles (NAP) and color dissolved organic matter (CDOM). During the last three decades, researchers have proposed several algorithms to retrieve Chla concentration from the remote sensing reflectance. In this study, seven algorithms are assessed with various band combinations from multi and hyper-spectral data with linear, polynomial and power regression approaches. To evaluate the performance of the 43 algorithm combination sets, 500,000 remote sensing reflectance spectra are simulated with a wide range of concentrations for Chla, NAP and CDOM. The concentrations of Chla and NAP vary from 1-200 (mg m-3) and 1-200 (gm m-3), respectively, and the absorption of CDOM at 440 nm has the range of 0.1-10 (m-1). It is found that the three-band algorithm (665, 709 and 754 nm) with the quadratic polynomial (3b_665_QP) indicates the best overall performance. 3b_665_QP has the least error with a root mean square error (RMSE) of 0.2 (mg m-3) and a mean absolute relative error (MARE) of 0.7 %. The less accurate retrieval of Chla was obtained by the synthetic chlorophyll index algorithm with RMSE and MARE of 35.8 mg m-3 and 160.4 %, respectively. In general, Chla algorithms which incorporates 665 nm band or band tuning technique performs better than those with 680 nm. In addition, the retrieval accuracy of Chla algorithms with quadratic polynomial and power regression approaches are consistently better than the linear ones. By analyzing Chla versus NAP concentrations, the 3b_665_QP outperforms the other algorithms for all Chla concentrations and NAP concentrations above 40

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

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…

Dark-bright quadratic solitons with a focusing effective Kerr nonlinearity

NASA Astrophysics Data System (ADS)

Chen, Manna; Ping, Xiaorou; Liang, Guo; Guo, Qi; Lu, Daquan; Hu, Wei

2018-01-01

Dark solitons are traditionally considered to exist in defocusing Kerr nonlinearity media. We investigate dark quadratic solitons with a focusing effective Kerr nonlinearity and a sine-oscillatory nonlocal response. A nonlinear refractive index with a focusing sine-oscillatory response leads to a defocusing effect with a strong degree of nonlocality, which causes the formation of dark solitons. By analyzing the modulational instability, we determine the parameter domain for dark quadratic solitons with a stable background and numerically obtain dark-bright soliton solutions in the form of pairs, which avoid radiative phenomena. Based on a numerical simulation, we find that all dark-bright soliton pairs are unstable after a relatively long propagation distance, and their stabilities are affected by the soliton interval and the degree of nonlocality.

A Hybrid Genetic Programming Algorithm for Automated Design of Dispatching Rules.

PubMed

Nguyen, Su; Mei, Yi; Xue, Bing; Zhang, Mengjie

2018-06-04

Designing effective dispatching rules for production systems is a difficult and timeconsuming task if it is done manually. In the last decade, the growth of computing power, advanced machine learning, and optimisation techniques has made the automated design of dispatching rules possible and automatically discovered rules are competitive or outperform existing rules developed by researchers. Genetic programming is one of the most popular approaches to discovering dispatching rules in the literature, especially for complex production systems. However, the large heuristic search space may restrict genetic programming from finding near optimal dispatching rules. This paper develops a new hybrid genetic programming algorithm for dynamic job shop scheduling based on a new representation, a new local search heuristic, and efficient fitness evaluators. Experiments show that the new method is effective regarding the quality of evolved rules. Moreover, evolved rules are also significantly smaller and contain more relevant attributes.

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

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

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.

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.

Confidence set inference with a prior quadratic bound

NASA Technical Reports Server (NTRS)

Backus, George E.

1989-01-01

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

Linear quadratic stochastic control of atomic hydrogen masers.

PubMed

Koppang, P; Leland, R

1999-01-01

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

Separation of left and right lungs using 3D information of sequential CT images and a guided dynamic programming algorithm

PubMed Central

Park, Sang Cheol; Leader, Joseph Ken; Tan, Jun; Lee, Guee Sang; Kim, Soo Hyung; Na, In Seop; Zheng, Bin

2011-01-01

Objective this article presents a new computerized scheme that aims to accurately and robustly separate left and right lungs on CT examinations. Methods we developed and tested a method to separate the left and right lungs using sequential CT information and a guided dynamic programming algorithm using adaptively and automatically selected start point and end point with especially severe and multiple connections. Results the scheme successfully identified and separated all 827 connections on the total 4034 CT images in an independent testing dataset of CT examinations. The proposed scheme separated multiple connections regardless of their locations, and the guided dynamic programming algorithm reduced the computation time to approximately 4.6% in comparison with the traditional dynamic programming and avoided the permeation of the separation boundary into normal lung tissue. Conclusions The proposed method is able to robustly and accurately disconnect all connections between left and right lungs and the guided dynamic programming algorithm is able to remove redundant processing. PMID:21412104

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…

The Texas Medication Algorithm Project Patient and Family Education Program: a consumer-guided initiative.

PubMed

Toprac, M G; Rush, A J; Conner, T M; Crismon, M L; Dees, M; Hopkins, C; Rowe, V; Shon, S P

2000-07-01

Educating patients with mental illness and their families about the illness and its treatment is essential to successful medication (disease) management. Specifically, education provides patients and families with the background they need to participate in treatment planning and implementation as full "partners" with clinicians. Thus, education increases the probability that appropriate and accurate treatment decisions will be made and that a treatment regimen will be followed. The Texas Medication Algorithm Project (TMAP) has incorporated these concepts into its philosophy of care and accordingly created a Patient and Family Education Program (PFEP) to complement the utilization of medication algorithms for the treatment of schizophrenic, bipolar, and major depressive disorders. This article describes how a team of mental health consumers, advocates, and professionals developed and implemented the PFEP. In keeping with the TMAP philosophy of care, consumers were true partners in the program's development and implementation. They not only created several components of the program and incorporated the consumer perspective, but they also served as program trainers and advocates. Initially, PFEP provides basic and subsequently more in-depth information about the illness and its treatment, including such topics as symptom monitoring and management and self-advocacy with one's treatment team. It includes written, pictorial, videotaped, and other media used in a phased manner by clinicians and consumer educators, in either individual or group formats.

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.

An interactive approach based on a discrete differential evolution algorithm for a class of integer bilevel programming problems

NASA Astrophysics Data System (ADS)

Li, Hong; Zhang, Li; Jiao, Yong-Chang

2016-07-01

This paper presents an interactive approach based on a discrete differential evolution algorithm to solve a class of integer bilevel programming problems, in which integer decision variables are controlled by an upper-level decision maker and real-value or continuous decision variables are controlled by a lower-level decision maker. Using the Karush--Kuhn-Tucker optimality conditions in the lower-level programming, the original discrete bilevel formulation can be converted into a discrete single-level nonlinear programming problem with the complementarity constraints, and then the smoothing technique is applied to deal with the complementarity constraints. Finally, a discrete single-level nonlinear programming problem is obtained, and solved by an interactive approach. In each iteration, for each given upper-level discrete variable, a system of nonlinear equations including the lower-level variables and Lagrange multipliers is solved first, and then a discrete nonlinear programming problem only with inequality constraints is handled by using a discrete differential evolution algorithm. Simulation results show the effectiveness of the proposed approach.

BWM*: A Novel, Provable, Ensemble-based Dynamic Programming Algorithm for Sparse Approximations of Computational Protein Design.

PubMed

Jou, Jonathan D; Jain, Swati; Georgiev, Ivelin S; Donald, Bruce R

2016-06-01

Sparse energy functions that ignore long range interactions between residue pairs are frequently used by protein design algorithms to reduce computational cost. Current dynamic programming algorithms that fully exploit the optimal substructure produced by these energy functions only compute the GMEC. This disproportionately favors the sequence of a single, static conformation and overlooks better binding sequences with multiple low-energy conformations. Provable, ensemble-based algorithms such as A* avoid this problem, but A* cannot guarantee better performance than exhaustive enumeration. We propose a novel, provable, dynamic programming algorithm called Branch-Width Minimization* (BWM*) to enumerate a gap-free ensemble of conformations in order of increasing energy. Given a branch-decomposition of branch-width w for an n-residue protein design with at most q discrete side-chain conformations per residue, BWM* returns the sparse GMEC in O([Formula: see text]) time and enumerates each additional conformation in merely O([Formula: see text]) time. We define a new measure, Total Effective Search Space (TESS), which can be computed efficiently a priori before BWM* or A* is run. We ran BWM* on 67 protein design problems and found that TESS discriminated between BWM*-efficient and A*-efficient cases with 100% accuracy. As predicted by TESS and validated experimentally, BWM* outperforms A* in 73% of the cases and computes the full ensemble or a close approximation faster than A*, enumerating each additional conformation in milliseconds. Unlike A*, the performance of BWM* can be predicted in polynomial time before running the algorithm, which gives protein designers the power to choose the most efficient algorithm for their particular design problem.

Mixing of ultrasonic Lamb waves in thin plates with quadratic nonlinearity.

PubMed

Li, Feilong; Zhao, Youxuan; Cao, Peng; Hu, Ning

2018-07-01

This paper investigates the propagation of Lamb waves in thin plates with quadratic nonlinearity by one-way mixing method using numerical simulations. It is shown that an A 0 -mode wave can be generated by a pair of S 0 and A 0 mode waves only when mixing condition is satisfied, and mixing wave signals are capable of locating the damage zone. Additionally, it is manifested that the acoustic nonlinear parameter increases linearly with quadratic nonlinearity but monotonously with the size of mixing zone. Furthermore, because of frequency deviation, the waveform of the mixing wave changes significantly from a regular diamond shape to toneburst trains. Copyright © 2018 Elsevier B.V. All rights reserved.

Design of linear quadratic regulators with eigenvalue placement in a specified region

NASA Technical Reports Server (NTRS)

Shieh, Leang-San; Zhen, Liu; Coleman, Norman P.

1990-01-01

Two linear quadratic regulators are developed for placing the closed-loop poles of linear multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at +/- pi/2k (for a specified integer k not less than 1) from the negative real axis, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane, and simultaneously minimizing a quadratic performance index. The design procedure mainly involves the solution of either Liapunov equations or Riccati equations. The general expression for finding the lower bound of a constant gain gamma is also developed.

Analysis of Quadratic Diophantine Equations with Fibonacci Number Solutions

ERIC Educational Resources Information Center

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

2004-01-01

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

Experimental evaluation of model predictive control and inverse dynamics control for spacecraft proximity and docking maneuvers

NASA Astrophysics Data System (ADS)

Virgili-Llop, Josep; Zagaris, Costantinos; Park, Hyeongjun; Zappulla, Richard; Romano, Marcello

2018-03-01

An experimental campaign has been conducted to evaluate the performance of two different guidance and control algorithms on a multi-constrained docking maneuver. The evaluated algorithms are model predictive control (MPC) and inverse dynamics in the virtual domain (IDVD). A linear-quadratic approach with a quadratic programming solver is used for the MPC approach. A nonconvex optimization problem results from the IDVD approach, and a nonlinear programming solver is used. The docking scenario is constrained by the presence of a keep-out zone, an entry cone, and by the chaser's maximum actuation level. The performance metrics for the experiments and numerical simulations include the required control effort and time to dock. The experiments have been conducted in a ground-based air-bearing test bed, using spacecraft simulators that float over a granite table.

ORACLS- OPTIMAL REGULATOR ALGORITHMS FOR THE CONTROL OF LINEAR SYSTEMS (CDC VERSION)

NASA Technical Reports Server (NTRS)

Armstrong, E. S.

1994-01-01

This control theory design package, called Optimal Regulator Algorithms for the Control of Linear Systems (ORACLS), was developed to aid in the design of controllers and optimal filters for systems which can be modeled by linear, time-invariant differential and difference equations. Optimal linear quadratic regulator theory, currently referred to as the Linear-Quadratic-Gaussian (LQG) problem, has become the most widely accepted method of determining optimal control policy. Within this theory, the infinite duration time-invariant problems, which lead to constant gain feedback control laws and constant Kalman-Bucy filter gains for reconstruction of the system state, exhibit high tractability and potential ease of implementation. A variety of new and efficient methods in the field of numerical linear algebra have been combined into the ORACLS program, which provides for the solution to time-invariant continuous or discrete LQG problems. The ORACLS package is particularly attractive to the control system designer because it provides a rigorous tool for dealing with multi-input and multi-output dynamic systems in both continuous and discrete form. The ORACLS programming system is a collection of subroutines which can be used to formulate, manipulate, and solve various LQG design problems. The ORACLS program is constructed in a manner which permits the user to maintain considerable flexibility at each operational state. This flexibility is accomplished by providing primary operations, analysis of linear time-invariant systems, and control synthesis based on LQG methodology. The input-output routines handle the reading and writing of numerical matrices, printing heading information, and accumulating output information. The basic vector-matrix operations include addition, subtraction, multiplication, equation, norm construction, tracing, transposition, scaling, juxtaposition, and construction of null and identity matrices. The analysis routines provide for the following

Hyers-Ulam stability of a generalized Apollonius type quadratic mapping

NASA Astrophysics Data System (ADS)

Park, Chun-Gil; Rassias, Themistocles M.

2006-10-01

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

Quadratic Expressions by Means of "Summing All the Matchsticks"

ERIC Educational Resources Information Center

Gierdien, M. Faaiz

2012-01-01

This note presents demonstrations of quadratic expressions that come about when particular problems are posed with respect to matchsticks that form regular triangles, squares, pentagons and so on. Usually when such "matchstick" problems are used as ways to foster algebraic thinking, the expressions for the number of matchstick quantities are…

Separation of left and right lungs using 3-dimensional information of sequential computed tomography images and a guided dynamic programming algorithm.

PubMed

Park, Sang Cheol; Leader, Joseph Ken; Tan, Jun; Lee, Guee Sang; Kim, Soo Hyung; Na, In Seop; Zheng, Bin

2011-01-01

This article presents a new computerized scheme that aims to accurately and robustly separate left and right lungs on computed tomography (CT) examinations. We developed and tested a method to separate the left and right lungs using sequential CT information and a guided dynamic programming algorithm using adaptively and automatically selected start point and end point with especially severe and multiple connections. The scheme successfully identified and separated all 827 connections on the total 4034 CT images in an independent testing data set of CT examinations. The proposed scheme separated multiple connections regardless of their locations, and the guided dynamic programming algorithm reduced the computation time to approximately 4.6% in comparison with the traditional dynamic programming and avoided the permeation of the separation boundary into normal lung tissue. The proposed method is able to robustly and accurately disconnect all connections between left and right lungs, and the guided dynamic programming algorithm is able to remove redundant processing.

Frequency modulation indicator, Arnold’s web and diffusion in the Stark Quadratic-Zeeman problem

NASA Astrophysics Data System (ADS)

Cordani, Bruno

2008-11-01

We notice that the fundamental frequencies of a slightly perturbed integrable Hamiltonian system are not time-constant inside a resonance but frequency modulated, as is evident from pendulum models and wavelet analysis. Exploiting an intrinsic imprecision inherent to the numerical frequency analysis algorithm itself, hence transforming a drawback into an opportunity, we define the Frequency Modulation Indicator, a very sensitive tool in detecting where fundamental frequencies are modulated, localizing so the resonances without having to resort, as in other methods, to the integration of variational equations. For the Kepler problem, the space of the orbits with a fixed energy has the topology of the product of two 2-spheres. The perturbation Hamiltonian, averaged over the mean anomaly, has surely a maximum and a minimum, to which correspond two periodic orbits in physical space. Studying the neighbourhood of these two elliptic stable points, we are able to define adapted action-angle variables, for example, the usual but “SO(4)-rotated” Delaunay variables. The procedure, implemented in the program KEPLER, is performed transparently for the user, providing a general scheme suited for generic perturbation. The method is then applied to the Stark-Quadratic-Zeeman problem, displaying very clearly the Arnold web of the resonances. Sectioning transversely one of the resonance strips so highlighted and performing a numerical frequency analysis, one is able to locate with great precision the thin stochastic layer surrounding a separatrix. Another very long (10 8 revolutions) frequency analysis on an orbit starting here reveals, as expected, a well defined pattern, which ensures that the integration errors do not eject the point out of the layer, and moreover a very slow drift in the frequency values, clearly due to Arnold diffusion.

Optomechanically induced opacity and amplification in a quadratically coupled optomechanical system

NASA Astrophysics Data System (ADS)

Si, Liu-Gang; Xiong, Hao; Zubairy, M. Suhail; Wu, Ying

2017-03-01

We analyze theoretically the features of the output field of a quadratically coupled optomechanical system, which is driven by a strong coupling field and a weak signal field, and in which the membrane (treated as a mechanical resonator) is excited by a weak coherent driving field with two-phonon resonance. We show that the system exhibits complex quantum coherent and interference effects resulting in transmission of the signal field from opacity to remarkable amplification. We also find that the total phase of the applied fields can significantly adjust the signal field's transmission spectrum. The study of the propagation of the signal field in such a quadratically coupled optomechanical system proves that the proposed device can operate as an optical transistor.

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.

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…

Multi-scale graph-cut algorithm for efficient water-fat separation.

PubMed

Berglund, Johan; Skorpil, Mikael

2017-09-01

To improve the accuracy and robustness to noise in water-fat separation by unifying the multiscale and graph cut based approaches to B 0 -correction. A previously proposed water-fat separation algorithm that corrects for B 0 field inhomogeneity in 3D by a single quadratic pseudo-Boolean optimization (QPBO) graph cut was incorporated into a multi-scale framework, where field map solutions are propagated from coarse to fine scales for voxels that are not resolved by the graph cut. The accuracy of the single-scale and multi-scale QPBO algorithms was evaluated against benchmark reference datasets. The robustness to noise was evaluated by adding noise to the input data prior to water-fat separation. Both algorithms achieved the highest accuracy when compared with seven previously published methods, while computation times were acceptable for implementation in clinical routine. The multi-scale algorithm was more robust to noise than the single-scale algorithm, while causing only a small increase (+10%) of the reconstruction time. The proposed 3D multi-scale QPBO algorithm offers accurate water-fat separation, robustness to noise, and fast reconstruction. The software implementation is freely available to the research community. Magn Reson Med 78:941-949, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Forecasting nonlinear chaotic time series with function expression method based on an improved genetic-simulated annealing algorithm.

PubMed

Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng

2015-01-01

The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior.

Flaw characterization through nonlinear ultrasonics and wavelet cross-correlation algorithms

NASA Astrophysics Data System (ADS)

Bunget, Gheorghe; Yee, Andrew; Stewart, Dylan; Rogers, James; Henley, Stanley; Bugg, Chris; Cline, John; Webster, Matthew; Farinholt, Kevin; Friedersdorf, Fritz

2018-04-01

Ultrasonic measurements have become increasingly important non-destructive techniques to characterize flaws found within various in-service industrial components. The prediction of remaining useful life based on fracture analysis depends on the accurate estimation of flaw size and orientation. However, amplitude-based ultrasonic measurements are not able to estimate the plastic zones that exist ahead of crack tips. Estimating the size of the plastic zone is an advantage since some flaws may propagate faster than others. This paper presents a wavelet cross-correlation (WCC) algorithm that was applied to nonlinear analysis of ultrasonically guided waves (GW). By using this algorithm, harmonics present in the waveforms were extracted and nonlinearity parameters were used to indicate both the tip of the cracks and size of the plastic zone. B-scans performed with the quadratic nonlinearities were sensitive to micro-damage specific to plastic zones.

A polynomial primal-dual Dikin-type algorithm for linear programming

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

Jansen, B.; Roos, R.; Terlaky, T.

1994-12-31

We present a new primal-dual affine scaling method for linear programming. The search direction is obtained by using Dikin`s original idea: minimize the objective function (which is the duality gap in a primal-dual algorithm) over a suitable ellipsoid. The search direction has no obvious relationship with the directions proposed in the literature so far. It guarantees a significant decrease in the duality gap in each iteration, and at the same time drives the iterates to the central path. The method admits a polynomial complexity bound that is better than the one for Monteiro et al.`s original primal-dual affine scaling method.

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.

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 Electro-optic Effect in a Novel Nonconjugated Conductive Polymer, iodine-doped Polynorbornene

NASA Astrophysics Data System (ADS)

Narayanan, Ananthakrishnan; Thakur, Mrinal

2009-03-01

Quadratic electro-optic effect in a novel nonconjugated conductive polymer, iodine-doped polynorbornene has been measured using field-induced birefringence at 633 nm. The electrical conductivity^1 of polynorbornene increases by twelve orders of magnitude to about 0.01 S/cm upon doping with iodine. The electro-optic measurement has been made in a film doped at the medium doping-level. The electro-optic modulation signal was recorded using a lock-in amplifier for various applied ac voltages (4 kHz) and the quadratic dependence of the modulation on the applied voltage was observed. A modulation of about 0.01% was observed for an applied electric field of 3 V/micron for a 100 nm thick film The Kerr coefficient as determined is about 1.77x10-11m/V^2. This exceptionally large quadratic electro-optic effect has been attributed to the confinement of this charge-transfer system within a sub-nanometer dimension. 1. A. Narayanan, A. Palthi and M. Thakur, J. Macromol. Sci. -- PAC, accepted.

Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing

NASA Technical Reports Server (NTRS)

Choi, Benjamin B.

2002-01-01

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

Asymptotic analysis of online algorithms and improved scheme for the flow shop scheduling problem with release dates

NASA Astrophysics Data System (ADS)

Bai, Danyu

2015-08-01

This paper discusses the flow shop scheduling problem to minimise the total quadratic completion time (TQCT) with release dates in offline and online environments. For this NP-hard problem, the investigation is focused on the performance of two online algorithms based on the Shortest Processing Time among Available jobs rule. Theoretical results indicate the asymptotic optimality of the algorithms as the problem scale is sufficiently large. To further enhance the quality of the original solutions, the improvement scheme is provided for these algorithms. A new lower bound with performance guarantee is provided, and computational experiments show the effectiveness of these heuristics. Moreover, several results of the single-machine TQCT problem with release dates are also obtained for the deduction of the main theorem.

ORACLS- OPTIMAL REGULATOR ALGORITHMS FOR THE CONTROL OF LINEAR SYSTEMS (DEC VAX VERSION)

NASA Technical Reports Server (NTRS)

Frisch, H.

1994-01-01

This control theory design package, called Optimal Regulator Algorithms for the Control of Linear Systems (ORACLS), was developed to aid in the design of controllers and optimal filters for systems which can be modeled by linear, time-invariant differential and difference equations. Optimal linear quadratic regulator theory, currently referred to as the Linear-Quadratic-Gaussian (LQG) problem, has become the most widely accepted method of determining optimal control policy. Within this theory, the infinite duration time-invariant problems, which lead to constant gain feedback control laws and constant Kalman-Bucy filter gains for reconstruction of the system state, exhibit high tractability and potential ease of implementation. A variety of new and efficient methods in the field of numerical linear algebra have been combined into the ORACLS program, which provides for the solution to time-invariant continuous or discrete LQG problems. The ORACLS package is particularly attractive to the control system designer because it provides a rigorous tool for dealing with multi-input and multi-output dynamic systems in both continuous and discrete form. The ORACLS programming system is a collection of subroutines which can be used to formulate, manipulate, and solve various LQG design problems. The ORACLS program is constructed in a manner which permits the user to maintain considerable flexibility at each operational state. This flexibility is accomplished by providing primary operations, analysis of linear time-invariant systems, and control synthesis based on LQG methodology. The input-output routines handle the reading and writing of numerical matrices, printing heading information, and accumulating output information. The basic vector-matrix operations include addition, subtraction, multiplication, equation, norm construction, tracing, transposition, scaling, juxtaposition, and construction of null and identity matrices. The analysis routines provide for the following

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…

Data Retrieval Algorithms for Validating the Optical Transient Detector and the Lightning Imaging Sensor

NASA Technical Reports Server (NTRS)

Koshak, W. J.; Blakeslee, R. J.; Bailey, J. C.

2000-01-01

A linear algebraic solution is provided for the problem of retrieving the location and time of occurrence of lightning ground strikes from an Advanced Lightning Direction Finder (ALDF) network. The ALDF network measures field strength, magnetic bearing, and arrival time of lightning radio emissions. Solutions for the plane (i.e., no earth curvature) are provided that implement all of these measurements. The accuracy of the retrieval method is tested using computer-simulated datasets, and the relative influence of bearing and arrival time data an the outcome of the final solution is formally demonstrated. The algorithm is sufficiently accurate to validate NASA:s Optical Transient Detector and Lightning Imaging Sensor. A quadratic planar solution that is useful when only three arrival time measurements are available is also introduced. The algebra of the quadratic root results are examined in detail to clarify what portions of the analysis region lead to fundamental ambiguities in sc)iirce location, Complex root results are shown to be associated with the presence of measurement errors when the lightning source lies near an outer sensor baseline of the ALDF network. For arbitrary noncollinear network geometries and in the absence of measurement errors, it is shown that the two quadratic roots are equivalent (no source location ambiguity) on the outer sensor baselines. The accuracy of the quadratic planar method is tested with computer-generated datasets, and the results are generally better than those obtained from the three-station linear planar method when bearing errors are about 2 deg.

Symmetry-breaking instability of quadratic soliton bound states

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

Delque, Michaeel; Departement d'Optique P.M. Duffieux, Institut FEMTO-ST, Universite de Franche-Comte, CNRS UMR 6174, F-25030 Besancon; Fanjoux, Gil

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

Linear quadratic regulators with eigenvalue placement in a horizontal strip

NASA Technical Reports Server (NTRS)

Shieh, Leang S.; Dib, Hani M.; Ganesan, Sekar

1987-01-01

A method for optimally shifting the imaginary parts of the open-loop poles of a multivariable control system to the desirable closed-loop locations is presented. The optimal solution with respect to a quadratic performance index is obtained by solving a linear matrix Liapunov equation.

Stochastic resonance in a fractional oscillator driven by multiplicative quadratic noise

NASA Astrophysics Data System (ADS)

Ren, Ruibin; Luo, Maokang; Deng, Ke

2017-02-01

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

Thermal response test data of five quadratic cross section precast pile heat exchangers.

PubMed

Alberdi-Pagola, Maria

2018-06-01

This data article comprises records from five Thermal Response Tests (TRT) of quadratic cross section pile heat exchangers. Pile heat exchangers, typically referred to as energy piles, consist of traditional foundation piles with embedded heat exchanger pipes. The data presented in this article are related to the research article entitled "Comparing heat flow models for interpretation of precast quadratic pile heat exchanger thermal response tests" (Alberdi-Pagola et al., 2018) [1]. The TRT data consists of measured inlet and outlet temperatures, fluid flow and injected heat rate recorded every 10 min. The field dataset is made available to enable model verification studies.

Self-repeating properties of four-petal Gaussian vortex beams in quadratic index medium

NASA Astrophysics Data System (ADS)

Zou, Defeng; Li, Xiaohui; Chai, Tong; Zheng, Hairong

2018-05-01

In this paper, we investigate the propagation properties of four-petal Gaussian vortex (FPGV) beams propagating through the quadratic index medium, obtaining the analytical expression of FPGV beams. The effects of beam order n, topological charge m and beam waist ω0 are investigated. Results show that quadratic index medium support periodic distributions of FPGV beams. A hollow optical wall or an optical central principal maximum surrounded by symmetrical sidelobes will occur at the center of a period. At length, they will evolve into four petals structure, exactly same as the intensity distributions at source plane.

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

Algorithm Calculates Cumulative Poisson Distribution

NASA Technical Reports Server (NTRS)

Bowerman, Paul N.; Nolty, Robert C.; Scheuer, Ernest M.

1992-01-01

Algorithm calculates accurate values of cumulative Poisson distribution under conditions where other algorithms fail because numbers are so small (underflow) or so large (overflow) that computer cannot process them. Factors inserted temporarily to prevent underflow and overflow. Implemented in CUMPOIS computer program described in "Cumulative Poisson Distribution Program" (NPO-17714).

A depth-first search algorithm to compute elementary flux modes by linear programming.

PubMed

Quek, Lake-Ee; Nielsen, Lars K

2014-07-30

The decomposition of complex metabolic networks into elementary flux modes (EFMs) provides a useful framework for exploring reaction interactions systematically. Generating a complete set of EFMs for large-scale models, however, is near impossible. Even for moderately-sized models (<400 reactions), existing approaches based on the Double Description method must iterate through a large number of combinatorial candidates, thus imposing an immense processor and memory demand. Based on an alternative elementarity test, we developed a depth-first search algorithm using linear programming (LP) to enumerate EFMs in an exhaustive fashion. Constraints can be introduced to directly generate a subset of EFMs satisfying the set of constraints. The depth-first search algorithm has a constant memory overhead. Using flux constraints, a large LP problem can be massively divided and parallelized into independent sub-jobs for deployment into computing clusters. Since the sub-jobs do not overlap, the approach scales to utilize all available computing nodes with minimal coordination overhead or memory limitations. The speed of the algorithm was comparable to efmtool, a mainstream Double Description method, when enumerating all EFMs; the attrition power gained from performing flux feasibility tests offsets the increased computational demand of running an LP solver. Unlike the Double Description method, the algorithm enables accelerated enumeration of all EFMs satisfying a set of constraints.

A depth-first search algorithm to compute elementary flux modes by linear programming

PubMed Central

2014-01-01

Background The decomposition of complex metabolic networks into elementary flux modes (EFMs) provides a useful framework for exploring reaction interactions systematically. Generating a complete set of EFMs for large-scale models, however, is near impossible. Even for moderately-sized models (<400 reactions), existing approaches based on the Double Description method must iterate through a large number of combinatorial candidates, thus imposing an immense processor and memory demand. Results Based on an alternative elementarity test, we developed a depth-first search algorithm using linear programming (LP) to enumerate EFMs in an exhaustive fashion. Constraints can be introduced to directly generate a subset of EFMs satisfying the set of constraints. The depth-first search algorithm has a constant memory overhead. Using flux constraints, a large LP problem can be massively divided and parallelized into independent sub-jobs for deployment into computing clusters. Since the sub-jobs do not overlap, the approach scales to utilize all available computing nodes with minimal coordination overhead or memory limitations. Conclusions The speed of the algorithm was comparable to efmtool, a mainstream Double Description method, when enumerating all EFMs; the attrition power gained from performing flux feasibility tests offsets the increased computational demand of running an LP solver. Unlike the Double Description method, the algorithm enables accelerated enumeration of all EFMs satisfying a set of constraints. PMID:25074068

Robust Blind Learning Algorithm for Nonlinear Equalization Using Input Decision Information.

PubMed

Xu, Lu; Huang, Defeng David; Guo, Yingjie Jay

2015-12-01

In this paper, we propose a new blind learning algorithm, namely, the Benveniste-Goursat input-output decision (BG-IOD), to enhance the convergence performance of neural network-based equalizers for nonlinear channel equalization. In contrast to conventional blind learning algorithms, where only the output of the equalizer is employed for updating system parameters, the BG-IOD exploits a new type of extra information, the input decision information obtained from the input of the equalizer, to mitigate the influence of the nonlinear equalizer structure on parameters learning, thereby leading to improved convergence performance. We prove that, with the input decision information, a desirable convergence capability that the output symbol error rate (SER) is always less than the input SER if the input SER is below a threshold, can be achieved. Then, the BG soft-switching technique is employed to combine the merits of both input and output decision information, where the former is used to guarantee SER convergence and the latter is to improve SER performance. Simulation results show that the proposed algorithm outperforms conventional blind learning algorithms, such as stochastic quadratic distance and dual mode constant modulus algorithm, in terms of both convergence performance and SER performance, for nonlinear equalization.

Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid

ERIC Educational Resources Information Center

Brilleslyper, Michael A.

2004-01-01

Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.

Entanglement in a model for Hawking radiation: An application of quadratic algebras

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

Bambah, Bindu A., E-mail: bbsp@uohyd.ernet.in; Mukku, C., E-mail: mukku@iiit.ac.in; Shreecharan, T., E-mail: shreecharan@gmail.com

2013-03-15

Quadratic polynomially deformed su(1,1) and su(2) algebras are utilized in model Hamiltonians to show how the gravitational system consisting of a black hole, infalling radiation and outgoing (Hawking) radiation can be solved exactly. The models allow us to study the long-time behaviour of the black hole and its outgoing modes. In particular, we calculate the bipartite entanglement entropies of subsystems consisting of (a) infalling plus outgoing modes and (b) black hole modes plus the infalling modes, using the Janus-faced nature of the model. The long-time behaviour also gives us glimpses of modifications in the character of Hawking radiation. Finally, wemore » study the phenomenon of superradiance in our model in analogy with atomic Dicke superradiance. - Highlights: Black-Right-Pointing-Pointer We examine a toy model for Hawking radiation with quantized black hole modes. Black-Right-Pointing-Pointer We use quadratic polynomially deformed su(1,1) algebras to study its entanglement properties. Black-Right-Pointing-Pointer We study the 'Dicke Superradiance' in black hole radiation using quadratically deformed su(2) algebras. Black-Right-Pointing-Pointer We study the modification of the thermal character of Hawking radiation due to quantized black hole modes.« less

A disturbance based control/structure design algorithm

NASA Technical Reports Server (NTRS)

Mclaren, Mark D.; Slater, Gary L.

1989-01-01

Some authors take a classical approach to the simultaneous structure/control optimization by attempting to simultaneously minimize the weighted sum of the total mass and a quadratic form, subject to all of the structural and control constraints. Here, the optimization will be based on the dynamic response of a structure to an external unknown stochastic disturbance environment. Such a response to excitation approach is common to both the structural and control design phases, and hence represents a more natural control/structure optimization strategy than relying on artificial and vague control penalties. The design objective is to find the structure and controller of minimum mass such that all the prescribed constraints are satisfied. Two alternative solution algorithms are presented which have been applied to this problem. Each algorithm handles the optimization strategy and the imposition of the nonlinear constraints in a different manner. Two controller methodologies, and their effect on the solution algorithm, will be considered. These are full state feedback and direct output feedback, although the problem formulation is not restricted solely to these forms of controller. In fact, although full state feedback is a popular choice among researchers in this field (for reasons that will become apparent), its practical application is severely limited. The controller/structure interaction is inserted by the imposition of appropriate closed-loop constraints, such as closed-loop output response and control effort constraints. Numerical results will be obtained for a representative flexible structure model to illustrate the effectiveness of the solution algorithms.

Fast Dating Using Least-Squares Criteria and Algorithms.

PubMed

To, Thu-Hien; Jung, Matthieu; Lycett, Samantha; Gascuel, Olivier

2016-01-01

Phylogenies provide a useful way to understand the evolutionary history of genetic samples, and data sets with more than a thousand taxa are becoming increasingly common, notably with viruses (e.g., human immunodeficiency virus (HIV)). Dating ancestral events is one of the first, essential goals with such data. However, current sophisticated probabilistic approaches struggle to handle data sets of this size. Here, we present very fast dating algorithms, based on a Gaussian model closely related to the Langley-Fitch molecular-clock model. We show that this model is robust to uncorrelated violations of the molecular clock. Our algorithms apply to serial data, where the tips of the tree have been sampled through times. They estimate the substitution rate and the dates of all ancestral nodes. When the input tree is unrooted, they can provide an estimate for the root position, thus representing a new, practical alternative to the standard rooting methods (e.g., midpoint). Our algorithms exploit the tree (recursive) structure of the problem at hand, and the close relationships between least-squares and linear algebra. We distinguish between an unconstrained setting and the case where the temporal precedence constraint (i.e., an ancestral node must be older that its daughter nodes) is accounted for. With rooted trees, the former is solved using linear algebra in linear computing time (i.e., proportional to the number of taxa), while the resolution of the latter, constrained setting, is based on an active-set method that runs in nearly linear time. With unrooted trees the computing time becomes (nearly) quadratic (i.e., proportional to the square of the number of taxa). In all cases, very large input trees (>10,000 taxa) can easily be processed and transformed into time-scaled trees. We compare these algorithms to standard methods (root-to-tip, r8s version of Langley-Fitch method, and BEAST). Using simulated data, we show that their estimation accuracy is similar to that

Fast Dating Using Least-Squares Criteria and Algorithms

PubMed Central

To, Thu-Hien; Jung, Matthieu; Lycett, Samantha; Gascuel, Olivier

2016-01-01

Phylogenies provide a useful way to understand the evolutionary history of genetic samples, and data sets with more than a thousand taxa are becoming increasingly common, notably with viruses (e.g., human immunodeficiency virus (HIV)). Dating ancestral events is one of the first, essential goals with such data. However, current sophisticated probabilistic approaches struggle to handle data sets of this size. Here, we present very fast dating algorithms, based on a Gaussian model closely related to the Langley–Fitch molecular-clock model. We show that this model is robust to uncorrelated violations of the molecular clock. Our algorithms apply to serial data, where the tips of the tree have been sampled through times. They estimate the substitution rate and the dates of all ancestral nodes. When the input tree is unrooted, they can provide an estimate for the root position, thus representing a new, practical alternative to the standard rooting methods (e.g., midpoint). Our algorithms exploit the tree (recursive) structure of the problem at hand, and the close relationships between least-squares and linear algebra. We distinguish between an unconstrained setting and the case where the temporal precedence constraint (i.e., an ancestral node must be older that its daughter nodes) is accounted for. With rooted trees, the former is solved using linear algebra in linear computing time (i.e., proportional to the number of taxa), while the resolution of the latter, constrained setting, is based on an active-set method that runs in nearly linear time. With unrooted trees the computing time becomes (nearly) quadratic (i.e., proportional to the square of the number of taxa). In all cases, very large input trees (>10,000 taxa) can easily be processed and transformed into time-scaled trees. We compare these algorithms to standard methods (root-to-tip, r8s version of Langley–Fitch method, and BEAST). Using simulated data, we show that their estimation accuracy is similar to

Quadratic semiparametric Von Mises calculus

PubMed Central

Robins, James; Li, Lingling; Tchetgen, Eric

2009-01-01

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

Forecasting Nonlinear Chaotic Time Series with Function Expression Method Based on an Improved Genetic-Simulated Annealing Algorithm

PubMed Central

Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng

2015-01-01

The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior. PMID:26000011

QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.

PubMed

Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

2014-01-01

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

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.

QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES

PubMed Central

RAND, ALEXANDER; GILLETTE, ANDREW; BAJAJ, CHANDRAJIT

2013-01-01

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

Iterative algorithms for computing the feedback Nash equilibrium point for positive systems

NASA Astrophysics Data System (ADS)

Ivanov, I.; Imsland, Lars; Bogdanova, B.

2017-03-01

The paper studies N-player linear quadratic differential games on an infinite time horizon with deterministic feedback information structure. It introduces two iterative methods (the Newton method as well as its accelerated modification) in order to compute the stabilising solution of a set of generalised algebraic Riccati equations. The latter is related to the Nash equilibrium point of the considered game model. Moreover, we derive the sufficient conditions for convergence of the proposed methods. Finally, we discuss two numerical examples so as to illustrate the performance of both of the algorithms.

Quadratic band touching points and flat bands in two-dimensional topological Floquet systems

NASA Astrophysics Data System (ADS)

Du, Liang; Zhou, Xiaoting; Fiete, Gregory A.

2017-01-01

In this paper we theoretically study, using Floquet-Bloch theory, the influence of circularly and linearly polarized light on two-dimensional band structures with Dirac and quadratic band touching points, and flat bands, taking the nearest neighbor hopping model on the kagome lattice as an example. We find circularly polarized light can invert the ordering of this three-band model, while leaving the flat band dispersionless. We find a small gap is also opened at the quadratic band touching point by two-photon and higher order processes. By contrast, linearly polarized light splits the quadratic band touching point (into two Dirac points) by an amount that depends only on the amplitude and polarization direction of the light, independent of the frequency, and generally renders dispersion to the flat band. The splitting is perpendicular to the direction of the polarization of the light. We derive an effective low-energy theory that captures these key results. Finally, we compute the frequency dependence of the optical conductivity for this three-band model and analyze the various interband contributions of the Floquet modes. Our results suggest strategies for optically controlling band structure and interaction strength in real systems.

An O(log sup 2 N) parallel algorithm for computing the eigenvalues of a symmetric tridiagonal matrix

NASA Technical Reports Server (NTRS)

Swarztrauber, Paul N.

1989-01-01

An O(log sup 2 N) parallel algorithm is presented for computing the eigenvalues of a symmetric tridiagonal matrix using a parallel algorithm for computing the zeros of the characteristic polynomial. The method is based on a quadratic recurrence in which the characteristic polynomial is constructed on a binary tree from polynomials whose degree doubles at each level. Intervals that contain exactly one zero are determined by the zeros of polynomials at the previous level which ensures that different processors compute different zeros. The exact behavior of the polynomials at the interval endpoints is used to eliminate the usual problems induced by finite precision arithmetic.

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.

Demonstration and Validation of the Geostatistical Temporal-Spatial Algorithm (GTS) for Optimization of Long-Term Monitoring (LTM) of Groundwater at Military and Government Sites

DTIC Science & Technology

2010-08-01

Long - Term Monitoring (LTM) of Groundwater at Military and...Geostatistical Temporal-Spatial Algorithm (GTS) for Optimization of Long - Term Monitoring (LTM) of Groundwater at Military and Government Sites 5a. CONTRACT NUMBER...Council LTM long - term monitoring LTMO long - term monitoring optimization LWQR locally weighted quadratic regression LZ Lower Zone MCL

Linear-Quadratic Control of a MEMS Micromirror using Kalman Filtering

DTIC Science & Technology

2011-12-01

LINEAR-QUADRATIC CONTROL OF A MEMS MICROMIRROR USING KALMAN FILTERING THESIS Jamie P...A MEMS MICROMIRROR USING KALMAN FILTERING THESIS Presented to the Faculty Department of Electrical Engineering Graduate School of...actuated micromirrors fabricated by PolyMUMPs. Successful application of these techniques enables demonstration of smooth, stable deflections of 50% and

A generalized global alignment algorithm.

PubMed

Huang, Xiaoqiu; Chao, Kun-Mao

2003-01-22

Homologous sequences are sometimes similar over some regions but different over other regions. Homologous sequences have a much lower global similarity if the different regions are much longer than the similar regions. We present a generalized global alignment algorithm for comparing sequences with intermittent similarities, an ordered list of similar regions separated by different regions. A generalized global alignment model is defined to handle sequences with intermittent similarities. A dynamic programming algorithm is designed to compute an optimal general alignment in time proportional to the product of sequence lengths and in space proportional to the sum of sequence lengths. The algorithm is implemented as a computer program named GAP3 (Global Alignment Program Version 3). The generalized global alignment model is validated by experimental results produced with GAP3 on both DNA and protein sequences. The GAP3 program extends the ability of standard global alignment programs to recognize homologous sequences of lower similarity. The GAP3 program is freely available for academic use at http://bioinformatics.iastate.edu/aat/align/align.html.

Elegant Ince-Gaussian beams in a quadratic-index medium

NASA Astrophysics Data System (ADS)

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

2011-09-01

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

A 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.

A quadratic regression modelling on paddy production in the area of Perlis

NASA Astrophysics Data System (ADS)

Goh, Aizat Hanis Annas; Ali, Zalila; Nor, Norlida Mohd; Baharum, Adam; Ahmad, Wan Muhamad Amir W.

2017-08-01

Polynomial regression models are useful in situations in which the relationship between a response variable and predictor variables is curvilinear. Polynomial regression fits the nonlinear relationship into a least squares linear regression model by decomposing the predictor variables into a kth order polynomial. The polynomial order determines the number of inflexions on the curvilinear fitted line. A second order polynomial forms a quadratic expression (parabolic curve) with either a single maximum or minimum, a third order polynomial forms a cubic expression with both a relative maximum and a minimum. This study used paddy data in the area of Perlis to model paddy production based on paddy cultivation characteristics and environmental characteristics. The results indicated that a quadratic regression model best fits the data and paddy production is affected by urea fertilizer application and the interaction between amount of average rainfall and percentage of area defected by pest and disease. Urea fertilizer application has a quadratic effect in the model which indicated that if the number of days of urea fertilizer application increased, paddy production is expected to decrease until it achieved a minimum value and paddy production is expected to increase at higher number of days of urea application. The decrease in paddy production with an increased in rainfall is greater, the higher the percentage of area defected by pest and disease.

Program for the analysis of time series. [by means of fast Fourier transform algorithm

NASA Technical Reports Server (NTRS)

Brown, T. J.; Brown, C. G.; Hardin, J. C.

1974-01-01

A digital computer program for the Fourier analysis of discrete time data is described. The program was designed to handle multiple channels of digitized data on general purpose computer systems. It is written, primarily, in a version of FORTRAN 2 currently in use on CDC 6000 series computers. Some small portions are written in CDC COMPASS, an assembler level code. However, functional descriptions of these portions are provided so that the program may be adapted for use on any facility possessing a FORTRAN compiler and random-access capability. Properly formatted digital data are windowed and analyzed by means of a fast Fourier transform algorithm to generate the following functions: (1) auto and/or cross power spectra, (2) autocorrelations and/or cross correlations, (3) Fourier coefficients, (4) coherence functions, (5) transfer functions, and (6) histograms.

Jerk-level synchronous repetitive motion scheme with gradient-type and zeroing-type dynamics algorithms applied to dual-arm redundant robot system control

NASA Astrophysics Data System (ADS)

Chen, Dechao; Zhang, Yunong

2017-10-01

Dual-arm redundant robot systems are usually required to handle primary tasks, repetitively and synchronously in practical applications. In this paper, a jerk-level synchronous repetitive motion scheme is proposed to remedy the joint-angle drift phenomenon and achieve the synchronous control of a dual-arm redundant robot system. The proposed scheme is novelly resolved at jerk level, which makes the joint variables, i.e. joint angles, joint velocities and joint accelerations, smooth and bounded. In addition, two types of dynamics algorithms, i.e. gradient-type (G-type) and zeroing-type (Z-type) dynamics algorithms, for the design of repetitive motion variable vectors, are presented in detail with the corresponding circuit schematics. Subsequently, the proposed scheme is reformulated as two dynamical quadratic programs (DQPs) and further integrated into a unified DQP (UDQP) for the synchronous control of a dual-arm robot system. The optimal solution of the UDQP is found by the piecewise-linear projection equation neural network. Moreover, simulations and comparisons based on a six-degrees-of-freedom planar dual-arm redundant robot system substantiate the operation effectiveness and tracking accuracy of the robot system with the proposed scheme for repetitive motion and synchronous control.

Constraints on both the quadratic and quartic symmetry energy coefficients by 2β --decay energies

NASA Astrophysics Data System (ADS)

Wan, Niu; Xu, Chang; Ren, Zhongzhou; Liu, Jie

2018-05-01

In this Rapid Communication, the 2 β- -decay energies Q (2 β-) given in the atomic mass evaluation are used to extract not only the quadratic volume symmetry energy coefficient csymv, but also the quartic one csym,4 v. Based on the modified Bethe-Weizsäcker nuclear mass formula of the liquid-drop model, the decay energy Q (2 β-) is found to be closely related to both the quadratic and quartic symmetry energy coefficients csymv and csym,4 v. There are totally 449 data of decay energies Q (2 β-) used in the present analysis where the candidate nuclei are carefully chosen by fulfilling the following criteria: (1) large neutron-proton number difference N -Z , (2) large isospin asymmetry I , and (3) limited shell effect. The values of csymv and csym,4 v are extracted to be 29.345 and 3.634 MeV, respectively. Moreover, the quadratic surface-volume symmetry energy coefficient ratio is determined to be κ =csyms/csymv=1.356 .

Discovering Link Communities in Complex Networks by an Integer Programming Model and a Genetic Algorithm

PubMed Central

Li, Zhenping; Zhang, Xiang-Sun; Wang, Rui-Sheng; Liu, Hongwei; Zhang, Shihua

2013-01-01

Identification of communities in complex networks is an important topic and issue in many fields such as sociology, biology, and computer science. Communities are often defined as groups of related nodes or links that correspond to functional subunits in the corresponding complex systems. While most conventional approaches have focused on discovering communities of nodes, some recent studies start partitioning links to find overlapping communities straightforwardly. In this paper, we propose a new quantity function for link community identification in complex networks. Based on this quantity function we formulate the link community partition problem into an integer programming model which allows us to partition a complex network into overlapping communities. We further propose a genetic algorithm for link community detection which can partition a network into overlapping communities without knowing the number of communities. We test our model and algorithm on both artificial networks and real-world networks. The results demonstrate that the model and algorithm are efficient in detecting overlapping community structure in complex networks. PMID:24386268

Design of Linear Quadratic Regulators and Kalman Filters

NASA Technical Reports Server (NTRS)

Lehtinen, B.; Geyser, L.

1986-01-01

AESOP solves problems associated with design of controls and state estimators for linear time-invariant systems. Systems considered are modeled in state-variable form by set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are linear quadratic regulator (LQR) design problem and steady-state Kalman filter design problem. AESOP is interactive. User solves design problems and analyzes solutions in single interactive session. Both numerical and graphical information available to user during the session.

Field-antifield and BFV formalisms for quadratic systems with open gauge algebras

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

Nirov, K.S.; Razumov, A.V.

1992-09-20

In this paper the Lagrangian field-antifield (BV) and Hamiltonian (BFV) BRST formalisms for the general quadratic systems with open gauge algebra are considered. The equivalence between the Lagrangian and Hamiltonian formalisms is proven.

Numerical solution of quadratic matrix equations for free vibration analysis of structures

NASA Technical Reports Server (NTRS)

Gupta, K. K.

1975-01-01

This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.

First report of soybean pest, Euschistus quadrator (Hempitera: pentatomidae) in Mississippi

USDA-ARS?s Scientific Manuscript database

Here we report on the first state and county record of Euschistus quadrator Ralston (Hemiptera: Pentatomidae) in Washington County, Mississippi. The species has been documented from Honduras to Virginia primarily on soybeans, cotton, various row crops, fruit, and non-crop hosts. The local impact...

Models of performance of evolutionary program induction algorithms based on indicators of problem difficulty.

PubMed

Graff, Mario; Poli, Riccardo; Flores, Juan J

2013-01-01

Modeling the behavior of algorithms is the realm of evolutionary algorithm theory. From a practitioner's point of view, theory must provide some guidelines regarding which algorithm/parameters to use in order to solve a particular problem. Unfortunately, most theoretical models of evolutionary algorithms are difficult to apply to realistic situations. However, in recent work (Graff and Poli, 2008, 2010), where we developed a method to practically estimate the performance of evolutionary program-induction algorithms (EPAs), we started addressing this issue. The method was quite general; however, it suffered from some limitations: it required the identification of a set of reference problems, it required hand picking a distance measure in each particular domain, and the resulting models were opaque, typically being linear combinations of 100 features or more. In this paper, we propose a significant improvement of this technique that overcomes the three limitations of our previous method. We achieve this through the use of a novel set of features for assessing problem difficulty for EPAs which are very general, essentially based on the notion of finite difference. To show the capabilities or our technique and to compare it with our previous performance models, we create models for the same two important classes of problems-symbolic regression on rational functions and Boolean function induction-used in our previous work. We model a variety of EPAs. The comparison showed that for the majority of the algorithms and problem classes, the new method produced much simpler and more accurate models than before. To further illustrate the practicality of the technique and its generality (beyond EPAs), we have also used it to predict the performance of both autoregressive models and EPAs on the problem of wind speed forecasting, obtaining simpler and more accurate models that outperform in all cases our previous performance models.

Importance of the cutoff value in the quadratic adaptive integrate-and-fire model.

PubMed

Touboul, Jonathan

2009-08-01

The quadratic adaptive integrate-and-fire model (Izhikevich, 2003 , 2007 ) is able to reproduce various firing patterns of cortical neurons and is widely used in large-scale simulations of neural networks. This model describes the dynamics of the membrane potential by a differential equation that is quadratic in the voltage, coupled to a second equation for adaptation. Integration is stopped during the rise phase of a spike at a voltage cutoff value V(c) or when it blows up. Subsequently the membrane potential is reset, and the adaptation variable is increased by a fixed amount. We show in this note that in the absence of a cutoff value, not only the voltage but also the adaptation variable diverges in finite time during spike generation in the quadratic model. The divergence of the adaptation variable makes the system very sensitive to the cutoff: changing V(c) can dramatically alter the spike patterns. Furthermore, from a computational viewpoint, the divergence of the adaptation variable implies that the time steps for numerical simulation need to be small and adaptive. However, divergence of the adaptation variable does not occur for the quartic model (Touboul, 2008 ) and the adaptive exponential integrate-and-fire model (Brette & Gerstner, 2005 ). Hence, these models are robust to changes in the cutoff value.

Quadratic band touching points and flat bands in two-dimensional topological Floquet systems

NASA Astrophysics Data System (ADS)

Du, Liang; Zhou, Xiaoting; Fiete, Gregory; The CenterComplex Quantum Systems Team

In this work we theoretically study, using Floquet-Bloch theory, the influence of circularly and linearly polarized light on two-dimensional band structures with Dirac and quadratic band touching points, and flat bands, taking the nearest neighbor hopping model on the kagome lattice as an example. We find circularly polarized light can invert the ordering of this three band model, while leaving the flat-band dispersionless. We find a small gap is also opened at the quadratic band touching point by 2-photon and higher order processes. By contrast, linearly polarized light splits the quadratic band touching point (into two Dirac points) by an amount that depends only on the amplitude and polarization direction of the light, independent of the frequency, and generally renders dispersion to the flat band. The splitting is perpendicular to the direction of the polarization of the light. We derive an effective low-energy theory that captures these key results. Finally, we compute the frequency dependence of the optical conductivity for this 3-band model and analyze the various interband contributions of the Floquet modes. Our results suggest strategies for optically controlling band structure and interaction strength in real systems. We gratefully acknowledge funding from ARO Grant W911NF-14-1-0579 and NSF DMR-1507621.

On a programming language for graph algorithms

NASA Technical Reports Server (NTRS)

Rheinboldt, W. C.; Basili, V. R.; Mesztenyi, C. K.

1971-01-01

An algorithmic language, GRAAL, is presented for describing and implementing graph algorithms of the type primarily arising in applications. The language is based on a set algebraic model of graph theory which defines the graph structure in terms of morphisms between certain set algebraic structures over the node set and arc set. GRAAL is modular in the sense that the user specifies which of these mappings are available with any graph. This allows flexibility in the selection of the storage representation for different graph structures. In line with its set theoretic foundation, the language introduces sets as a basic data type and provides for the efficient execution of all set and graph operators. At present, GRAAL is defined as an extension of ALGOL 60 (revised) and its formal description is given as a supplement to the syntactic and semantic definition of ALGOL. Several typical graph algorithms are written in GRAAL to illustrate various features of the language and to show its applicability.

Confidence set interference with a prior quadratic bound. [in geophysics

NASA Technical Reports Server (NTRS)

Backus, George E.

1989-01-01

Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.

One cutting plane algorithm using auxiliary functions

NASA Astrophysics Data System (ADS)

Zabotin, I. Ya; Kazaeva, K. E.

2016-11-01

We propose an algorithm for solving a convex programming problem from the class of cutting methods. The algorithm is characterized by the construction of approximations using some auxiliary functions, instead of the objective function. Each auxiliary function bases on the exterior penalty function. In proposed algorithm the admissible set and the epigraph of each auxiliary function are embedded into polyhedral sets. In connection with the above, the iteration points are found by solving linear programming problems. We discuss the implementation of the algorithm and prove its convergence.

Algorithms for synthesizing management solutions based on OLAP-technologies

NASA Astrophysics Data System (ADS)

Pishchukhin, A. M.; Akhmedyanova, G. F.

2018-05-01

OLAP technologies are a convenient means of analyzing large amounts of information. An attempt was made in their work to improve the synthesis of optimal management decisions. The developed algorithms allow forecasting the needs and accepted management decisions on the main types of the enterprise resources. Their advantage is the efficiency, based on the simplicity of quadratic functions and differential equations of only the first order. At the same time, the optimal redistribution of resources between different types of products from the assortment of the enterprise is carried out, and the optimal allocation of allocated resources in time. The proposed solutions can be placed on additional specially entered coordinates of the hypercube representing the data warehouse.

Discrete-time Markovian-jump linear quadratic optimal control

NASA Technical Reports Server (NTRS)

Chizeck, H. J.; Willsky, A. S.; Castanon, D.

1986-01-01

This paper is concerned with the optimal control of discrete-time linear systems that possess randomly jumping parameters described by finite-state Markov processes. For problems having quadratic costs and perfect observations, the optimal control laws and expected costs-to-go can be precomputed from a set of coupled Riccati-like matrix difference equations. Necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite, with finite optimal expected cost.

A Fast Algorithm of Convex Hull Vertices Selection for Online Classification.

PubMed

Ding, Shuguang; Nie, Xiangli; Qiao, Hong; Zhang, Bo

2018-04-01

Reducing samples through convex hull vertices selection (CHVS) within each class is an important and effective method for online classification problems, since the classifier can be trained rapidly with the selected samples. However, the process of CHVS is NP-hard. In this paper, we propose a fast algorithm to select the convex hull vertices, based on the convex hull decomposition and the property of projection. In the proposed algorithm, the quadratic minimization problem of computing the distance between a point and a convex hull is converted into a linear equation problem with a low computational complexity. When the data dimension is high, an approximate, instead of exact, convex hull is allowed to be selected by setting an appropriate termination condition in order to delete more nonimportant samples. In addition, the impact of outliers is also considered, and the proposed algorithm is improved by deleting the outliers in the initial procedure. Furthermore, a dimension convention technique via the kernel trick is used to deal with nonlinearly separable problems. An upper bound is theoretically proved for the difference between the support vector machines based on the approximate convex hull vertices selected and all the training samples. Experimental results on both synthetic and real data sets show the effectiveness and validity of the proposed algorithm.

A Functional Programming Approach to AI Search Algorithms

ERIC Educational Resources Information Center

Panovics, Janos

2012-01-01

The theory and practice of search algorithms related to state-space represented problems form the major part of the introductory course of Artificial Intelligence at most of the universities and colleges offering a degree in the area of computer science. Students usually meet these algorithms only in some imperative or object-oriented language…

A General Program for Item-Response Analysis That Employs the Stabilized Newton-Raphson Algorithm. Research Report. ETS RR-13-32

ERIC Educational Resources Information Center

Haberman, Shelby J.

2013-01-01

A general program for item-response analysis is described that uses the stabilized Newton-Raphson algorithm. This program is written to be compliant with Fortran 2003 standards and is sufficiently general to handle independent variables, multidimensional ability parameters, and matrix sampling. The ability variables may be either polytomous or…

Selecting the correct weighting factors for linear and quadratic calibration curves with least-squares regression algorithm in bioanalytical LC-MS/MS assays and impacts of using incorrect weighting factors on curve stability, data quality, and assay performance.

PubMed

Gu, Huidong; Liu, Guowen; Wang, Jian; Aubry, Anne-Françoise; Arnold, Mark E

2014-09-16

A simple procedure for selecting the correct weighting factors for linear and quadratic calibration curves with least-squares regression algorithm in bioanalytical LC-MS/MS assays is reported. The correct weighting factor is determined by the relationship between the standard deviation of instrument responses (σ) and the concentrations (x). The weighting factor of 1, 1/x, or 1/x(2) should be selected if, over the entire concentration range, σ is a constant, σ(2) is proportional to x, or σ is proportional to x, respectively. For the first time, we demonstrated with detailed scientific reasoning, solid historical data, and convincing justification that 1/x(2) should always be used as the weighting factor for all bioanalytical LC-MS/MS assays. The impacts of using incorrect weighting factors on curve stability, data quality, and assay performance were thoroughly investigated. It was found that the most stable curve could be obtained when the correct weighting factor was used, whereas other curves using incorrect weighting factors were unstable. It was also found that there was a very insignificant impact on the concentrations reported with calibration curves using incorrect weighting factors as the concentrations were always reported with the passing curves which actually overlapped with or were very close to the curves using the correct weighting factor. However, the use of incorrect weighting factors did impact the assay performance significantly. Finally, the difference between the weighting factors of 1/x(2) and 1/y(2) was discussed. All of the findings can be generalized and applied into other quantitative analysis techniques using calibration curves with weighted least-squares regression algorithm.

An Efficient Supervised Training Algorithm for Multilayer Spiking Neural Networks

PubMed Central

Xie, Xiurui; Qu, Hong; Liu, Guisong; Zhang, Malu; Kurths, Jürgen

2016-01-01

The spiking neural networks (SNNs) are the third generation of neural networks and perform remarkably well in cognitive tasks such as pattern recognition. The spike emitting and information processing mechanisms found in biological cognitive systems motivate the application of the hierarchical structure and temporal encoding mechanism in spiking neural networks, which have exhibited strong computational capability. However, the hierarchical structure and temporal encoding approach require neurons to process information serially in space and time respectively, which reduce the training efficiency significantly. For training the hierarchical SNNs, most existing methods are based on the traditional back-propagation algorithm, inheriting its drawbacks of the gradient diffusion and the sensitivity on parameters. To keep the powerful computation capability of the hierarchical structure and temporal encoding mechanism, but to overcome the low efficiency of the existing algorithms, a new training algorithm, the Normalized Spiking Error Back Propagation (NSEBP) is proposed in this paper. In the feedforward calculation, the output spike times are calculated by solving the quadratic function in the spike response model instead of detecting postsynaptic voltage states at all time points in traditional algorithms. Besides, in the feedback weight modification, the computational error is propagated to previous layers by the presynaptic spike jitter instead of the gradient decent rule, which realizes the layer-wised training. Furthermore, our algorithm investigates the mathematical relation between the weight variation and voltage error change, which makes the normalization in the weight modification applicable. Adopting these strategies, our algorithm outperforms the traditional SNN multi-layer algorithms in terms of learning efficiency and parameter sensitivity, that are also demonstrated by the comprehensive experimental results in this paper. PMID:27044001

ALDF Data Retrieval Algorithms for Validating the Optical Transient Detector (OTD) and the Lightning Imaging Sensor (LIS)

NASA Technical Reports Server (NTRS)

Koshak, W. J.; Blakeslee, R. J.; Bailey, J. C.

1997-01-01

A linear algebraic solution is provided for the problem of retrieving the location and time of occurrence of lightning ground strikes from in Advanced Lightning Direction Finder (ALDF) network. The ALDF network measures field strength, magnetic bearing, and arrival time of lightning radio emissions and solutions for the plane (i.e.. no Earth curvature) are provided that implement all of these measurements. The accuracy of the retrieval method is tested using computer-simulated data sets and the relative influence of bearing and arrival time data on the outcome of the final solution is formally demonstrated. The algorithm is sufficiently accurate to validate NASA's Optical Transient Detector (OTD) and Lightning Imaging System (LIS). We also introduce a quadratic planar solution that is useful when only three arrival time measurements are available. The algebra of the quadratic root results are examined in detail to clarify what portions of the analysis region lead to fundamental ambiguities in source location. Complex root results are shown to be associated with the presence of measurement errors when the lightning source lies near an outer sensor baseline of the ALDF network. For arbitrary noncollinear network geometries and in the absence of measurement errors, it is shown that the two quadratic roots are equivalent (no source location ambiguity) on the outer sensor baselines. The accuracy of the quadratic planar method is tested with computer-generated data sets and the results are generally better than those obtained from the three station linear planar method when bearing errors are about 2 degrees.

Design of Linear-Quadratic-Regulator for a CSTR process

NASA Astrophysics Data System (ADS)

Meghna, P. R.; Saranya, V.; Jaganatha Pandian, B.

2017-11-01

This paper aims at creating a Linear Quadratic Regulator (LQR) for a Continuous Stirred Tank Reactor (CSTR). A CSTR is a common process used in chemical industries. It is a highly non-linear system. Therefore, in order to create the gain feedback controller, the model is linearized. The controller is designed for the linearized model and the concentration and volume of the liquid in the reactor are kept at a constant value as required.

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

NASA Technical Reports Server (NTRS)

Koppang, Paul; Leland, Robert

1996-01-01

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

Fourier transform and particle swarm optimization based modified LQR algorithm for mitigation of vibrations using magnetorheological dampers

NASA Astrophysics Data System (ADS)

Kumar, Gaurav; Kumar, Ashok

2017-11-01

Structural control has gained significant attention in recent times. The standalone issue of power requirement during an earthquake has already been solved up to a large extent by designing semi-active control systems using conventional linear quadratic control theory, and many other intelligent control algorithms such as fuzzy controllers, artificial neural networks, etc. In conventional linear-quadratic regulator (LQR) theory, it is customary to note that the values of the design parameters are decided at the time of designing the controller and cannot be subsequently altered. During an earthquake event, the response of the structure may increase or decrease, depending the quasi-resonance occurring between the structure and the earthquake. In this case, it is essential to modify the value of the design parameters of the conventional LQR controller to obtain optimum control force to mitigate the vibrations due to the earthquake. A few studies have been done to sort out this issue but in all these studies it was necessary to maintain a database of the earthquake. To solve this problem and to find the optimized design parameters of the LQR controller in real time, a fast Fourier transform and particle swarm optimization based modified linear quadratic regulator method is presented here. This method comprises four different algorithms: particle swarm optimization (PSO), the fast Fourier transform (FFT), clipped control algorithm and the LQR. The FFT helps to obtain the dominant frequency for every time window. PSO finds the optimum gain matrix through the real-time update of the weighting matrix R, thereby, dispensing with the experimentation. The clipped control law is employed to match the magnetorheological (MR) damper force with the desired force given by the controller. The modified Bouc-Wen phenomenological model is taken to recognize the nonlinearities in the MR damper. The assessment of the advised method is done by simulation of a three-story structure

Biological sequence compression algorithms.

PubMed

Matsumoto, T; Sadakane, K; Imai, H

2000-01-01

Today, more and more DNA sequences are becoming available. The information about DNA sequences are stored in molecular biology databases. The size and importance of these databases will be bigger and bigger in the future, therefore this information must be stored or communicated efficiently. Furthermore, sequence compression can be used to define similarities between biological sequences. The standard compression algorithms such as gzip or compress cannot compress DNA sequences, but only expand them in size. On the other hand, CTW (Context Tree Weighting Method) can compress DNA sequences less than two bits per symbol. These algorithms do not use special structures of biological sequences. Two characteristic structures of DNA sequences are known. One is called palindromes or reverse complements and the other structure is approximate repeats. Several specific algorithms for DNA sequences that use these structures can compress them less than two bits per symbol. In this paper, we improve the CTW so that characteristic structures of DNA sequences are available. Before encoding the next symbol, the algorithm searches an approximate repeat and palindrome using hash and dynamic programming. If there is a palindrome or an approximate repeat with enough length then our algorithm represents it with length and distance. By using this preprocessing, a new program achieves a little higher compression ratio than that of existing DNA-oriented compression algorithms. We also describe new compression algorithm for protein sequences.

Visualising the Complex Roots of Quadratic Equations with Real Coefficients

ERIC Educational Resources Information Center

Bardell, Nicholas S.

2012-01-01

The roots of the general quadratic equation y = ax[superscript 2] + bx + c (real a, b, c) are known to occur in the following sets: (i) real and distinct; (ii) real and coincident; and (iii) a complex conjugate pair. Case (iii), which provides the focus for this investigation, can only occur when the values of the real coefficients a, b, and c are…

Vagal activity is quadratically related to prosocial traits, prosocial emotions, and observer perceptions of prosociality.

PubMed

Kogan, Aleksandr; Oveis, Christopher; Carr, Evan W; Gruber, June; Mauss, Iris B; Shallcross, Amanda; Impett, Emily A; van der Lowe, Ilmo; Hui, Bryant; Cheng, Cecilia; Keltner, Dacher

2014-12-01

In the present article, we introduce the quadratic vagal activity-prosociality hypothesis, a theoretical framework for understanding the vagus nerve's involvement in prosociality. We argue that vagus nerve activity supports prosocial behavior by regulating physiological systems that enable emotional expression, empathy for others' mental and emotional states, the regulation of one's own distress, and the experience of positive emotions. However, we contend that extremely high levels of vagal activity can be detrimental to prosociality. We present 3 studies providing support for our model, finding consistent evidence of a quadratic relationship between respiratory sinus arrhythmia--the degree to which the vagus nerve modulates the heart rate--and prosociality. Individual differences in vagal activity were quadratically related to prosocial traits (Study 1), prosocial emotions (Study 2), and outside ratings of prosociality by complete strangers (Study 3). Thus, too much or too little vagal activity appears to be detrimental to prosociality. The present article provides the 1st theoretical and empirical account of the nonlinear relationship between vagal activity and prosociality.

Quadratic integrand double-hybrid made spin-component-scaled

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

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

2016-03-28

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

Finite pure integer programming algorithms employing only hyperspherically deduced cuts

NASA Technical Reports Server (NTRS)

Young, R. D.

1971-01-01

Three algorithms are developed that may be based exclusively on hyperspherically deduced cuts. The algorithms only apply, therefore, to problems structured so that these cuts are valid. The algorithms are shown to be finite.

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

Exact and heuristic algorithms for Space Information Flow.

PubMed

Uwitonze, Alfred; Huang, Jiaqing; Ye, Yuanqing; Cheng, Wenqing; Li, Zongpeng

2018-01-01

Space Information Flow (SIF) is a new promising research area that studies network coding in geometric space, such as Euclidean space. The design of algorithms that compute the optimal SIF solutions remains one of the key open problems in SIF. This work proposes the first exact SIF algorithm and a heuristic SIF algorithm that compute min-cost multicast network coding for N (N ≥ 3) given terminal nodes in 2-D Euclidean space. Furthermore, we find that the Butterfly network in Euclidean space is the second example besides the Pentagram network where SIF is strictly better than Euclidean Steiner minimal tree. The exact algorithm design is based on two key techniques: Delaunay triangulation and linear programming. Delaunay triangulation technique helps to find practically good candidate relay nodes, after which a min-cost multicast linear programming model is solved over the terminal nodes and the candidate relay nodes, to compute the optimal multicast network topology, including the optimal relay nodes selected by linear programming from all the candidate relay nodes and the flow rates on the connection links. The heuristic algorithm design is also based on Delaunay triangulation and linear programming techniques. The exact algorithm can achieve the optimal SIF solution with an exponential computational complexity, while the heuristic algorithm can achieve the sub-optimal SIF solution with a polynomial computational complexity. We prove the correctness of the exact SIF algorithm. The simulation results show the effectiveness of the heuristic SIF algorithm.

Nonnegative constraint quadratic program technique to enhance the resolution of γ spectra

NASA Astrophysics Data System (ADS)

Li, Jinglun; Xiao, Wuyun; Ai, Xianyun; Chen, Ye

2018-04-01

Two concepts of the nonnegative least squares problem (NNLS) and the linear complementarity problem (LCP) are introduced for the resolution enhancement of the γ spectra. The respective algorithms such as the active set method and the primal-dual interior point method are applied to solve the above two problems. In mathematics, the nonnegative constraint results in the sparsity of the optimal solution of the deconvolution, and it is this sparsity that enhances the resolution. Finally, a comparison in the peak position accuracy and the computation time is made between these two methods and the boosted L_R and Gold methods.

Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality

NASA Technical Reports Server (NTRS)

Acikmese, Ahmet Behcet; Martin, Corless

2004-01-01

We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.

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.

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.

Optimal Golomb Ruler Sequences Generation for Optical WDM Systems: A Novel Parallel Hybrid Multi-objective Bat Algorithm

NASA Astrophysics Data System (ADS)

Bansal, Shonak; Singh, Arun Kumar; Gupta, Neena

2017-02-01

In real-life, multi-objective engineering design problems are very tough and time consuming optimization problems due to their high degree of nonlinearities, complexities and inhomogeneity. Nature-inspired based multi-objective optimization algorithms are now becoming popular for solving multi-objective engineering design problems. This paper proposes original multi-objective Bat algorithm (MOBA) and its extended form, namely, novel parallel hybrid multi-objective Bat algorithm (PHMOBA) to generate shortest length Golomb ruler called optimal Golomb ruler (OGR) sequences at a reasonable computation time. The OGRs found their application in optical wavelength division multiplexing (WDM) systems as channel-allocation algorithm to reduce the four-wave mixing (FWM) crosstalk. The performances of both the proposed algorithms to generate OGRs as optical WDM channel-allocation is compared with other existing classical computing and nature-inspired algorithms, including extended quadratic congruence (EQC), search algorithm (SA), genetic algorithms (GAs), biogeography based optimization (BBO) and big bang-big crunch (BB-BC) optimization algorithms. Simulations conclude that the proposed parallel hybrid multi-objective Bat algorithm works efficiently as compared to original multi-objective Bat algorithm and other existing algorithms to generate OGRs for optical WDM systems. The algorithm PHMOBA to generate OGRs, has higher convergence and success rate than original MOBA. The efficiency improvement of proposed PHMOBA to generate OGRs up to 20-marks, in terms of ruler length and total optical channel bandwidth (TBW) is 100 %, whereas for original MOBA is 85 %. Finally the implications for further research are also discussed.

Ascent guidance algorithm using lidar wind measurements

NASA Technical Reports Server (NTRS)

Cramer, Evin J.; Bradt, Jerre E.; Hardtla, John W.

1990-01-01

The formulation of a general nonlinear programming guidance algorithm that incorporates wind measurements in the computation of ascent guidance steering commands is discussed. A nonlinear programming (NLP) algorithm that is designed to solve a very general problem has the potential to address the diversity demanded by future launch systems. Using B-splines for the command functional form allows the NLP algorithm to adjust the shape of the command profile to achieve optimal performance. The algorithm flexibility is demonstrated by simulation of ascent with dynamic loading constraints through a set of random wind profiles with and without wind sensing capability.

Dynamical correlation functions of the quadratic coupling spin-Boson model

NASA Astrophysics Data System (ADS)

Zheng, Da-Chuan; Tong, Ning-Hua

2017-06-01

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

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

Research on trust-region algorithms for nonlinear programming. Final technical report, 1 January 1990--31 December 1992

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

Dennis, J.E. Jr.; Tapia, R.A.

Goal of the research was to develop and test effective, robust algorithms for general nonlinear programming (NLP) problems, particularly large or otherwise expensive NLP problems. We discuss the research conducted over the 3-year period Jan. 1990-Dec. 1992. We also describe current and future directions of our research.

A fast least-squares algorithm for population inference

PubMed Central

2013-01-01

Background Population inference is an important problem in genetics used to remove population stratification in genome-wide association studies and to detect migration patterns or shared ancestry. An individual’s genotype can be modeled as a probabilistic function of ancestral population memberships, Q, and the allele frequencies in those populations, P. The parameters, P and Q, of this binomial likelihood model can be inferred using slow sampling methods such as Markov Chain Monte Carlo methods or faster gradient based approaches such as sequential quadratic programming. This paper proposes a least-squares simplification of the binomial likelihood model motivated by a Euclidean interpretation of the genotype feature space. This results in a faster algorithm that easily incorporates the degree of admixture within the sample of individuals and improves estimates without requiring trial-and-error tuning. Results We show that the expected value of the least-squares solution across all possible genotype datasets is equal to the true solution when part of the problem has been solved, and that the variance of the solution approaches zero as its size increases. The Least-squares algorithm performs nearly as well as Admixture for these theoretical scenarios. We compare least-squares, Admixture, and FRAPPE for a variety of problem sizes and difficulties. For particularly hard problems with a large number of populations, small number of samples, or greater degree of admixture, least-squares performs better than the other methods. On simulated mixtures of real population allele frequencies from the HapMap project, Admixture estimates sparsely mixed individuals better than Least-squares. The least-squares approach, however, performs within 1.5% of the Admixture error. On individual genotypes from the HapMap project, Admixture and least-squares perform qualitatively similarly and within 1.2% of each other. Significantly, the least-squares approach nearly always converges 1

A fast least-squares algorithm for population inference.

PubMed

Parry, R Mitchell; Wang, May D

2013-01-23

Population inference is an important problem in genetics used to remove population stratification in genome-wide association studies and to detect migration patterns or shared ancestry. An individual's genotype can be modeled as a probabilistic function of ancestral population memberships, Q, and the allele frequencies in those populations, P. The parameters, P and Q, of this binomial likelihood model can be inferred using slow sampling methods such as Markov Chain Monte Carlo methods or faster gradient based approaches such as sequential quadratic programming. This paper proposes a least-squares simplification of the binomial likelihood model motivated by a Euclidean interpretation of the genotype feature space. This results in a faster algorithm that easily incorporates the degree of admixture within the sample of individuals and improves estimates without requiring trial-and-error tuning. We show that the expected value of the least-squares solution across all possible genotype datasets is equal to the true solution when part of the problem has been solved, and that the variance of the solution approaches zero as its size increases. The Least-squares algorithm performs nearly as well as Admixture for these theoretical scenarios. We compare least-squares, Admixture, and FRAPPE for a variety of problem sizes and difficulties. For particularly hard problems with a large number of populations, small number of samples, or greater degree of admixture, least-squares performs better than the other methods. On simulated mixtures of real population allele frequencies from the HapMap project, Admixture estimates sparsely mixed individuals better than Least-squares. The least-squares approach, however, performs within 1.5% of the Admixture error. On individual genotypes from the HapMap project, Admixture and least-squares perform qualitatively similarly and within 1.2% of each other. Significantly, the least-squares approach nearly always converges 1.5- to 6-times faster

Integer programming model for optimizing bus timetable using genetic algorithm

NASA Astrophysics Data System (ADS)

Wihartiko, F. D.; Buono, A.; Silalahi, B. P.

2017-01-01

Bus timetable gave an information for passengers to ensure the availability of bus services. Timetable optimal condition happened when bus trips frequency could adapt and suit with passenger demand. In the peak time, the number of bus trips would be larger than the off-peak time. If the number of bus trips were more frequent than the optimal condition, it would make a high operating cost for bus operator. Conversely, if the number of trip was less than optimal condition, it would make a bad quality service for passengers. In this paper, the bus timetabling problem would be solved by integer programming model with modified genetic algorithm. Modification was placed in the chromosomes design, initial population recovery technique, chromosomes reconstruction and chromosomes extermination on specific generation. The result of this model gave the optimal solution with accuracy 99.1%.

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.

Simulation of superconducting tapes and coils with convex quadratic programming method

NASA Astrophysics Data System (ADS)

Zhang, Yan; Song, Yuntao; Wang, Lei; Liu, Xufeng

2015-08-01

Second-generation (2G) high-temperature superconducting coated conductors are playing an increasingly important role in power applications due to their large current density under high magnetic fields. In this paper, we conclude and explore the ability and possible potential of J formulation from the mathematical modeling point of view. An equivalent matrix form of J formulation has been presented and a relation between electromagnetic quantities and Karush-Kuhn-Tucker (KKT) conditions in optimization theory has been discovered. The use of the latest formulae to calculate inductance in a coil system and the primal-dual interior-point method algorithm is a trial to make the process of modeling stylized and build a bridge to commercial optimization solvers. Two different dependences of the critical current density on the magnetic field have been used in order to make a comparison with those published papers.

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

On the classification of elliptic foliations induced by real quadratic fields with center

NASA Astrophysics Data System (ADS)

Puchuri, Liliana; Bueno, Orestes

2016-12-01

Related to the study of Hilbert's infinitesimal problem, is the problem of determining the existence and estimating the number of limit cycles of the linear perturbation of Hamiltonian fields. A classification of the elliptic foliations in the projective plane induced by the fields obtained by quadratic fields with center was already studied by several authors. In this work, we devise a unified proof of the classification of elliptic foliations induced by quadratic fields with center. This technique involves using a formula due to Cerveau & Lins Neto to calculate the genus of the generic fiber of a first integral of foliations of these kinds. Furthermore, we show that these foliations induce several examples of linear families of foliations which are not bimeromorphically equivalent to certain remarkable examples given by Lins Neto.

Robustness in linear quadratic feedback design with application to an aircraft control problem

NASA Technical Reports Server (NTRS)

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

1977-01-01

Some new results concerning robustness and asymptotic properties of error bounds of a linear quadratic feedback design are applied to an aircraft control problem. An autopilot for the flare control of the Augmentor Wing Jet STOL Research Aircraft (AWJSRA) is designed based on Linear Quadratic (LQ) theory and the results developed in this paper. The variation of the error bounds to changes in the weighting matrices in the LQ design is studied by computer simulations, and appropriate weighting matrices are chosen to obtain a reasonable error bound for variations in the system matrix and at the same time meet the practical constraints for the flare maneuver of the AWJSRA. Results from the computer simulation of a satisfactory autopilot design for the flare control of the AWJSRA are presented.

Probabilistic dual heuristic programming-based adaptive critic

NASA Astrophysics Data System (ADS)

Herzallah, Randa

2010-02-01

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

A space-efficient algorithm for local similarities.

PubMed

Huang, X Q; Hardison, R C; Miller, W

1990-10-01

Existing dynamic-programming algorithms for identifying similar regions of two sequences require time and space proportional to the product of the sequence lengths. Often this space requirement is more limiting than the time requirement. We describe a dynamic-programming local-similarity algorithm that needs only space proportional to the sum of the sequence lengths. The method can also find repeats within a single long sequence. To illustrate the algorithm's potential, we discuss comparison of a 73,360 nucleotide sequence containing the human beta-like globin gene cluster and a corresponding 44,594 nucleotide sequence for rabbit, a problem well beyond the capabilities of other dynamic-programming software.

Performance analysis of a dual-tree algorithm for computing spatial distance histograms

PubMed Central

Chen, Shaoping; Tu, Yi-Cheng; Xia, Yuni

2011-01-01

Many scientific and engineering fields produce large volume of spatiotemporal data. The storage, retrieval, and analysis of such data impose great challenges to database systems design. Analysis of scientific spatiotemporal data often involves computing functions of all point-to-point interactions. One such analytics, the Spatial Distance Histogram (SDH), is of vital importance to scientific discovery. Recently, algorithms for efficient SDH processing in large-scale scientific databases have been proposed. These algorithms adopt a recursive tree-traversing strategy to process point-to-point distances in the visited tree nodes in batches, thus require less time when compared to the brute-force approach where all pairwise distances have to be computed. Despite the promising experimental results, the complexity of such algorithms has not been thoroughly studied. In this paper, we present an analysis of such algorithms based on a geometric modeling approach. The main technique is to transform the analysis of point counts into a problem of quantifying the area of regions where pairwise distances can be processed in batches by the algorithm. From the analysis, we conclude that the number of pairwise distances that are left to be processed decreases exponentially with more levels of the tree visited. This leads to the proof of a time complexity lower than the quadratic time needed for a brute-force algorithm and builds the foundation for a constant-time approximate algorithm. Our model is also general in that it works for a wide range of point spatial distributions, histogram types, and space-partitioning options in building the tree. PMID:21804753

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.

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.

GENPLOT: A formula-based Pascal program for data manipulation and plotting

NASA Astrophysics Data System (ADS)

Kramer, Matthew J.

Geochemical processes involving alteration, differentiation, fractionation, or migration of elements may be elucidated by a number of discrimination or variation diagrams (e.g., AFM, Harker, Pearce, and many others). The construction of these diagrams involves arithmetic combination of selective elements (involving major, minor, or trace elements). GENPLOT utilizes a formula-based algorithm (an expression parser) which enables the program to manipulate multiparameter databases and plot XY, ternary, tetrahedron, and REE type plots without needing to change either the source code or rearranging databases. Formulae may be any quadratic expression whose variables are the column headings of the data matrix. A full-screen editor with limited equations and arithmetic functions (spreadsheet) has been incorporated into the program to aid data entry and editing. Data are stored as ASCII files to facilitate interchange of data between other programs and computers. GENPLOT was developed in Turbo Pascal for the IBM and compatible computers but also is available in Apple Pascal for the Apple Ile and Ill. Because the source code is too extensive to list here (about 5200 lines of Pascal code), the expression parsing routine, which is central to GENPLOT's flexibility is incorporated into a smaller demonstration program named SOLVE. The following paper includes a discussion on how the expression parser works and a detailed description of GENPLOT's capabilities.

An intelligent allocation algorithm for parallel processing

NASA Technical Reports Server (NTRS)

Carroll, Chester C.; Homaifar, Abdollah; Ananthram, Kishan G.

1988-01-01

The problem of allocating nodes of a program graph to processors in a parallel processing architecture is considered. The algorithm is based on critical path analysis, some allocation heuristics, and the execution granularity of nodes in a program graph. These factors, and the structure of interprocessor communication network, influence the allocation. To achieve realistic estimations of the executive durations of allocations, the algorithm considers the fact that nodes in a program graph have to communicate through varying numbers of tokens. Coarse and fine granularities have been implemented, with interprocessor token-communication duration, varying from zero up to values comparable to the execution durations of individual nodes. The effect on allocation of communication network structures is demonstrated by performing allocations for crossbar (non-blocking) and star (blocking) networks. The algorithm assumes the availability of as many processors as it needs for the optimal allocation of any program graph. Hence, the focus of allocation has been on varying token-communication durations rather than varying the number of processors. The algorithm always utilizes as many processors as necessary for the optimal allocation of any program graph, depending upon granularity and characteristics of the interprocessor communication network.

Inversion of oceanic constituents in case I and II waters with genetic programming algorithms.

PubMed

Chami, Malik; Robilliard, Denis

2002-10-20

A stochastic inverse technique based on agenetic programming (GP) algorithm was developed toinvert oceanic constituents from simulated data for case I and case II water applications. The simulations were carried out with the Ordre Successifs Ocean Atmosphere (OSOA) radiative transfer model. They include the effects of oceanic substances such as algal-related chlorophyll, nonchlorophyllous suspended matter, and dissolved organic matter. The synthetic data set also takes into account the directional effects of particles through a variation of their phase function that makes the simulated data realistic. It is shown that GP can be successfully applied to the inverse problem with acceptable stability in the presence of realistic noise in the data. GP is compared with neural network methodology for case I waters; GP exhibits similar retrieval accuracy, which is greater than for traditional techniques such as band ratio algorithms. The application of GP to real satellite data [a Sea-viewing Wide Field-of-view Sensor (SeaWiFS)] was also carried out for case I waters as a validation. Good agreement was obtained when GP results were compared with the SeaWiFS empirical algorithm. For case II waters the accuracy of GP is less than 33%, which remains satisfactory, at the present time, for remote-sensing purposes.

Rigorous Numerical Study of Low-Period Windows for the Quadratic Map

NASA Astrophysics Data System (ADS)

Galias, Zbigniew

An efficient method to find all low-period windows for the quadratic map is proposed. The method is used to obtain very accurate rigorous bounds of positions of all periodic windows with periods p ≤ 32. The contribution of period-doubling windows on the total width of periodic windows is discussed. Properties of periodic windows are studied numerically.

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

ERIC Educational Resources Information Center

Dinç, Emre

2017-01-01

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

Differentiation of Students' Reasoning on Linear and Quadratic Geometric Number Patterns

ERIC Educational Resources Information Center

Lin, Fou-Lai; Yang, Kai-Lin

2004-01-01

There are two purposes in this study. One is to compare how 7th and 8th graders reason on linear and quadratic geometric number patterns when they have not learned this kind of tasks in school. The other is to explore the hierarchical relations among the four components of reasoning on geometric number patterns: understanding, generalizing,…

Genetic algorithms and genetic programming for multiscale modeling: Applications in materials science and chemistry and advances in scalability

NASA Astrophysics Data System (ADS)

Sastry, Kumara Narasimha

2007-03-01

Effective and efficient rnultiscale modeling is essential to advance both the science and synthesis in a, wide array of fields such as physics, chemistry, materials science; biology, biotechnology and pharmacology. This study investigates the efficacy and potential of rising genetic algorithms for rnultiscale materials modeling and addresses some of the challenges involved in designing competent algorithms that solve hard problems quickly, reliably and accurately. In particular, this thesis demonstrates the use of genetic algorithms (GAs) and genetic programming (GP) in multiscale modeling with the help of two non-trivial case studies in materials science and chemistry. The first case study explores the utility of genetic programming (GP) in multi-timescaling alloy kinetics simulations. In essence, GP is used to bridge molecular dynamics and kinetic Monte Carlo methods to span orders-of-magnitude in simulation time. Specifically, GP is used to regress symbolically an inline barrier function from a limited set of molecular dynamics simulations to enable kinetic Monte Carlo that simulate seconds of real time. Results on a non-trivial example of vacancy-assisted migration on a surface of a face-centered cubic (fcc) Copper-Cobalt (CuxCo 1-x) alloy show that GP predicts all barriers with 0.1% error from calculations for less than 3% of active configurations, independent of type of potentials used to obtain the learning set of barriers via molecular dynamics. The resulting method enables 2--9 orders-of-magnitude increase in real-time dynamics simulations taking 4--7 orders-of-magnitude less CPU time. The second case study presents the application of multiobjective genetic algorithms (MOGAs) in multiscaling quantum chemistry simulations. Specifically, MOGAs are used to bridge high-level quantum chemistry and semiempirical methods to provide accurate representation of complex molecular excited-state and ground-state behavior. Results on ethylene and benzene---two common

A graph-based evolutionary algorithm: Genetic Network Programming (GNP) and its extension using reinforcement learning.

PubMed

Mabu, Shingo; Hirasawa, Kotaro; Hu, Jinglu

2007-01-01

This paper proposes a graph-based evolutionary algorithm called Genetic Network Programming (GNP). Our goal is to develop GNP, which can deal with dynamic environments efficiently and effectively, based on the distinguished expression ability of the graph (network) structure. The characteristics of GNP are as follows. 1) GNP programs are composed of a number of nodes which execute simple judgment/processing, and these nodes are connected by directed links to each other. 2) The graph structure enables GNP to re-use nodes, thus the structure can be very compact. 3) The node transition of GNP is executed according to its node connections without any terminal nodes, thus the past history of the node transition affects the current node to be used and this characteristic works as an implicit memory function. These structural characteristics are useful for dealing with dynamic environments. Furthermore, we propose an extended algorithm, "GNP with Reinforcement Learning (GNPRL)" which combines evolution and reinforcement learning in order to create effective graph structures and obtain better results in dynamic environments. In this paper, we applied GNP to the problem of determining agents' behavior to evaluate its effectiveness. Tileworld was used as the simulation environment. The results show some advantages for GNP over conventional 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.

Optimal algorithm for automatic detection of microaneurysms based on receiver operating characteristic curve

NASA Astrophysics Data System (ADS)

Xu, Lili; Luo, Shuqian

2010-11-01

Microaneurysms (MAs) are the first manifestations of the diabetic retinopathy (DR) as well as an indicator for its progression. Their automatic detection plays a key role for both mass screening and monitoring and is therefore in the core of any system for computer-assisted diagnosis of DR. The algorithm basically comprises the following stages: candidate detection aiming at extracting the patterns possibly corresponding to MAs based on mathematical morphological black top hat, feature extraction to characterize these candidates, and classification based on support vector machine (SVM), to validate MAs. Feature vector and kernel function of SVM selection is very important to the algorithm. We use the receiver operating characteristic (ROC) curve to evaluate the distinguishing performance of different feature vectors and different kernel functions of SVM. The ROC analysis indicates the quadratic polynomial SVM with a combination of features as the input shows the best discriminating performance.

Optimal algorithm for automatic detection of microaneurysms based on receiver operating characteristic curve.

PubMed

Xu, Lili; Luo, Shuqian

2010-01-01

Microaneurysms (MAs) are the first manifestations of the diabetic retinopathy (DR) as well as an indicator for its progression. Their automatic detection plays a key role for both mass screening and monitoring and is therefore in the core of any system for computer-assisted diagnosis of DR. The algorithm basically comprises the following stages: candidate detection aiming at extracting the patterns possibly corresponding to MAs based on mathematical morphological black top hat, feature extraction to characterize these candidates, and classification based on support vector machine (SVM), to validate MAs. Feature vector and kernel function of SVM selection is very important to the algorithm. We use the receiver operating characteristic (ROC) curve to evaluate the distinguishing performance of different feature vectors and different kernel functions of SVM. The ROC analysis indicates the quadratic polynomial SVM with a combination of features as the input shows the best discriminating performance.

Optical Algorithms at Satellite Wavelengths for Total Suspended Matter in Tropical Coastal Waters

PubMed Central

Ouillon, Sylvain; Douillet, Pascal; Petrenko, Anne; Neveux, Jacques; Dupouy, Cécile; Froidefond, Jean-Marie; Andréfouët, Serge; Muñoz-Caravaca, Alain

2008-01-01

Is it possible to derive accurately Total Suspended Matter concentration or its proxy, turbidity, from remote sensing data in tropical coastal lagoon waters? To investigate this question, hyperspectral remote sensing reflectance, turbidity and chlorophyll pigment concentration were measured in three coral reef lagoons. The three sites enabled us to get data over very diverse environments: oligotrophic and sediment-poor waters in the southwest lagoon of New Caledonia, eutrophic waters in the Cienfuegos Bay (Cuba), and sediment-rich waters in the Laucala Bay (Fiji). In this paper, optical algorithms for turbidity are presented per site based on 113 stations in New Caledonia, 24 stations in Cuba and 56 stations in Fiji. Empirical algorithms are tested at satellite wavebands useful to coastal applications. Global algorithms are also derived for the merged data set (193 stations). The performances of global and local regression algorithms are compared. The best one-band algorithms on all the measurements are obtained at 681 nm using either a polynomial or a power model. The best two-band algorithms are obtained with R412/R620, R443/R670 and R510/R681. Two three-band algorithms based on Rrs620.Rrs681/Rrs412 and Rrs620.Rrs681/Rrs510 also give fair regression statistics. Finally, we propose a global algorithm based on one or three bands: turbidity is first calculated from Rrs681 and then, if < 1 FTU, it is recalculated using an algorithm based on Rrs620.Rrs681/Rrs412. On our data set, this algorithm is suitable for the 0.2-25 FTU turbidity range and for the three sites sampled (mean bias: 3.6 %, rms: 35%, mean quadratic error: 1.4 FTU). This shows that defining global empirical turbidity algorithms in tropical coastal waters is at reach. PMID:27879929

Optical Algorithms at Satellite Wavelengths for Total Suspended Matter in Tropical Coastal Waters.

PubMed

Ouillon, Sylvain; Douillet, Pascal; Petrenko, Anne; Neveux, Jacques; Dupouy, Cécile; Froidefond, Jean-Marie; Andréfouët, Serge; Muñoz-Caravaca, Alain

2008-07-10

Is it possible to derive accurately Total Suspended Matter concentration or its proxy, turbidity, from remote sensing data in tropical coastal lagoon waters? To investigate this question, hyperspectral remote sensing reflectance, turbidity and chlorophyll pigment concentration were measured in three coral reef lagoons. The three sites enabled us to get data over very diverse environments: oligotrophic and sediment-poor waters in the southwest lagoon of New Caledonia, eutrophic waters in the Cienfuegos Bay (Cuba), and sediment-rich waters in the Laucala Bay (Fiji). In this paper, optical algorithms for turbidity are presented per site based on 113 stations in New Caledonia, 24 stations in Cuba and 56 stations in Fiji. Empirical algorithms are tested at satellite wavebands useful to coastal applications. Global algorithms are also derived for the merged data set (193 stations). The performances of global and local regression algorithms are compared. The best one-band algorithms on all the measurements are obtained at 681 nm using either a polynomial or a power model. The best two-band algorithms are obtained with R412/R620, R443/R670 and R510/R681. Two three-band algorithms based on Rrs620.Rrs681/Rrs412 and Rrs620.Rrs681/Rrs510 also give fair regression statistics. Finally, we propose a global algorithm based on one or three bands: turbidity is first calculated from Rrs681 and then, if < 1 FTU, it is recalculated using an algorithm based on Rrs620.Rrs681/Rrs412. On our data set, this algorithm is suitable for the 0.2-25 FTU turbidity range and for the three sites sampled (mean bias: 3.6 %, rms: 35%, mean quadratic error: 1.4 FTU). This shows that defining global empirical turbidity algorithms in tropical coastal waters is at reach.

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.

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).

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

NASA Technical Reports Server (NTRS)

Athans, M.

1986-01-01

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

Numerical Roll Reversal Predictor Corrector Aerocapture and Precision Landing Guidance Algorithms for the Mars Surveyor Program 2001 Missions

NASA Technical Reports Server (NTRS)

Powell, Richard W.

1998-01-01

This paper describes the development and evaluation of a numerical roll reversal predictor-corrector guidance algorithm for the atmospheric flight portion of the Mars Surveyor Program 2001 Orbiter and Lander missions. The Lander mission utilizes direct entry and has a demanding requirement to deploy its parachute within 10 km of the target deployment point. The Orbiter mission utilizes aerocapture to achieve a precise captured orbit with a single atmospheric pass. Detailed descriptions of these predictor-corrector algorithms are given. Also, results of three and six degree-of-freedom Monte Carlo simulations which include navigation, aerodynamics, mass properties and atmospheric density uncertainties are presented.

A bivariate rational interpolation with a bi-quadratic denominator

NASA Astrophysics Data System (ADS)

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

2006-10-01

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

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.

A homotopy algorithm for digital optimal projection control GASD-HADOC

NASA Technical Reports Server (NTRS)

Collins, Emmanuel G., Jr.; Richter, Stephen; Davis, Lawrence D.

1993-01-01

The linear-quadratic-gaussian (LQG) compensator was developed to facilitate the design of control laws for multi-input, multi-output (MIMO) systems. The compensator is computed by solving two algebraic equations for which standard closed-loop solutions exist. Unfortunately, the minimal dimension of an LQG compensator is almost always equal to the dimension of the plant and can thus often violate practical implementation constraints on controller order. This deficiency is especially highlighted when considering control-design for high-order systems such as flexible space structures. This deficiency motivated the development of techniques that enable the design of optimal controllers whose dimension is less than that of the design plant. A homotopy approach based on the optimal projection equations that characterize the necessary conditions for optimal reduced-order control. Homotopy algorithms have global convergence properties and hence do not require that the initializing reduced-order controller be close to the optimal reduced-order controller to guarantee convergence. However, the homotopy algorithm previously developed for solving the optimal projection equations has sublinear convergence properties and the convergence slows at higher authority levels and may fail. A new homotopy algorithm for synthesizing optimal reduced-order controllers for discrete-time systems is described. Unlike the previous homotopy approach, the new algorithm is a gradient-based, parameter optimization formulation and was implemented in MATLAB. The results reported may offer the foundation for a reliable approach to optimal, reduced-order controller design.

Quadratically Convergent Method for Simultaneously Approaching the Roots of Polynomial Solutions of a Class of Differential Equations

NASA Astrophysics Data System (ADS)

Recchioni, Maria Cristina

2001-12-01

This paper investigates the application of the method introduced by L. Pasquini (1989) for simultaneously approaching the zeros of polynomial solutions to a class of second-order linear homogeneous ordinary differential equations with polynomial coefficients to a particular case in which these polynomial solutions have zeros symmetrically arranged with respect to the origin. The method is based on a family of nonlinear equations which is associated with a given class of differential equations. The roots of the nonlinear equations are related to the roots of the polynomial solutions of differential equations considered. Newton's method is applied to find the roots of these nonlinear equations. In (Pasquini, 1994) the nonsingularity of the roots of these nonlinear equations is studied. In this paper, following the lines in (Pasquini, 1994), the nonsingularity of the roots of these nonlinear equations is studied. More favourable results than the ones in (Pasquini, 1994) are proven in the particular case of polynomial solutions with symmetrical zeros. The method is applied to approximate the roots of Hermite-Sobolev type polynomials and Freud polynomials. A lower bound for the smallest positive root of Hermite-Sobolev type polynomials is given via the nonlinear equation. The quadratic convergence of the method is proven. A comparison with a classical method that uses the Jacobi matrices is carried out. We show that the algorithm derived by the proposed method is sometimes preferable to the classical QR type algorithms for computing the eigenvalues of the Jacobi matrices even if these matrices are real and symmetric.

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