Large-scale sequential quadratic programming algorithms
Eldersveld, S.K.
1992-09-01
The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.
Some Randomized Algorithms for Convex Quadratic Programming
Goldbach, R.
1999-01-15
We adapt some randomized algorithms of Clarkson [3] for linear programming to the framework of so-called LP-type problems, which was introduced by Sharir and Welzl [10]. This framework is quite general and allows a unified and elegant presentation and analysis. We also show that LP-type problems include minimization of a convex quadratic function subject to convex quadratic constraints as a special case, for which the algorithms can be implemented efficiently, if only linear constraints are present. We show that the expected running times depend only linearly on the number of constraints, and illustrate this by some numerical results. Even though the framework of LP-type problems may appear rather abstract at first, application of the methods considered in this paper to a given problem of that type is easy and efficient. Moreover, our proofs are in fact rather simple, since many technical details of more explicit problem representations are handled in a uniform manner by our approach. In particular, we do not assume boundedness of the feasible set as required in related methods.
Memetic algorithms for the unconstrained binary quadratic programming problem.
Merz, Peter; Katayama, Kengo
2004-12-01
This paper presents a memetic algorithm, a highly effective evolutionary algorithm incorporating local search for solving the unconstrained binary quadratic programming problem (BQP). To justify the approach, a fitness landscape analysis is conducted experimentally for several instances of the BQP. The results of the analysis show that recombination-based variation operators are well suited for the evolutionary algorithms with local search. Therefore, the proposed approach includes--besides a highly effective randomized k-opt local search--a new variation operator that has been tailored specially for the application in the hybrid evolutionary framework. The operator is called innovative variation and is fundamentally different from traditional crossover operators, since new genetic material is included in the offspring which is not contained in one of the parents. The evolutionary heuristic is tested on 35 publicly available BQP instances, and it is shown experimentally that the algorithm is capable of finding best-known solutions to large BQPs in a short time and with a high frequency. In comparison to other approaches for the BQP, the approach appears to be much more effective, particularly for large instances of 1000 or 2500 binary variables.
NASA Technical Reports Server (NTRS)
Frost, Susan A.; Bodson, Marc; Acosta, Diana M.
2009-01-01
The Next Generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five effectors, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude and flight path of the aircraft. The NextGen aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship does not exist anymore between the required effector deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands and attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples that the solutions provided using the l2 norm of quadratic programming are less sensitive than those using the l1 norm of linear programming.
A Sequential Quadratic Programming Algorithm Using An Incomplete Solution of the Subproblem
1993-05-01
Subproblem by Walter Murray * and Francisco J. Prietot TECHNICAL REPORT SOL 93-3 May 1993 DTIC ELECTE JUL27 1993 93-16793 E epPTOYS6a b~ Department of...Quadratic Programming Algorithm Using An Incomplete Solution of the Subproblem by Walter Murray * and Francisco J. Prietot TECHNICAL REPORT SOL 93-3 May...ALGORITHM USING AN INCOMPLETE SOLUTION OF THE SUBPROBLEM WALTER MURRAY * AND FRANCISCO J. PRIETOt *Systems Optimization Laboratory Department of Operations
An Algorithm for Structured, Large-Scale Quadratic Programming Problems.
1981-09-01
of the Madison Academic Computing Center of the University of Wisconsin-Madison. In the program we set the stopping criterio as follows. -4l = 10 - 4...for Large Systems, Macmillan. Madison Academic Computing Center (MACC, 1976), Nonlinear programming routines, reference manual . Madison Academic...Computing Center (MACC, 1978), Random number routines, reference manual . Mangasarian, 0. L. (1969), Nonlinear Programming, McGraw-Hill. Rockafellar, R. T
NASA Astrophysics Data System (ADS)
Liu, Wei; Ma, Shunjian; Sun, Mingwei; Yi, Haidong; Wang, Zenghui; Chen, Zengqiang
2016-08-01
Path planning plays an important role in aircraft guided systems. Multiple no-fly zones in the flight area make path planning a constrained nonlinear optimization problem. It is necessary to obtain a feasible optimal solution in real time. In this article, the flight path is specified to be composed of alternate line segments and circular arcs, in order to reformulate the problem into a static optimization one in terms of the waypoints. For the commonly used circular and polygonal no-fly zones, geometric conditions are established to determine whether or not the path intersects with them, and these can be readily programmed. Then, the original problem is transformed into a form that can be solved by the sequential quadratic programming method. The solution can be obtained quickly using the Sparse Nonlinear OPTimizer (SNOPT) package. Mathematical simulations are used to verify the effectiveness and rapidity of the proposed algorithm.
Vinogradov, S A; Wilson, D F
1994-01-01
A new method for analysis of phosphorescence lifetime distributions in heterogeneous systems has been developed. This method is based on decomposition of the data vector to a linearly independent set of exponentials and uses quadratic programming principles for x2 minimization. Solution of the resulting algorithm requires a finite number of calculations (it is not iterative) and is computationally fast and robust. The algorithm has been tested on various simulated decays and for analysis of phosphorescence measurements of experimental systems with descrete distributions of lifetimes. Critical analysis of the effect of signal-to-noise on the resolving capability of the algorithm is presented. This technique is recommended for resolution of the distributions of quencher concentration in heterogeneous samples, of which oxygen distributions in tissue is an important example. Phosphors of practical importance for biological oxygen measurements: Pd-meso-tetra (4-carboxyphenyl) porphyrin (PdTCPP) and Pd-meso-porphyrin (PdMP) have been used to provide experimental test of the algorithm. PMID:7858142
A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions
Jian Jinbao Hu Qingjie; Tang Chunming; Zheng Haiyan
2007-12-15
In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported.
NASA Astrophysics Data System (ADS)
Chen, Zheng; Mi, Chris Chunting; Xiong, Rui; Xu, Jun; You, Chenwen
2014-02-01
This paper introduces an online and intelligent energy management controller to improve the fuel economy of a power-split plug-in hybrid electric vehicle (PHEV). Based on analytic analysis between fuel-rate and battery current at different driveline power and vehicle speed, quadratic equations are applied to simulate the relationship between battery current and vehicle fuel-rate. The power threshold at which engine is turned on is optimized by genetic algorithm (GA) based on vehicle fuel-rate, battery state of charge (SOC) and driveline power demand. The optimal battery current when the engine is on is calculated using quadratic programming (QP) method. The proposed algorithm can control the battery current effectively, which makes the engine work more efficiently and thus reduce the fuel-consumption. Moreover, the controller is still applicable when the battery is unhealthy. Numerical simulations validated the feasibility of the proposed controller.
A Sequential Quadratic Programming Algorithm for Solving Large, Sparse Nonlinear Programs.
1984-05-01
w* as defined by the matrix norm are also achieved by a modification to the conjugate gradient algorithm (see Polyak [1969]) which minimizes a...W,". -. t ,: VT’A .,’, .,’, LV . .# -. 0: gj(xC-)<RHSj or [gj(xc)-RHSj and Vgj(xC-)tsc 4 0.0] Gj (xC) Vgj(xc) ’sC: otherwise for equality constraints...Publishing Co., New .5’ York. Polyak , B. T. (1969). "The conjugate gradient method in extremal problems," USSR Computational Mathematics and
NASA Astrophysics Data System (ADS)
Liu, Hua-Long; Liu, Hua-Dong
2014-10-01
Partial discharge (PD) in power transformers is one of the prime reasons resulting in insulation degradation and power faults. Hence, it is of great importance to study the techniques of the detection and localization of PD in theory and practice. The detection and localization of PD employing acoustic emission (AE) techniques, as a kind of non-destructive testing, plus due to the advantages of powerful capability of locating and high precision, have been paid more and more attention. The localization algorithm is the key factor to decide the localization accuracy in AE localization of PD. Many kinds of localization algorithms exist for the PD source localization adopting AE techniques including intelligent and non-intelligent algorithms. However, the existed algorithms possess some defects such as the premature convergence phenomenon, poor local optimization ability and unsuitability for the field applications. To overcome the poor local optimization ability and easily caused premature convergence phenomenon of the fundamental genetic algorithm (GA), a new kind of improved GA is proposed, namely the sequence quadratic programming-genetic algorithm (SQP-GA). For the hybrid optimization algorithm, SQP-GA, the sequence quadratic programming (SQP) algorithm which is used as a basic operator is integrated into the fundamental GA, so the local searching ability of the fundamental GA is improved effectively and the premature convergence phenomenon is overcome. Experimental results of the numerical simulations of benchmark functions show that the hybrid optimization algorithm, SQP-GA, is better than the fundamental GA in the convergence speed and optimization precision, and the proposed algorithm in this paper has outstanding optimization effect. At the same time, the presented SQP-GA in the paper is applied to solve the ultrasonic localization problem of PD in transformers, then the ultrasonic localization method of PD in transformers based on the SQP-GA is proposed. And
NASA Astrophysics Data System (ADS)
Kong, X. M.; Huang, G. H.; Fan, Y. R.; Li, Y. P.
2016-04-01
In this study, a duality theorem-based algorithm (DTA) for inexact quadratic programming (IQP) is developed for municipal solid waste (MSW) management under uncertainty. It improves upon the existing numerical solution method for IQP problems. The comparison between DTA and derivative algorithm (DAM) shows that the DTA method provides better solutions than DAM with lower computational complexity. It is not necessary to identify the uncertain relationship between the objective function and decision variables, which is required for the solution process of DAM. The developed method is applied to a case study of MSW management and planning. The results indicate that reasonable solutions have been generated for supporting long-term MSW management and planning. They could provide more information as well as enable managers to make better decisions to identify desired MSW management policies in association with minimized cost under uncertainty.
A Sequential Quadratic Programming Algorithm Using an Incomplete Solution of the Subproblem
1990-09-01
KKT point of NP. Such points are feasible and satisfy the following conditions : VF(x*) = Vc(x*)TA*, A*ci(x*) = 0 i = 1,...,m for some nonnegative...the same as the one for which the multiplier was obtained. The following conditions on Ilk are sufficient to ensure that the algorithm has the desired...It is shown in [Pr89] that there exists a constant M such that if Pk > M, condition MC2 is sufficient . Theorem 4.1. Under assumptions Al-AT, and
Quadratic Programming for Allocating Control Effort
NASA Technical Reports Server (NTRS)
Singh, Gurkirpal
2005-01-01
A computer program calculates an optimal allocation of control effort in a system that includes redundant control actuators. The program implements an iterative (but otherwise single-stage) algorithm of the quadratic-programming type. In general, in the quadratic-programming problem, one seeks the values of a set of variables that minimize a quadratic cost function, subject to a set of linear equality and inequality constraints. In this program, the cost function combines control effort (typically quantified in terms of energy or fuel consumed) and control residuals (differences between commanded and sensed values of variables to be controlled). In comparison with prior control-allocation software, this program offers approximately equal accuracy but much greater computational efficiency. In addition, this program offers flexibility, robustness to actuation failures, and a capability for selective enforcement of control requirements. The computational efficiency of this program makes it suitable for such complex, real-time applications as controlling redundant aircraft actuators or redundant spacecraft thrusters. The program is written in the C language for execution in a UNIX operating system.
Degenerate nonlinear programming with a quadratic growth condition.
Anitescu, M.; Mathematics and Computer Science
2000-01-01
We show that the quadratic growth condition and the Mangasarian-Fromovitz constraint qualification (MFCQ) imply that local minima of nonlinear programs are isolated stationary points. As a result, when started sufficiently close to such points, an L1 exact penalty sequential quadratic programming algorithm will induce at least R-linear convergence of the iterates to such a local minimum. We construct an example of a degenerate nonlinear program with a unique local minimum satisfying the quadratic growth and the MFCQ but for which no positive semidefinite augmented Lagrangian exists. We present numerical results obtained using several nonlinear programming packages on this example and discuss its implications for some algorithms.
Fast Approximate Quadratic Programming for Graph Matching
Vogelstein, Joshua T.; Conroy, John M.; Lyzinski, Vince; Podrazik, Louis J.; Kratzer, Steven G.; Harley, Eric T.; Fishkind, Donniell E.; Vogelstein, R. Jacob; Priebe, Carey E.
2015-01-01
Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. PMID:25886624
Fast approximate quadratic programming for graph matching.
Vogelstein, Joshua T; Conroy, John M; Lyzinski, Vince; Podrazik, Louis J; Kratzer, Steven G; Harley, Eric T; Fishkind, Donniell E; Vogelstein, R Jacob; Priebe, Carey E
2015-01-01
Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance.
PSQP -- Puzzle Solving by Quadratic Programming.
Andalo, Fernanda; Taubin, Gabriel; Goldenstein, Siome
2016-03-25
In this article we present the first effective global method for the reconstruction of image puzzles comprising rectangle pieces - Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.
PSQP: Puzzle Solving by Quadratic Programming.
Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome
2017-02-01
In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.
Alignment of protein interaction networks by integer quadratic programming.
Li, Zhenping; Wang, Yong; Zhang, Shihua; Zhang, Xiang-Sun; Chen, Luonan
2006-01-01
With more and more data on protein-protein interaction (PPI) network available, the discovery of conserved patterns in these networks becomes an increasingly important problem. In this paper, to find the conserved substructures, we develop an efficient algorithm for aligning PPI networks based on both the protein sequence similarity and the network architecture similarity, by using integer quadratic programming (IQP). Such an IQP can be relaxed into the corresponding quadratic programming (QP) which in the case of biological data sets almost always ensures the integer solution. Therefore, a QP algorithm can be adopted to efficiently solve this IQP with out any approximation, thereby making PPI network alignment tractable. From the viewpoint of graph theory, the proposed method can identify similar subsets between two graphs, which allow gaps for nodes and edges.
An alternative method on quadratic programming problems
NASA Astrophysics Data System (ADS)
Dasril, Y.; Mohd, I. B.; Mustaffa, I.; Aminuddin, MMM.
2015-05-01
In this paper we proposed an alternative approach to find the optimum solution of quadratic programming problems (QPP) in its original form without additional information such as slack variable, surplus variable or artificial variable as done in other favourite methods. This approached is based on the violated constraints by the unconstrained optimum. The optimal solution of QPP obtained by searching from initial point to another point alongside of feasible region.
Convergence properties of the softassign quadratic assignment algorithm.
Rangarajan, A; Vuille, A; Mjolsness, E
1999-08-15
The softassign quadratic assignment algorithm is a discrete-time, continuous-state, synchronous updating optimizing neural network. While its effectiveness has been shown in the traveling salesman problem, graph matching, and graph partitioning in thousands of simulations, its convergence properties have not been studied. Here, we construct discrete-time Lyapunov functions for the cases of exact and approximate doubly stochastic constraint satisfaction, which show convergence to a fixed point. The combination of good convergence properties and experimental success makes the softassign algorithm an excellent choice for neural quadratic assignment optimization.
Clustered Self Organising Migrating Algorithm for the Quadratic Assignment Problem
NASA Astrophysics Data System (ADS)
Davendra, Donald; Zelinka, Ivan; Senkerik, Roman
2009-08-01
An approach of population dynamics and clustering for permutative problems is presented in this paper. Diversity indicators are created from solution ordering and its mapping is shown as an advantage for population control in metaheuristics. Self Organising Migrating Algorithm (SOMA) is modified using this approach and vetted with the Quadratic Assignment Problem (QAP). Extensive experimentation is conducted on benchmark problems in this area.
Restart-Based Genetic Algorithm for the Quadratic Assignment Problem
NASA Astrophysics Data System (ADS)
Misevicius, Alfonsas
The power of genetic algorithms (GAs) has been demonstrated for various domains of the computer science, including combinatorial optimization. In this paper, we propose a new conceptual modification of the genetic algorithm entitled a "restart-based genetic algorithm" (RGA). An effective implementation of RGA for a well-known combinatorial optimization problem, the quadratic assignment problem (QAP), is discussed. The results obtained from the computational experiments on the QAP instances from the publicly available library QAPLIB show excellent performance of RGA. This is especially true for the real-life like QAPs.
Digital image restoration using quadratic programming.
Abdelmalek, N N; Kasvand, T
1980-10-01
The problem of digital image restoration is considered by obtaining an approximate solution to the Fredholm integral equation of the first kind in two variables. The system of linear equations resulting from the discretization of the integral equation is converted to a consistent system of linear equations. The problem is then solved as a quadratic programming problem with bounded variables where the unknown solution is minimized in the L(2) norm. In this method minimum computer storage is needed, and the repeated solutions are obtained in an efficient way. Also the rank of the consistent system which gives a best or near best solution is estimated. Computer simulated examples using spatially separable pointspread functions are presented. Comments and conclusion are given.
Alignment of molecular networks by integer quadratic programming.
Zhenping, Li; Zhang, Shihua; Wang, Yong; Zhang, Xiang-Sun; Chen, Luonan
2007-07-01
With more and more data on molecular networks (e.g. protein interaction networks, gene regulatory networks and metabolic networks) available, the discovery of conserved patterns or signaling pathways by comparing various kinds of networks among different species or within a species becomes an increasingly important problem. However, most of the conventional approaches either restrict comparative analysis to special structures, such as pathways, or adopt heuristic algorithms due to computational burden. In this article, to find the conserved substructures, we develop an efficient algorithm for aligning molecular networks based on both molecule similarity and architecture similarity, by using integer quadratic programming (IQP). Such an IQP can be relaxed into the corresponding quadratic programming (QP) which almost always ensures an integer solution, thereby making molecular network alignment tractable without any approximation. The proposed framework is very flexible and can be applied to many kinds of molecular networks including weighted and unweighted, directed and undirected networks with or without loops. Matlab code and data are available from http://zhangroup.aporc.org/bioinfo/MNAligner or http://intelligent.eic.osaka-sandai.ac.jp/chenen/software/MNAligner, or upon request from authors. Supplementary data are available at Bioinformatics online.
Nonlinear equality constraints in feasible sequential quadratic programming
Lawrence, C.; Tits, A.
1994-12-31
In this talk we show that convergence of a feasible sequential quadratic programming algorithm modified to handle smooth nonlinear equality constraints. The modification of the algorithm to incorporate equality constraints is based on a scheme proposed by Mayne and Polak and is implemented in fsqp/cfsqp, an optimization package that generates feasible iterates. Nonlinear equality constraints are treated as {open_quotes}{<=}-type constraints to be satisfied by all iterates, thus precluding any positive value, and an exact penalty term is added to the objective function which penalizes negative values. For example, the problem minimize f(x) s.t. h(x) = 0, with h(x) a scalar, is replaced by minimize f(x) - ch(x) s.t. h(x) {<=} 0. The modified problem is equivalent to the original problem when c is large enough (but finite). Such a value is determined automatically via iterative adjustments.
Consultant-Guided Search Algorithms for the Quadratic Assignment Problem
NASA Astrophysics Data System (ADS)
Iordache, Serban
Consultant-Guided Search (CGS) is a recent swarm intelligence metaheuristic for combinatorial optimization problems, inspired by the way real people make decisions based on advice received from consultants. Until now, CGS has been successfully applied to the Traveling Salesman Problem. Because a good metaheuristic should be able to tackle efficiently a large variety of problems, it is important to see how CGS behaves when applied to other classes of problems. In this paper, we propose an algorithm for the Quadratic Assignment Problem (QAP), which hybridizes CGS with a local search procedure. Our experimental results show that CGS is able to compete in terms of solution quality with one of the best Ant Colony Optimization algorithms, the MAX-MIN Ant System.
Reduced order parameter estimation using quasilinearization and quadratic programming
NASA Astrophysics Data System (ADS)
Siade, Adam J.; Putti, Mario; Yeh, William W.-G.
2012-06-01
The ability of a particular model to accurately predict how a system responds to forcing is predicated on various model parameters that must be appropriately identified. There are many algorithms whose purpose is to solve this inverse problem, which is often computationally intensive. In this study, we propose a new algorithm that significantly reduces the computational burden associated with parameter identification. The algorithm is an extension of the quasilinearization approach where the governing system of differential equations is linearized with respect to the parameters. The resulting inverse problem therefore becomes a linear regression or quadratic programming problem (QP) for minimizing the sum of squared residuals; the solution becomes an update on the parameter set. This process of linearization and regression is repeated until convergence takes place. This algorithm has not received much attention, as the QPs can become quite large, often infeasible for real-world systems. To alleviate this drawback, proper orthogonal decomposition is applied to reduce the size of the linearized model, thereby reducing the computational burden of solving each QP. In fact, this study shows that the snapshots need only be calculated once at the very beginning of the algorithm, after which no further calculations of the reduced-model subspace are required. The proposed algorithm therefore only requires one linearized full-model run per parameter at the first iteration followed by a series of reduced-order QPs. The method is applied to a groundwater model with about 30,000 computation nodes where as many as 15 zones of hydraulic conductivity are estimated.
Variational viewpoint of the quadratic Markov measure field models: theory and algorithms.
Rivera, Mariano; Dalmau, Oscar
2012-03-01
We present a framework for image segmentation based on quadratic programming, i.e., by minimization of a quadratic regularized energy linearly constrained. In particular, we present a new variational derivation of the quadratic Markov measure field (QMMF) models, which can be understood as a procedure for regularizing model preferences (memberships or likelihoods). We also present efficient optimization algorithms. In the QMMFs, the uncertainty in the computed regularized probability measure field is controlled by penalizing Gini's coefficient, and hence, it affects the convexity of the quadratic programming problem. The convex case is reduced to the solution of a positive definite linear system, and for that case, an efficient Gauss-Seidel (GS) scheme is presented. On the other hand, we present an efficient projected GS with subspace minimization for optimizing the nonconvex case. We demonstrate the proposal capabilities by experiments and numerical comparisons with interactive two-class segmentation, as well as the simultaneous estimation of segmentation and (parametric and nonparametric) generative models. We present extensions to the original formulation for including color and texture clues, as well as imprecise user scribbles in an interactive framework.
Blind deconvolution estimation of fluorescence measurements through quadratic programming
NASA Astrophysics Data System (ADS)
Campos-Delgado, Daniel U.; Gutierrez-Navarro, Omar; Arce-Santana, Edgar R.; Skala, Melissa C.; Walsh, Alex J.; Jo, Javier A.
2015-07-01
Time-deconvolution of the instrument response from fluorescence lifetime imaging microscopy (FLIM) data is usually necessary for accurate fluorescence lifetime estimation. In many applications, however, the instrument response is not available. In such cases, a blind deconvolution approach is required. An iterative methodology is proposed to address the blind deconvolution problem departing from a dataset of FLIM measurements. A linear combination of a base conformed by Laguerre functions models the fluorescence impulse response of the sample at each spatial point in our formulation. Our blind deconvolution estimation (BDE) algorithm is formulated as a quadratic approximation problem, where the decision variables are the samples of the instrument response and the scaling coefficients of the basis functions. In the approximation cost function, there is a bilinear dependence on the decision variables. Hence, due to the nonlinear nature of the estimation process, an alternating least-squares scheme iteratively solves the approximation problem. Our proposal searches for the samples of the instrument response with a global perspective, and the scaling coefficients of the basis functions locally at each spatial point. First, the iterative methodology relies on a least-squares solution for the instrument response, and quadratic programming for the scaling coefficients applied just to a subset of the measured fluorescence decays to initially estimate the instrument response to speed up the convergence. After convergence, the final stage computes the fluorescence impulse response at all spatial points. A comprehensive validation stage considers synthetic and experimental FLIM datasets of ex vivo atherosclerotic plaques and human breast cancer cell samples that highlight the advantages of the proposed BDE algorithm under different noise and initial conditions in the iterative scheme and parameters of the proposal.
Blind deconvolution estimation of fluorescence measurements through quadratic programming.
Campos-Delgado, Daniel U; Gutierrez-Navarro, Omar; Arce-Santana, Edgar R; Skala, Melissa C; Walsh, Alex J; Jo, Javier A
2015-07-01
Time-deconvolution of the instrument response from fluorescence lifetime imaging microscopy (FLIM) data is usually necessary for accurate fluorescence lifetime estimation. In many applications, however, the instrument response is not available. In such cases, a blind deconvolution approach is required. An iterative methodology is proposed to address the blind deconvolution problem departing from a dataset of FLIM measurements. A linear combination of a base conformed by Laguerre functions models the fluorescence impulse response of the sample at each spatial point in our formulation. Our blind deconvolution estimation (BDE) algorithm is formulated as a quadratic approximation problem, where the decision variables are the samples of the instrument response and the scaling coefficients of the basis functions. In the approximation cost function, there is a bilinear dependence on the decision variables. Hence, due to the nonlinear nature of the estimation process, an alternating least-squares scheme iteratively solves the approximation problem. Our proposal searches for the samples of the instrument response with a global perspective, and the scaling coefficients of the basis functions locally at each spatial point. First, the iterative methodology relies on a least-squares solution for the instrument response, and quadratic programming for the scaling coefficients applied just to a subset of the measured fluorescence decays to initially estimate the instrument response to speed up the convergence. After convergence, the final stage computes the fluorescence impulse response at all spatial points. A comprehensive validation stage considers synthetic and experimental FLIM datasets of ex vivo atherosclerotic plaques and human breast cancer cell samples that highlight the advantages of the proposed BDE algorithm under different noise and initial conditions in the iterative scheme and parameters of the proposal.
Detection of code spread OFDM based on 0-1 integer quadratic programming
NASA Astrophysics Data System (ADS)
Elghariani, Ali; Zoltowski, Michael D.
2012-05-01
In this paper we introduce Integer Quadratic Programming (MIQP) approach to optimally detect QPSK Code Spread OFDM (CS-OFDM) by formulating the problem as a combinatorial optimization problem. The Branch and Bound (BB) algorithm is utilized to solve this integer quadratic programming problem. Furthermore, we propose combined preprocessing steps that can be applied prior to BB so that the computational complexity of the optimum receiver is reduced. The first step in this combination is to detect as much as possible symbols using procedures presented in [9], which is basically based on the gradient of quadratic function. The second step detects the undetected symbols from the first step using MMSE estimator. The result of the latter step will be used to predict the initial upper bound of the BB algorithm. Simulation results show that the proposed preprocessing combination when applied prior to BB provides optimal performance with a significantly reduced computational complexity.
Local classifier weighting by quadratic programming.
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.
Solving quadratic programming problems by delayed projection neural network.
Yang, Yongqing; Cao, Jinde
2006-11-01
In this letter, the delayed projection neural network for solving convex quadratic programming problems is proposed. The neural network is proved to be globally exponentially stable and can converge to an optimal solution of the optimization problem. Three examples show the effectiveness of the proposed network.
NASA Technical Reports Server (NTRS)
Fleming, P.
1983-01-01
A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a nonlinear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer. One concerns helicopter longitudinal dynamics and the other the flight dynamics of an aerodynamically unstable aircraft.
Sequential Quadratic Programming Algorithms for Optimization
1989-08-01
series expansion for the activo constraints, -(X) = 0 = c(x*) + A*dkl1k - x*ll + O(ll.rk - X*I1I), 3.5. The penalty parameter 37 which implies that...sequence of Q P statiot ary miitts (no to that the sequence is bouinded). From the assumption that the correct activo ett ha been identified, it must hold
Large-Scale Sequential Quadratic Programming Algorithms
1992-09-01
KKT conditions for the QP subproblem shows that Pk(gk) = pk(VL). To see why, note that the KKT necessary and sufficient conditions ...number of active functional constraints at x*). Let Z* be a basis for the null space of A* (so that A*Z* = 0). The KKT necessary conditions for (x*, A... optimal (i.e. when the working set has identified the active set). Let g* FkP* +9k and omit the subscript k. Consider the first-order KKT conditions for
Assessment Guidelines for Ant Colony Algorithms when Solving Quadratic Assignment Problems
NASA Astrophysics Data System (ADS)
See, Phen Chiak; Yew Wong, Kuan; Komarudin, Komarudin
2009-08-01
To date, no consensus exists on how to evaluate the performance of a new Ant Colony Optimization (ACO) algorithm when solving Quadratic Assignment Problems (QAPs). Different performance measures and problems sets are used by researchers to evaluate their algorithms. This paper is aimed to provide a recapitulation of the relevant issues and suggest some guidelines for assessing the performance of new ACO algorithms.
Projection-free parallel quadratic programming for linear model predictive control
NASA Astrophysics Data System (ADS)
Di Cairano, S.; Brand, M.; Bortoff, S. A.
2013-08-01
A key component in enabling the application of model predictive control (MPC) in fields such as automotive, aerospace, and factory automation is the availability of low-complexity fast optimisation algorithms to solve the MPC finite horizon optimal control problem in architectures with reduced computational capabilities. In this paper, we introduce a projection-free iterative optimisation algorithm and discuss its application to linear MPC. The algorithm, originally developed by Brand for non-negative quadratic programs, is based on a multiplicative update rule and it is shown to converge to a fixed point which is the optimum. An acceleration technique based on a projection-free line search is also introduced, to speed-up the convergence to the optimum. The algorithm is applied to MPC through the dual of the quadratic program (QP) formulated from the MPC finite time optimal control problem. We discuss how termination conditions with guaranteed degree of suboptimality can be enforced, and how the algorithm performance can be optimised by pre-computing the matrices in a parametric form. We show computational results of the algorithm in three common case studies and we compare such results with the results obtained by other available free and commercial QP solvers.
Evolving evolutionary algorithms using linear genetic programming.
Oltean, Mihai
2005-01-01
A new model for evolving Evolutionary Algorithms is proposed in this paper. The model is based on the Linear Genetic Programming (LGP) technique. Every LGP chromosome encodes an EA which is used for solving a particular problem. Several Evolutionary Algorithms for function optimization, the Traveling Salesman Problem and the Quadratic Assignment Problem are evolved by using the considered model. Numerical experiments show that the evolved Evolutionary Algorithms perform similarly and sometimes even better than standard approaches for several well-known benchmarking problems.
Primal-Dual Interior Methods for Quadratic Programming
NASA Astrophysics Data System (ADS)
Shustrova, Anna
Interior methods are a class of computational methods for solving a con- strained optimization problem. Interior methods follow a continuous path to the solution that passes through the interior of the feasible region (i.e., the set of points that satisfy the constraints). Interior-point methods may also be viewed as methods that replace the constrained problem by a sequence of unconstrained problems in which the objective function is augmented by a weighted "barrier" term that is infinite at the boundary of the feasible region. Convergence to a solution of the constrained problem is achieved by solving a sequence of unconstrained problems in which the weight on the barrier term is steadily reduced to zero. This thesis concerns the formulation and analysis of interior methods for the solution of a quadratic programming (QP) problem, which is an optimization problem with a quadratic objective function and linear constraints. The linear constraints may include an arbitrary mixture of equality and inequality constraints, where the inequality constraints may be subject to lower and/or upper bounds. QP problems arise in a wide variety of applications. An important application is in sequential quadratic programming methods for nonlinear optimization, which involve minimizing a sequence of QP subproblems based on a quadratic approximation of the nonlinear objective function and a set of linearized nonlinear constraints. Two new interior methods for QP are proposed. Each is based on the properties of a barrier function defined in terms of both the primal and dual variables. The first method is suitable for a QP with all inequality constraints. At each iteration, the Newton equations for minimizing a quadratic model of the primal-dual barrier function are reformulated in terms of a symmetric indefinite system of equations that is solved using an inertia controlling factorization. This factorization provides an effective method for the detection and convexification of
Orsi, R. J.; Mahony, R. E.; Moore, J. B.
1999-09-15
This paper considers the problem of minimizing a quadratic cost subject to purely quadratic equality constraints. This problem is tackled by first relating it to a standard semidefinite programming problem. The approach taken leads to a dynamical systems analysis of semidefinite programming and the formulation of a gradient descent flow which can be used to solve semidefinite programming problems. Though the reformulation of the initial problem as a semidefinite pro- gramming problem does not in general lead directly to a solution of the original problem, the initial problem is solved by using a modified flow incorporating a penalty function.
A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints
NASA Technical Reports Server (NTRS)
Hanson, R. J.; Krogh, Fred T.
1992-01-01
A new algorithm for solving nonlinear least-squares and nonlinear equation problems is proposed which is based on approximating the nonlinear functions using the quadratic-tensor model by Schnabel and Frank. The algorithm uses a trust region defined by a box containing the current values of the unknowns. The algorithm is found to be effective for problems with linear constraints and dense Jacobian matrices.
A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints
NASA Technical Reports Server (NTRS)
Hanson, R. J.; Krogh, Fred T.
1992-01-01
A new algorithm for solving nonlinear least-squares and nonlinear equation problems is proposed which is based on approximating the nonlinear functions using the quadratic-tensor model by Schnabel and Frank. The algorithm uses a trust region defined by a box containing the current values of the unknowns. The algorithm is found to be effective for problems with linear constraints and dense Jacobian matrices.
A variable-metric algorithm employing linear and quadratic penalties. [for optimal control
NASA Technical Reports Server (NTRS)
Kelley, H. J.; Lefton, L.; Johnson, I. L., Jr.
1975-01-01
A variable-metric algorithm is described that uses both linear and quadratic penalty terms for handling nonlinear constraints. Quadratic penalty coefficients are adjusted in a process which maintains a positive-definite matrix of second partial derivatives of the function without generating the large positive eigenvalues which cause zigzagging and slow convergence. The schemes suggested use inferred second-order properties not only in terms of the variable metric of the Davidson-Fletcher-Powell algorithm (or its relatives) but by estimating of second directional derivatives by fitting cubics to various functions along search directions.
Chang, Weng-Long
2012-03-01
Assume that n is a positive integer. If there is an integer such that M (2) ≡ C (mod n), i.e., the congruence has a solution, then C is said to be a quadratic congruence (mod n). If the congruence does not have a solution, then C is said to be a quadratic noncongruence (mod n). The task of solving the problem is central to many important applications, the most obvious being cryptography. In this article, we describe a DNA-based algorithm for solving quadratic congruence and factoring integers. In additional to this novel contribution, we also show the utility of our encoding scheme, and of the algorithm's submodules. We demonstrate how a variety of arithmetic, shifted and comparative operations, namely bitwise and full addition, subtraction, left shifter and comparison perhaps are performed using strands of DNA.
Quadratic adaptive algorithm for solving cardiac action potential models.
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
NASA Astrophysics Data System (ADS)
Kassa, Semu Mitiku; Tsegay, Teklay Hailay
2017-08-01
Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fractional objective functions at each of the three levels. A solution algorithm has been proposed by applying fuzzy goal programming approach and by reformulating the fractional constraints to equivalent but non-fractional non-linear constraints. Based on the transformed formulation, an iterative procedure is developed that can yield a satisfactory solution to the tri-level problem. The numerical results on various illustrative examples demonstrated that the proposed algorithm is very much promising and it can also be used to solve larger-sized as well as n-level problems of similar structure.
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.
Neural network for solving convex quadratic bilevel programming problems.
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.
Longitudinal force distribution using quadratically constrained linear programming
NASA Astrophysics Data System (ADS)
Klomp, M.
2011-12-01
In this paper, a new method is presented for the optimisation of force distribution for combined traction/braking and cornering. In order to provide a general, simple and flexible problem formulation, the optimisation is addressed as a quadratically constrained linear programming (QCLP) problem. Apart from fast numerical solutions, different driveline configurations can be included in the QCLP problem in a very straightforward fashion. The optimisation of the distribution of the individual wheel forces using the quasi-steady-state assumption is known to be useful for the study of the influence of particular driveline configurations on the combined lateral and longitudinal grip envelope of a particular vehicle-driveline configuration. The addition of the QCLP problem formulation makes another powerful tool available to the vehicle dynamics analyst to perform such studies.
A quadratic programming framework for constrained and robust jet engine health monitoring
NASA Astrophysics Data System (ADS)
Borguet, S.; Léonard, O.
2009-09-01
Kalman filters are largely used in the jet engine community for condition monitoring purpose. This algorithm gives a good estimate of the engine condition provided that the residuals between the model prediction and the measurements are zero-mean, Gaussian random variables. In the case of sensor faults, this assumption does not hold anymore and consequently, the diagnosis is spoiled. This contribution presents a recursive estimation algorithm based on a Quadratic Programming (QP) formulation which provides robustness against sensor faults and allows constraints on the health parameters to be specified. The improvements in estimation accuracy brought by this new algorithm are illustrated on a series of typical test-cases that may be encountered on current turbofan engines.
MM Algorithms for Geometric and Signomial Programming.
Lange, Kenneth; Zhou, Hua
2014-02-01
This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.
MM Algorithms for Geometric and Signomial Programming
Lange, Kenneth; Zhou, Hua
2013-01-01
This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates. PMID:24634545
A Neurodynamic Optimization Approach to Bilevel Quadratic Programming.
Qin, Sitian; Le, Xinyi; Wang, Jun
2016-08-19
This paper presents a neurodynamic optimization approach to bilevel quadratic programming (BQP). Based on the Karush-Kuhn-Tucker (KKT) theorem, the BQP problem is reduced to a one-level mathematical program subject to complementarity constraints (MPCC). It is proved that the global solution of the MPCC is the minimal one of the optimal solutions to multiple convex optimization subproblems. A recurrent neural network is developed for solving these convex optimization subproblems. From any initial state, the state of the proposed neural network is convergent to an equilibrium point of the neural network, which is just the optimal solution of the convex optimization subproblem. Compared with existing recurrent neural networks for BQP, the proposed neural network is guaranteed for delivering the exact optimal solutions to any convex BQP problems. Moreover, it is proved that the proposed neural network for bilevel linear programming is convergent to an equilibrium point in finite time. Finally, three numerical examples are elaborated to substantiate the efficacy of the proposed approach.
NASA Technical Reports Server (NTRS)
Fleming, P.
1985-01-01
A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.
NASA Technical Reports Server (NTRS)
Fleming, P.
1985-01-01
A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.
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.
Binary Quadratic Programing for Online Tracking of Hundreds of People in Extremely Crowded Scenes.
Dehghan, Afshin; Shah, Mubarak
2017-03-24
Multi-object tracking has been studied for decades. However, when it comes to tracking pedestrians in extremely crowded scenes, we are limited to only few works. This is an important problem which gives rise to several challenges. Pre-trained object detectors fail to localize targets in crowded sequences. This consequently limits the use of data-association based multi-target tracking methods which rely on the outcome of an object detector. Additionally, the small apparent target size makes it challenging to extract features to discriminate targets from their surroundings. Finally, the large number of targets greatly increases computational complexity which in turn makes it hard to extend existing multi-target tracking approaches to high-density crowd scenarios. In this paper, we propose a tracker that addresses the aforementioned problems and is capable of tracking hundreds of people efficiently. We formulate online crowd tracking as Binary Quadratic Programing. Our formulation employs target's individual information in the form of appearance and motion as well as contextual cues in the form of neighborhood motion, spatial proximity and grouping, and solves detection and data association simultaneously. In order to solve the proposed quadratic optimization efficiently, where state-of art commercial quadratic programing solvers fail to find the solution in a reasonable amount of time, we propose to use the most recent version of the Modified Frank Wolfe algorithm, which takes advantage of SWAP-steps to speed up the optimization. We show that the proposed formulation can track hundreds of targets efficiently and improves state-of-art results by significant margins on eleven challenging high density crowd sequences.
Identify Beta-Hairpin Motifs with Quadratic Discriminant Algorithm Based on the Chemical Shifts.
YongE, Feng; GaoShan, Kou
2015-01-01
Successful prediction of the beta-hairpin motif will be helpful for understanding the of the fold recognition. Some algorithms have been proposed for the prediction of beta-hairpin motifs. However, the parameters used by these methods were primarily based on the amino acid sequences. Here, we proposed a novel model for predicting beta-hairpin structure based on the chemical shift. Firstly, we analyzed the statistical distribution of chemical shifts of six nuclei in not beta-hairpin and beta-hairpin motifs. Secondly, we used these chemical shifts as features combined with three algorithms to predict beta-hairpin structure. Finally, we achieved the best prediction, namely sensitivity of 92%, the specificity of 94% with 0.85 of Mathew's correlation coefficient using quadratic discriminant analysis algorithm, which is clearly superior to the same method for the prediction of beta-hairpin structure from 20 amino acid compositions in the three-fold cross-validation. Our finding showed that the chemical shift is an effective parameter for beta-hairpin prediction, suggesting the quadratic discriminant analysis is a powerful algorithm for the prediction of beta-hairpin.
NASA Astrophysics Data System (ADS)
Badreddine, Hassan; Vandewalle, Stefan; Meyers, Johan
2014-01-01
The current work focuses on the development and application of an efficient algorithm for optimization of three-dimensional turbulent flows, simulated using Direct Numerical Simulation (DNS) or Large-Eddy Simulations, and further characterized by large-dimensional optimization-parameter spaces. The optimization algorithm is based on Sequential Quadratic Programming (SQP) in combination with a damped formulation of the limited-memory BFGS method. The latter is suitable for solving large-scale constrained optimization problems whose Hessian matrices cannot be computed and stored at a reasonable cost. We combine the algorithm with a line-search merit function based on an L1-norm to enforce the convergence from any remote point. It is first shown that the proposed form of the damped L-BFGS algorithm is suitable for solving equality constrained Rosenbrock type functions. Then, we apply the algorithm to an optimal-control test problem that consists of finding the optimal initial perturbations to a turbulent temporal mixing layer such that mixing is improved at the end of a simulation time horizon T. The controls are further subject to a non-linear equality constraint on the total control energy. DNSs are used to resolve all turbulent scales of motion, and a continuous adjoint formulation is employed to calculate the gradient of the cost functionals. We compare the convergence speed of the SQP L-BFGS algorithm to a conventional non-linear conjugate-gradient method (i.e. the current standard in DNS-based optimal control), and find that the SQP algorithm is more than an order of magnitude faster than the conjugate-gradient method.
CFSQP: A C code for feasible sequential quadratic programming
Lawrence, C.; Tits, A.
1994-12-31
cfsqp is a set of C functions for the minimization of the maximum of a set of smooth objective functions (possibly a single one) subject to smooth equality and inequality constraints. cfsqp has many distinguishing features. First, the generated iterates satisfy all inequality and linear equality constraints (after an initial feasible point has been automatically constructed). Second, nonlinear equality constraints are relaxed into {open_quotes}{<=}{close_quotes}-type constraints to be satisfied by all iterates, thus precluding any positive value, and the maximum of the objective functions is replaced by an exact penalty function penalizing negative values. Third, the user has the option of requiring that the maximum of the objective functions (penalty function if nonlinear equality constraints are present) decrease at each iteration (monotone line search), or that it decrease within at most four iterations (nonmonotone line search). Recently, a new enhancement was added to cfsqp that is useful when solving problems with many sequentially related constraints (or objectives), such as discretized semi-infinite programming (SIP) problems. cfsqp gives the user the option to greatly reduce computational effort by using an algorithm that more efficiently handles large groups of objectives or constraints. In this talk we will review the cfsqp algorithm and implementation, as well as discuss numerical results obtained on various problems.
Dang, Chuangyin; Liang, Jianqing; Yang, Yang
2013-03-01
A deterministic annealing algorithm is proposed for approximating a solution of the linearly constrained nonconvex quadratic minimization problem. The algorithm is derived from applications of a Hopfield-type barrier function in dealing with box constraints and Lagrange multipliers in handling linear equality constraints, and attempts to obtain a solution of good quality by generating a minimum point of a barrier problem for a sequence of descending values of the barrier parameter. For any given value of the barrier parameter, the algorithm searches for a minimum point of the barrier problem in a feasible descent direction, which has a desired property that the box constraints are always satisfied automatically if the step length is a number between zero and one. At each iteration, the feasible descent direction is found by updating Lagrange multipliers with a globally convergent iterative procedure. For any given value of the barrier parameter, the algorithm converges to a stationary point of the barrier problem. Preliminary numerical results show that the algorithm seems effective and efficient. Copyright © 2012 Elsevier Ltd. All rights reserved.
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…
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
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.
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…
Aceves-Lara, C A; Aguilar-Garnica, E; Alcaraz-González, V; González-Reynoso, O; Steyer, J P; Dominguez-Beltran, J L; González-Alvarez, V
2005-01-01
In this work, an optimization method is implemented in an anaerobic digestion model to estimate its kinetic parameters and yield coefficients. This method combines the use of advanced state estimation schemes and powerful nonlinear programming techniques to yield fast and accurate estimates of the aforementioned parameters. In this method, we first implement an asymptotic observer to provide estimates of the non-measured variables (such as biomass concentration) and good guesses for the initial conditions of the parameter estimation algorithm. These results are then used by the successive quadratic programming (SQP) technique to calculate the kinetic parameters and yield coefficients of the anaerobic digestion process. The model, provided with the estimated parameters, is tested with experimental data from a pilot-scale fixed bed reactor treating raw industrial wine distillery wastewater. It is shown that SQP reaches a fast and accurate estimation of the kinetic parameters despite highly noise corrupted experimental data and time varying inputs variables. A statistical analysis is also performed to validate the combined estimation method. Finally, a comparison between the proposed method and the traditional Marquardt technique shows that both yield similar results; however, the calculation time of the traditional technique is considerable higher than that of the proposed method.
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.
A new one-layer neural network for linear and quadratic programming.
Gao, Xingbao; Liao, Li-Zhi
2010-06-01
In this paper, we present a new neural network for solving linear and quadratic programming problems in real time by introducing some new vectors. The proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem when the objective function is convex on the set defined by equality constraints. Compared with existing one-layer neural networks for quadratic programming problems, the proposed neural network has the least neurons and requires weak stability conditions. The validity and transient behavior of the proposed neural network are demonstrated by some simulation results.
Quadratic phase error compensation algorithm based on phase cancellation for ISAIL
NASA Astrophysics Data System (ADS)
Zang, Bo; Li, Qi; Ji, Hong-Bing; Tang, Yu
2013-09-01
As a product combining inverse synthetic aperture technology with coherent laser technology, Inverse Synthetic Aperture Imaging Ladar (ISAIL) overcomes the diffraction limit of the telescope's aperture, while it supplies a much better range resolution which will not get worse at long range when the diameter telescope optics becomes smaller. Compared with traditional microwave imaging radar, SAIL can provide a much higher-resolution image because of shorter wavelength, and its shorter imaging time for coherent integration takes a great part in practical application. The rotational motion of target generates Migration through Range Cells (MTRC) because of the ultra-high resolution of ISAIL. Quadratic Phase Error (QPE) caused by Migration through Range Cells (MTRC) during the imaging time makes ISAIL image smeared. It is difficult to estimate the QPE through traditional motion compensation algorithm. To solve this problem in the case of uniform rotation rate, a novel QPE compensation method, based on Phase Cancellation (PC), is proposed. Firstly, a rough range of QPE coefficient related to the wave-length, length of the target, and the rotating angle is estimated. Then, through 1-D search, the QPE coefficient is obtained exactly. Finally, the QPE compensation is achieved. The ISAIL imaging experiments with numerical data validate the feasibility and effectiveness of the proposed algorithm.
A Genetic Algorithm with the Improved 2-opt Method for Quadratic Assignment Problem
NASA Astrophysics Data System (ADS)
Matayoshi, Mitsukuni; Nakamura, Morikazu; Miyagi, Hayao
We propose a new 2-opt base method as a local search approach used with Genetic Algorithms (GAs) in Memetic Algorithm. We got a hint from the fast 2-opt method and devised the new 2-opt method. The main different point is such that our method exchanges genes by using histories of contributions to fitness value improvement. The contribution level is represented by the value `Priority’. In computer experiment, Quadratic Assignment Problem (QAP) instances are solved by GA with the 2-opt method(First Admissible Move Strategy, the Best Admissible Move Strategy), the fast 2-opt, and our proposed method for comparative evaluation. The results showed that our improved method obtained better solutions at ealier generation of the GA and our method required less computation time than the others at some upper bound value of appropriate `Priority’ setting values. Specially, at the average elapsed time of the fast 2-opt method’s 1000th generation, the exact solution findings of ours is more than the others. In further experiment, we observe that the searching capability depends on the number of levels of `Priority’. The ratio between two different Priority level sets becomes 1.59 in computation time in solving problem instance “char25a". This characteristic is shown to be statistically significant in ten instances among eleven.
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
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.
NASA Astrophysics Data System (ADS)
Zimmermann, Karl-Heinz; Achtziger, Wolfgang
2001-09-01
The size of a systolic array synthesized from a uniform recurrence equation, whose computations are mapped by a linear function to the processors, matches the problem size. In practice, however, there exist several limiting factors on the array size. There are two dual schemes available to derive arrays of smaller size from large-size systolic arrays based on the partitioning of the large-size arrays into subarrays. In LSGP, the subarrays are clustered one-to-one into the processors of a small-size array, while in LPGS, the subarrays are serially assigned to a reduced-size array. In this paper, we propose a common methodology for both LSGP and LPGS based on polyhedral partitionings of large-size k-dimensional systolic arrays which are synthesized from n-dimensional uniform recurrences by linear mappings for allocation and timing. In particular, we address the optimization problem of finding optimal piecewise linear timing functions for small-size arrays. These are mappings composed of linear timing functions for the computations of the subarrays. We study a continuous approximation of this problem by passing from piecewise linear to piecewise quasi-linear timing functions. The resultant problem formulation is then a quadratic programming problem which can be solved by standard algorithms for nonlinear optimization problems.
Chao, R.M.; Ko, S.H.; Lin, I.H.; Pai, F.S.; Chang, C.C.
2009-12-15
The historically high cost of crude oil price is stimulating research into solar (green) energy as an alternative energy source. In general, applications with large solar energy output require a maximum power point tracking (MPPT) algorithm to optimize the power generated by the photovoltaic effect. This work aims to provide a stand-alone solution for solar energy applications by integrating a DC/DC buck converter to a newly developed quadratic MPPT algorithm along with its appropriate software and hardware. The quadratic MPPT method utilizes three previously used duty cycles with their corresponding power outputs. It approaches the maximum value by using a second order polynomial formula, which converges faster than the existing MPPT algorithm. The hardware implementation takes advantage of the real-time controller system from National Instruments, USA. Experimental results have shown that the proposed solar mechatronics system can correctly and effectively track the maximum power point without any difficulties. (author)
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
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.
Optimum structural design using MSC/NASTRAN and sequential quadratic programming
NASA Astrophysics Data System (ADS)
Mahmoud, K. G.; Engl, H. W.; Holzleitner, L.
1994-08-01
A methodology is described for structural optimization using the commercial finite element package MSC/NASTRAN for structural analysis, a quasi-analytical method for design sensitivity analysis, and sequential quadratic programming with an active set strategy for optimization. The optimization and sensitivity analysis modules are efficiently coupled with MSC/NASTRAN using DMAP (direct matrix abstraction program) statements. To demonstrate the feasibility of the proposed methodology, the design optimization of a unit injector rocker arm is presented as an example.
A new gradient-based neural network for solving linear and quadratic programming problems.
Leung, Y; Chen, K Z; Jiao, Y C; Gao, X B; Leung, K S
2001-01-01
A new gradient-based neural network is constructed on the basis of the duality theory, optimization theory, convex analysis theory, Lyapunov stability theory, and LaSalle invariance principle to solve linear and quadratic programming problems. In particular, a new function F(x, y) is introduced into the energy function E(x, y) such that the function E(x, y) is convex and differentiable, and the resulting network is more efficient. This network involves all the relevant necessary and sufficient optimality conditions for convex quadratic programming problems. For linear programming and quadratic programming (QP) problems with unique and infinite number of solutions, we have proven strictly that for any initial point, every trajectory of the neural network converges to an optimal solution of the QP and its dual problem. The proposed network is different from the existing networks which use the penalty method or Lagrange method, and the inequality constraints are properly handled. The simulation results show that the proposed neural network is feasible and efficient.
Interval-parameter robust quadratic programming for water quality management under uncertainty
NASA Astrophysics Data System (ADS)
Li, Y. P.; Huang, G. H.; Nie, S. L.; Mo, D. W.
2008-07-01
Effective planning of water quality management is important for facilitating sustainable socio-economic development in watershed systems. An interval-parameter robust quadratic programming (IRQP) method is developed by incorporating techniques of robust programming and interval quadratic programming within a general optimization framework. The IRQP improves upon existing quadratic programming methods, and can tackle uncertainties presented as interval numbers and fuzzy sets as well as their combinations. Moreover, it can deal with nonlinearities in the objective function such that economies-of-scale effects can be reflected. The developed method is applied to a case study of a water quality management under uncertainty. A number of decision alternatives are generated based on the interval solutions as well as the projected applicable conditions. They represent multiple decision options with various environmental and economic considerations. Willingness to accept a low economic revenue will guarantee satisfying the water quality requirements. A strong desire to acquire a high benefit will run the risk of violating environmental criteria.
Fitting timeseries by continuous-time Markov chains: A quadratic programming approach
NASA Astrophysics Data System (ADS)
Crommelin, D. T.; Vanden-Eijnden, E.
2006-09-01
Construction of stochastic models that describe the effective dynamics of observables of interest is an useful instrument in various fields of application, such as physics, climate science, and finance. We present a new technique for the construction of such models. From the timeseries of an observable, we construct a discrete-in-time Markov chain and calculate the eigenspectrum of its transition probability (or stochastic) matrix. As a next step we aim to find the generator of a continuous-time Markov chain whose eigenspectrum resembles the observed eigenspectrum as closely as possible, using an appropriate norm. The generator is found by solving a minimization problem: the norm is chosen such that the object function is quadratic and convex, so that the minimization problem can be solved using quadratic programming techniques. The technique is illustrated on various toy problems as well as on datasets stemming from simulations of molecular dynamics and of atmospheric flows.
Fitting timeseries by continuous-time Markov chains: A quadratic programming approach
Crommelin, D.T. . E-mail: crommelin@cims.nyu.edu; Vanden-Eijnden, E. . E-mail: eve2@cims.nyu.edu
2006-09-20
Construction of stochastic models that describe the effective dynamics of observables of interest is an useful instrument in various fields of application, such as physics, climate science, and finance. We present a new technique for the construction of such models. From the timeseries of an observable, we construct a discrete-in-time Markov chain and calculate the eigenspectrum of its transition probability (or stochastic) matrix. As a next step we aim to find the generator of a continuous-time Markov chain whose eigenspectrum resembles the observed eigenspectrum as closely as possible, using an appropriate norm. The generator is found by solving a minimization problem: the norm is chosen such that the object function is quadratic and convex, so that the minimization problem can be solved using quadratic programming techniques. The technique is illustrated on various toy problems as well as on datasets stemming from simulations of molecular dynamics and of atmospheric flows.
An algorithm for the solution of dynamic linear programs
NASA Technical Reports Server (NTRS)
Psiaki, Mark L.
1989-01-01
The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation
NASA Astrophysics Data System (ADS)
Hongwu, Zhang; Xinwei, Zhang
2002-12-01
The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems.
Kou, Gaoshan; Feng, Yonge
2015-09-07
The biological function of protein is largely determined by its spatial structure. The research on the relationship between structure and function is the basis of protein structure prediction. However, the prediction of super secondary structure is an important step in the prediction of protein spatial structure. Many algorithms have been proposed for the prediction of protein super secondary structure. However, the parameters used by these methods were primarily based on amino acid sequences. In this paper, we proposed a novel model for predicting five kinds of protein super secondary structures based on the chemical shifts (CSs). Firstly, we analyzed the statistical distribution of chemical shifts of six nuclei in five kinds of protein super secondary structures by using the analysis of variance (ANOVA). Secondly, we used chemical shifts of six nuclei as features, and combined with quadratic discriminant analysis (QDA) to predict five kinds of protein super secondary structures. Finally, we achieved the averaged sensitivity, specificity and the overall accuracy of 81.8%, 95.19%, 82.91%, respectively in seven-fold cross-validation. Moreover, we have performed the prediction by combining the five different chemical shifts as features, the maximum overall accuracy up to 89.87% by using the C,Cα,Cβ,N,Hα of Hα chemical shifts, which are clearly superior to that of the quadratic discriminant analysis (QDA) algorithm by using 20 amino acid compositions (AAC) as feature in the seven-fold cross-validation. These results demonstrated that chemical shifts (CSs) are indeed an outstanding parameter for the prediction of five kinds of super secondary structures. In addition, we compared the prediction of the quadratic discriminant analysis (QDA) with that of support vector machine (SVM) by using the same six CSs as features. The result suggested that the quadratic discriminant analysis method by using chemical shifts as features is a good predictor for protein super
Becker, R
2006-03-03
The goal is to examine the dependence of the plastic flow direction as a function of strain increment for a generalized quadratic flow potential; and from that, extract a scheme for constructing a plastic flow direction for a more general class of yield and flow surfaces.
Algorithmic advances in stochastic programming
Morton, D.P.
1993-07-01
Practical planning problems with deterministic forecasts of inherently uncertain parameters often yield unsatisfactory solutions. Stochastic programming formulations allow uncertain parameters to be modeled as random variables with known distributions, but the size of the resulting mathematical programs can be formidable. Decomposition-based algorithms take advantage of special structure and provide an attractive approach to such problems. We consider two classes of decomposition-based stochastic programming algorithms. The first type of algorithm addresses problems with a ``manageable`` number of scenarios. The second class incorporates Monte Carlo sampling within a decomposition algorithm. We develop and empirically study an enhanced Benders decomposition algorithm for solving multistage stochastic linear programs within a prespecified tolerance. The enhancements include warm start basis selection, preliminary cut generation, the multicut procedure, and decision tree traversing strategies. Computational results are presented for a collection of ``real-world`` multistage stochastic hydroelectric scheduling problems. Recently, there has been an increased focus on decomposition-based algorithms that use sampling within the optimization framework. These approaches hold much promise for solving stochastic programs with many scenarios. A critical component of such algorithms is a stopping criterion to ensure the quality of the solution. With this as motivation, we develop a stopping rule theory for algorithms in which bounds on the optimal objective function value are estimated by sampling. Rules are provided for selecting sample sizes and terminating the algorithm under which asymptotic validity of confidence interval statements for the quality of the proposed solution can be verified. Issues associated with the application of this theory to two sampling-based algorithms are considered, and preliminary empirical coverage results are presented.
NASA Astrophysics Data System (ADS)
Lipinski, Piotr
This paper concerns the quadratic three-dimensional assignment problem (Q3AP), an extension of the quadratic assignment problem (QAP), and proposes an efficient hybrid evolutionary algorithm combining stochastic optimization and local search with a number of crossover operators, a number of mutation operators and an auto-adaptation mechanism. Auto-adaptation manages the pool of evolutionary operators applying different operators in different computation phases to better explore the search space and to avoid premature convergence. Local search additionally optimizes populations of candidate solutions and accelerates evolutionary search. It uses a many-core graphics processor to optimize a number of solutions in parallel, which enables its incorporation into the evolutionary algorithm without excessive increases in the computation time. Experiments performed on benchmark Q3AP instances derived from the classic QAP instances proposed by Nugent et al. confirmed that the proposed algorithm is able to find optimal solutions to Q3AP in a reasonable time and outperforms best known results found in the literature.
Programming the gradient projection algorithm
NASA Technical Reports Server (NTRS)
Hargrove, A.
1983-01-01
The gradient projection method of numerical optimization which is applied to problems having linear constraints but nonlinear objective functions is described and analyzed. The algorithm is found to be efficient and thorough for small systems, but requires the addition of auxiliary methods and programming for large scale systems with severe nonlinearities. In order to verify the theoretical results a digital computer is used to simulate the algorithm.
An Augmented Lagrangian Method for a Class of Inverse Quadratic Programming Problems
Zhang Jianzhong; Zhang Liwei
2010-02-15
We consider an inverse quadratic programming (QP) problem in which the parameters in the objective function of a given QP problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a minimization problem with a positive semidefinite cone constraint and its dual is a linearly constrained semismoothly differentiable (SC{sup 1}) convex programming problem with fewer variables than the original one. We demonstrate the global convergence of the augmented Lagrangian method for the dual problem and prove that the convergence rate of primal iterates, generated by the augmented Lagrange method, is proportional to 1/r, and the rate of multiplier iterates is proportional to 1/{radical}r, where r is the penalty parameter in the augmented Lagrangian. As the objective function of the dual problem is a SC{sup 1} function involving the projection operator onto the cone of symmetrically semi-definite matrices, the analysis requires extensive tools such as the singular value decomposition of matrices, an implicit function theorem for semismooth functions, and properties of the projection operator in the symmetric-matrix space. Furthermore, the semismooth Newton method with Armijo line search is applied to solve the subproblems in the augmented Lagrange approach, which is proven to have global convergence and local quadratic rate. Finally numerical results, implemented by the augmented Lagrangian method, are reported.
Liu, Q; Wang, J
2008-04-01
In this paper, a one-layer recurrent neural network with a discontinuous hard-limiting activation function is proposed for quadratic programming. This neural network is capable of solving a large class of quadratic programming problems. The state variables of the neural network are proven to be globally stable and the output variables are proven to be convergent to optimal solutions as long as the objective function is strictly convex on a set defined by the equality constraints. In addition, a sequential quadratic programming approach based on the proposed recurrent neural network is developed for general nonlinear programming. Simulation results on numerical examples and support vector machine (SVM) learning show the effectiveness and performance of the neural network.
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.
Quadratic programming-based approach for autonomous vehicle path planning in space
NASA Astrophysics Data System (ADS)
Chen, Yang; Han, Jianda; Wu, Huaiyu
2012-07-01
Path planning for space vehicles is still a challenging problem although considerable progress has been made over the past decades. The major difficulties are that most of existing methods only adapt to static environment instead of dynamic one, and also can not solve the inherent constraints arising from the robot body and the exterior environment. To address these difficulties, this research aims to provide a feasible trajectory based on quadratic programming(QP) for path planning in three-dimensional space where an autonomous vehicle is requested to pursue a target while avoiding static or dynamic obstacles. First, the objective function is derived from the pursuit task which is defined in terms of the relative distance to the target, as well as the angle between the velocity and the position in the relative velocity coordinates(RVCs). The optimization is in quadratic polynomial form according to QP formulation. Then, the avoidance task is modeled with linear constraints in RVCs. Some other constraints, such as kinematics, dynamics, and sensor range, are included. Last, simulations with typical multiple obstacles are carried out, including in static and dynamic environments and one of human-in-the-loop. The results indicate that the optimal trajectories of the autonomous robot in three-dimensional space satisfy the required performances. Therefore, the QP model proposed in this paper not only adapts to dynamic environment with uncertainty, but also can satisfy all kinds of constraints, and it provides an efficient approach to solve the problems of path planning in three-dimensional space.
A Linear Quadratic Regulator Weight Selection Algorithm for Robust Pole Assignment
1990-12-01
MATLAB . Five test cases are run with the algorithm. First and second order systems that can be solved in closed form are compared with the algorithm poles...The MATLAB "m"-file used to solve the second order SISO system is included in appendix A. Run time on the Compaq 286 was 4 minutes. Table I! Second...poles but it should get close. When this system 3 was run on MATLAB with the algorithm m-files, the achievable poles were found to be -2.096 z 2.389j
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.
Quadratic eigenvalue problems.
Walsh, Timothy Francis; Day, David Minot
2007-04-01
In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.
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
Using convex quadratic programming to model random media with Gaussian random fields
Quintanilla, John A.; Jones, W. Max
2007-04-15
Excursion sets of Gaussian random fields (GRFs) have been frequently used in the literature to model two-phase random media with measurable phase autocorrelation functions. The goal of successful modeling is finding the optimal field autocorrelation function that best approximates the prescribed phase autocorrelation function. In this paper, we present a technique which uses convex quadratic programming to find the best admissible field autocorrelation function under a prescribed discretization. Unlike previous methods, this technique efficiently optimizes over all admissible field autocorrelation functions, instead of optimizing only over a predetermined parametrized family. The results from using this technique indicate that the GRF model is significantly more versatile than observed in previous studies. An application to modeling a base-catalyzed tetraethoxysilane aerogel system given small-angle neutron scattering data is also presented.
An efficient ensemble of radial basis functions method based on quadratic programming
NASA Astrophysics Data System (ADS)
Shi, Renhe; Liu, Li; Long, Teng; Liu, Jian
2016-07-01
Radial basis function (RBF) surrogate models have been widely applied in engineering design optimization problems to approximate computationally expensive simulations. Ensemble of radial basis functions (ERBF) using the weighted sum of stand-alone RBFs improves the approximation performance. To achieve a good trade-off between the accuracy and efficiency of the modelling process, this article presents a novel efficient ERBF method to determine the weights through solving a quadratic programming subproblem, denoted ERBF-QP. Several numerical benchmark functions are utilized to test the performance of the proposed ERBF-QP method. The results show that ERBF-QP can significantly improve the modelling efficiency compared with several existing ERBF methods. Moreover, ERBF-QP also provides satisfactory performance in terms of approximation accuracy. Finally, the ERBF-QP method is applied to a satellite multidisciplinary design optimization problem to illustrate its practicality and effectiveness for real-world engineering applications.
SEMI-DEFINITE PROGRAMMING TECHNIQUES FOR STRUCTURED QUADRATIC INVERSE EIGENVALUE PROBLEMS
LIN, MATTHEW M.; DONG, BO; CHU, MOODY T.
2014-01-01
In the past decade or so, semi-definite programming (SDP) has emerged as a powerful tool capable of handling a remarkably wide range of problems. This article describes an innovative application of SDP techniques to quadratic inverse eigenvalue problems (QIEPs). The notion of QIEPs is of fundamental importance because its ultimate goal of constructing or updating a vibration system from some observed or desirable dynamical behaviors while respecting some inherent feasibility constraints well suits many engineering applications. Thus far, however, QIEPs have remained challenging both theoretically and computationally due to the great variations of structural constraints that must be addressed. Of notable interest and significance are the uniformity and the simplicity in the SDP formulation that solves effectively many otherwise very difficult QIEPs. PMID:25392603
Yang, Zhirong; Oja, Erkki
2011-12-01
Multiplicative updates have been widely used in approximative nonnegative matrix factorization (NMF) optimization because they are convenient to deploy. Their convergence proof is usually based on the minimization of an auxiliary upper-bounding function, the construction of which however remains specific and only available for limited types of dissimilarity measures. Here we make significant progress in developing convergent multiplicative algorithms for NMF. First, we propose a general approach to derive the auxiliary function for a wide variety of NMF problems, as long as the approximation objective can be expressed as a finite sum of monomials with real exponents. Multiplicative algorithms with theoretical guarantee of monotonically decreasing objective function sequence can thus be obtained. The solutions of NMF based on most commonly used dissimilarity measures such as α- and β-divergence as well as many other more comprehensive divergences can be derived by the new unified principle. Second, our method is extended to a nonseparable case that includes e.g., γ-divergence and Rényi divergence. Third, we develop multiplicative algorithms for NMF using second-order approximative factorizations, in which each factorizing matrix may appear twice. Preliminary numerical experiments demonstrate that the multiplicative algorithms developed using the proposed procedure can achieve satisfactory Karush-Kuhn-Tucker optimality. We also demonstrate NMF problems where algorithms by the conventional method fail to guarantee descent at each iteration but those by our principle are immune to such violation.
Trigonometric quadratic B-spline subdomain Galerkin algorithm for the Burgers' equation
NASA Astrophysics Data System (ADS)
Ay, Buket; Dag, Idris; Gorgulu, Melis Zorsahin
2015-12-01
A variant of the subdomain Galerkin method has been set up to find numerical solutions of the Burgers' equation. Approximate function consists of the combination of the trigonometric B-splines. Integration of Burgers' equation has been achived by aid of the subdomain Galerkin method based on the trigonometric B-splines as an approximate functions. The resulting first order ordinary differential system has been converted into an iterative algebraic equation by use of the Crank-Nicolson method at successive two time levels. The suggested algorithm is tested on somewell-known problems for the Burgers' equation.
Enhanced algorithms for stochastic programming
Krishna, A.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 of 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.
User's guide for SOL/QPSOL: a Fortran package for quadratic programming
Gill, P.E.; Murray, W.; Saunders, M.A.; Wright, M.H.
1983-07-01
This report forms the user's guide for Version 3.1 of SOL/QPSOL, a set of Fortran subroutines designed to locate the minimum value of an arbitrary quadratic function subject to linear constraints and simple upper and lower bounds. If the quadratic function is convex, a global minimum is found; otherwise, a local minimum is found. The method used is most efficient when many constraints or bounds are active at the solution. QPSOL treats the Hessian and general constraints as dense matrices, and hence is not intended for large sparse problems. This document replaces the previous user's guide of June 1982.
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.
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
Cirugeda-Roldán, E M; Cuesta-Frau, D; Miró-Martínez, P; Oltra-Crespo, S; Vigil-Medina, L; Varela-Entrecanales, M
2014-05-01
This paper describes a new method to optimize the computation of the quadratic sample entropy (QSE) metric. The objective is to enhance its segmentation capability between pathological and healthy subjects for short and unevenly sampled biomedical records, like those obtained using ambulatory blood pressure monitoring (ABPM). In ABPM, blood pressure is measured every 20-30 min during 24h while patients undergo normal daily activities. ABPM is indicated for a number of applications such as white-coat, suspected, borderline, or masked hypertension. Hypertension is a very important clinical issue that can lead to serious health implications, and therefore its identification and characterization is of paramount importance. Nonlinear processing of signals by means of entropy calculation algorithms has been used in many medical applications to distinguish among signal classes. However, most of these methods do not perform well if the records are not long enough and/or not uniformly sampled. That is the case for ABPM records. These signals are extremely short and scattered with outliers or missing/resampled data. This is why ABPM Blood pressure signal screening using nonlinear methods is a quite unexplored field. We propose an additional stage for the computation of QSE independently of its parameter r and the input signal length. This enabled us to apply a segmentation process to ABPM records successfully. The experimental dataset consisted of 61 blood pressure data records of control and pathological subjects with only 52 samples per time series. The entropy estimation values obtained led to the segmentation of the two groups, while other standard nonlinear methods failed.
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…
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…
Genetic algorithms using SISAL parallel programming language
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.
NASA Astrophysics Data System (ADS)
Wu, Cheng-Wei
1997-11-01
Nuclear safeguards for Special Nuclear Materials is to protect the nuclear materials against malevolent use and to insure their peaceful usage. The nondestructive assay technique (NDA) offers an efficient and proliferation resistance method for nuclear safeguards technology. NDA techniques were investigated for multi-isotopic transuranic waste interrogation. This work was originally intended for the Integral Fast Reactor (IFR) under development at Argonne National Laboratory. One major feature of the IFR is its integral fuel cycle based on a pyrometallurgical process. More than 99% of transuranics produced in the fuel are returned to the makeup fuel and burned in the reactor. With the long-lived actinides removed from the waste stream, the waste produced will decay sufficiently in 300 years dropping below the cancer risk level of natural uranium ore and easing the perceived waste management problem. The feasibility of using nondestructive assay techniques for the IFR fuel cycle waste interrogation were studied. A special DNNDA experimental device was designed and analysis techniques were developed. The DNNDA technique uses the delayed neutrons emitted after the activation of a 14 MeV neutron source as the characteristic signature for each fissionable isotope. A tantalum/polyethylene filter was employed to enhance the discrimination between the fissile and the fissionable isotopes. Spontaneous fissions from 240Pu were also measured to assist the mass assay. A nonlinear overdetermined system was established based on the DNNDA measurements. An Iterative Quadratic Programming (IQP) method was applied to perform the estimates. The IQP method has several advantages over the linear least squares and Kalman filter methods, it has the flexibility of adding additional constraints, it has superlinear global convergence and it can be utilized for nonlinear problems. The results show that using the IQP method with the DNNDA technique is quite promising for multi-isotopic assay
KENO-VI: A Monte Carlo Criticality Program with generalized quadratic geometry
Hollenbach, D.F.; Petrie, L.M.; Landers, N.F.
1993-07-01
This report discusses KENO-VI which is a new version of the KENO monte Carlo Criticality Safety developed at Oak Ridge National Laboratory. The purpose of KENO-VI is to provide a criticality safety code similar to KENO-V.a that possesses a more general and flexible geometry package. KENO-VI constructs and processes geometry data as sets of quadratic equations. A lengthy set of simple, easy-to-use geometric functions, similar to those provided in KENO-V.a., and the ability to build more complex geometric shapes represented by sets of quadratic equations are the heart of the geometry package in KENO-VI. The code`s flexibility is increased by allowing intersecting geometry regions, hexagonal as well as cuboidal arrays, and the ability to specify an array boundary that intersects the array.
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.
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
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
Genetic algorithms as discovery programs
Hilliard, M.R.; Liepins, G.
1986-01-01
Genetic algorithms are mathematical counterparts to natural selection and gene recombination. As such, they have provided one of the few significant breakthroughs in machine learning. Used with appropriate reward functions and apportionment of credit, they have been successfully applied to gas pipeline operation, x-ray registration and mathematical optimization problems. This paper discusses the basics of genetic algorithms, describes a few successes, and reports on current progress at Oak Ridge National Laboratory in applications to set covering and simulated robots.
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)
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.
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.
Evolving a Nelder-Mead Algorithm for Optimization with Genetic Programming.
Fajfar, Iztok; Puhan, Janez; Bűrmen, Árpád
2016-01-25
We used genetic programming to evolve a direct search optimization algorithm, similar to that of the standard downhill simplex optimization method proposed by Nelder and Mead (1965). In the training process, we used several ten-dimensional quadratic functions with randomly displaced parameters and different randomly generated starting simplices. The genetically obtained optimization algorithm showed overall better performance than the original Nelder-Mead method on a standard set of test functions. We observed that many parts of the genetically produced algorithm were seldom or never executed, which allowed us to greatly simplify the algorithm by removing the redundant parts. The resulting algorithm turns out to be considerably simpler than the original Nelder-Mead method while still performing better than the original method.
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.
Quantum Algorithm for Linear Programming Problems
NASA Astrophysics Data System (ADS)
Joag, Pramod; Mehendale, Dhananjay
The quantum algorithm (PRL 103, 150502, 2009) solves a system of linear equations with exponential speedup over existing classical algorithms. We show that the above algorithm can be readily adopted in the iterative algorithms for solving linear programming (LP) problems. The first iterative algorithm that we suggest for LP problem follows from duality theory. It consists of finding nonnegative solution of the equation forduality condition; forconstraints imposed by the given primal problem and for constraints imposed by its corresponding dual problem. This problem is called the problem of nonnegative least squares, or simply the NNLS problem. We use a well known method for solving the problem of NNLS due to Lawson and Hanson. This algorithm essentially consists of solving in each iterative step a new system of linear equations . The other iterative algorithms that can be used are those based on interior point methods. The same technique can be adopted for solving network flow problems as these problems can be readily formulated as LP problems. The suggested quantum algorithm cansolveLP problems and Network Flow problems of very large size involving millions of variables.
NASA Astrophysics Data System (ADS)
Setiawan, Dedy K.; Anggraeni, Rina
2017-03-01
For optimization of electricity production, especially in the thermal power plant required analysis of input-output characteristics and operated optimally. Input-output characteristics will oversee the curve and detected the plant need for maintenance or not. Input-output characteristics can be calculated by quadratic least squares regression method. Operated load properly, making electricity production corresponding maximum desired load with lowest cost. Load calculations performed by dynamic genetic algorithm method. This method is applied to data from PT. Pembangkit Jawa Bali (PJB) Unit Pembangkit Gresik in July 2015 has saving 3.162,9147 kNm3 (kilo Normal cubic meters) fuel consumption and 22,773 fuel costs compared PJB. While applied to data December 2012 has saving 16.532,2189 liters fuel consumption and 84,654.79 fuel costs compared PT. PJB.
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)
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)
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. PMID:25950725
A Polynomial Primal-Dual Interior Point Method for Convex Programming with Quadratic Constraints
1993-04-01
Delft Un~versity of Technology, Delft, Netherlands. [3H Bazaraa , M. S., J. J. Jarvis, and H. D. Sh’rali. 199a Linar Pgrammning a" N]tdiwk Flow, John... Bazaraa , M. S., J. J. Jarvis, and H. D. Sherali. 1990. IjnW Programming and Network Flw, John Wiley and Sons, New York. [4] Charnes, A., and K. 0. Kortanek...often used in linear programming. For a detailed discussion of that 90 application, see Bazaraa . Jarvis. and Sherali(1990). Given J£, let T denote the
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.
An Algorithm for Linearly Constrained Nonlinear Programming Programming Problems.
1980-01-01
ALGORITHM FOR LINEARLY CONSTRAINED NONLINEAR PROGRAMMING PROBLEMS Mokhtar S. Bazaraa and Jamie J. Goode In this paper an algorithm for solving a linearly...distance pro- gramr.ing, as in the works of Bazaraa and Goode 12], and Wolfe [16 can be used for solving this problem. Special methods that take advantage of...34 Pacific Journal of Mathematics, Volume 16, pp. 1-3, 1966. 2. M. S. Bazaraa and J. j. Goode, "An Algorithm for Finding the Shortest Element of a
Automated programming for bioinformatics algorithm deployment.
Alterovitz, Gil; Jiwaji, Adnaan; Ramoni, Marco F
2008-02-01
Many bioinformatics solutions suffer from the lack of usable interface/platform from which results can be analyzed and visualized. Overcoming this hurdle would allow for more widespread dissemination of bioinformatics algorithms within the biological and medical communities. The algorithms should be accessible without extensive technical support or programming knowledge. Here, we propose a dynamic wizard platform that provides users with a Graphical User Interface (GUI) for most Java bioinformatics library toolkits. The application interface is generated in real-time based on the original source code. This platform lets developers focus on designing algorithms and biologists/physicians on testing hypotheses and analyzing results. The open source code can be downloaded from: http://bcl.med.harvard.edu/proteomics/proj/APBA/.
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
Factorising a Quadratic Expression with Geometric Insights
ERIC Educational Resources Information Center
Joarder, Anwar H.
2015-01-01
An algorithm is presented for factorising a quadratic expression to facilitate instruction and learning. It appeals to elementary geometry which may provide better insights to some students or teachers. There have been many methods for factorising a quadratic expression described in school text books. However, students often seem to struggle with…
Hu, Xiaolin; Wang, Jun
2008-12-01
This paper presents a novel recurrent neural network for solving a class of convex quadratic programming (QP) problems, in which the quadratic term in the objective function is the square of the Euclidean norm of the variable. This special structure leads to a set of simple optimality conditions for the problem, based on which the neural network model is formulated. Compared with existing neural networks for general convex QP, the new model is simpler in structure and easier to implement. The new model can be regarded as an improved version of the dual neural network in the literature. Based on the new model, a simple neural network capable of solving the k-winners-take-all ( k-WTA) problem is formulated. The stability and global convergence of the proposed neural network is proved rigorously and substantiated by simulation results.
Feasible and Accurate Algorithms for Covering Semidefinite Programs
NASA Astrophysics Data System (ADS)
Iyengar, Garud; Phillips, David J.; Stein, Cliff
In this paper we describe an algorithm to approximately solve a class of semidefinite programs called covering semidefinite programs. This class includes many semidefinite programs that arise in the context of developing algorithms for important optimization problems such as Undirected Sparsest Cut, wireless multicasting, and pattern classification. We give algorithms for covering SDPs whose dependence on ɛ is ɛ - 1. These algorithms, therefore, have a better dependence on ɛ than other combinatorial approaches, with a tradeoff of a somewhat worse dependence on the other parameters. For many reasons, including numerical stability and a variety of implementation concerns, the dependence on ɛ is critical, and the algorithms in this paper may be preferable to those of the previous work. Our algorithms exploit the structural similarity between packing and covering semidefinite programs and packing and covering linear programs.
Solving Integer Programming Problems by Using Artificial Bee Colony Algorithm
NASA Astrophysics Data System (ADS)
Akay, Bahriye; Karaboga, Dervis
This paper presents a study that applies the Artificial Bee Colony algorithm to integer programming problems and compares its performance with those of Particle Swarm Optimization algorithm variants and Branch and Bound technique presented to the literature. In order to cope with integer programming problems, in neighbour solution production unit, solutions are truncated to the nearest integer values. The experimental results show that Artificial Bee Colony algorithm can handle integer programming problems efficiently and Artificial Bee Colony algorithm can be considered to be very robust by the statistics calculated such as mean, median, standard deviation.
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.
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…
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…
Hu, Xiaolin; Zhang, Bo
2009-04-01
In this paper, a new recurrent neural network is proposed for solving convex quadratic programming (QP) problems. Compared with existing neural networks, the proposed one features global convergence property under weak conditions, low structural complexity, and no calculation of matrix inverse. It serves as a competitive alternative in the neural network family for solving linear or quadratic programming problems. In addition, it is found that by some variable substitution, the proposed network turns out to be an existing model for solving minimax problems. In this sense, it can be also viewed as a special case of the minimax neural network. Based on this scheme, a k-winners-take-all ( k-WTA) network with O(n) complexity is designed, which is characterized by simple structure, global convergence, and capability to deal with some ill cases. Numerical simulations are provided to validate the theoretical results obtained. More importantly, the network design method proposed in this paper has great potential to inspire other competitive inventions along the same line.
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.
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.
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.
Application of a Dynamic Programming Algorithm for Weapon Target Assignment
2016-02-01
dynamic programming algorithm for Weapon Target Assignment which, after more rigorous testing, could be used as a concept demonstrator and as an auxiliary...for specific use in maritime combat scenarios. After successful testing, the WTA algorithm could potentially be used as a training aid, a concept ... concept when considering optimal WTA solutions. The runtime for an algorithm can be expressed in terms of the order of the size of the input ‘n
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.
Earth Tide Algorithms for the OMNIS Computer Program System.
1986-04-01
This report presents five computer algorithms that jointly specify the gravitational action by which the tidal redistributions of the Earth’s masses...routine is a simplified version of the fourth and is provided for use during computer program verification. All computer algorithms express the tidal
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…
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…
Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows.
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.
Solving Classification Problems Using Genetic Programming Algorithms on GPUs
NASA Astrophysics Data System (ADS)
Cano, Alberto; Zafra, Amelia; Ventura, Sebastián
Genetic Programming is very efficient in problem solving compared to other proposals but its performance is very slow when the size of the data increases. This paper proposes a model for multi-threaded Genetic Programming classification evaluation using a NVIDIA CUDA GPUs programming model to parallelize the evaluation phase and reduce computational time. Three different well-known Genetic Programming classification algorithms are evaluated using the parallel evaluation model proposed. Experimental results using UCI Machine Learning data sets compare the performance of the three classification algorithms in single and multithreaded Java, C and CUDA GPU code. Results show that our proposal is much more efficient.
WHAT IS A SATISFACTORY QUADRATIC EQUATION SOLVER?
The report discusses precise requirements for a satisfactory computer program to solve a quadratic equation with floating - point coefficients. The principal practical problem is coping with overflow and underflow.
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.
Quantum algorithms for the ordered search problem via semidefinite programming
Childs, Andrew M.; Landahl, Andrew J.; Parrilo, Pablo A.
2007-03-15
One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log{sub 2} N queries to the list, a quantum computer can solve the problem using a constant factor fewer queries. However, the precise value of this constant is unknown. By characterizing a class of quantum query algorithms for the ordered search problem in terms of a semidefinite program, we find quantum algorithms for small instances of the ordered search problem. Extending these algorithms to arbitrarily large instances using recursion, we show that there is an exact quantum ordered search algorithm using 4 log{sub 605} N{approx_equal}0.433 log{sub 2} N queries, which improves upon the previously best known exact algorithm.
Stochastic Semidefinite Programming: Applications and Algorithms
2012-03-03
doi: 2011/09/07 13:38:21 13 TOTAL: 1 Number of Papers published in non peer-reviewed journals: Baha M. Alzalg and K. A. Ariyawansa, Stochastic...symmetric programming over integers. International Conference on Scientific Computing, Las Vegas, Nevada, July 18--21, 2011. Baha M. Alzalg. On recent...Proceeding publications (other than abstracts): PaperReceived Baha M. Alzalg, K. A. Ariyawansa. Stochastic mixed integer second-order cone programming
Grant, C W; Lenderman, J S; Gansemer, J D
2011-02-24
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 by Lawrence Livermore National Laboratory (LLNL) under IAA HSHQVT-07-X-00002 P00004 from the Department of Homeland Security (DHS).
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.
Simplified partial digest problem: enumerative and dynamic programming algorithms.
Blazewicz, Jacek; Burke, Edmund; Kasprzak, Marta; Kovalev, Alexandr; Kovalyov, Mikhail
2007-01-01
We study the Simplified Partial Digest Problem (SPDP), which is a mathematical model for a new simplified partial digest method of genome mapping. This method is easy for laboratory implementation and robust with respect to the experimental errors. SPDP is NP-hard in the strong sense. We present an $O(n2;n)$ time enumerative algorithm and an O(n(2q)) time dynamic programming algorithm for the error-free SPDP, where $n$ is the number of restriction sites and n is the number of distinct intersite distances. We also give examples of the problem, in which there are 2(n+2)/(3)-1 non-congruent solutions. These examples partially answer a question recently posed in the literature about the number of solutions of SPDP. We adapt our enumerative algorithm for handling SPDP with imprecise input data. Finally, we describe and discuss the results of the computer experiments with our algorithms.
An Approach to the Programming of Biased Regression Algorithms.
1978-11-01
Due to the near nonexistence of computer algorithms for calculating estimators and ancillary statistics that are needed for biased regression methodologies, many users of these methodologies are forced to write their own programs. Brute-force coding of such programs can result in a great waste of computer core and computing time, as well as inefficient and inaccurate computing techniques. This article proposes some guides to more efficient programming by taking advantage of mathematical similarities among several of the more popular biased regression estimators.
Quadratic spline subroutine package
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)
Decomposition algorithms for stochastic programming on a computational grid.
Linderoth, J.; Wright, S.; Mathematics and Computer Science; Axioma Inc.
2003-01-01
We describe algorithms for two-stage stochastic linear programming with recourse and their implementation on a grid computing platform. In particular, we examine serial and asynchronous versions of the L-shaped method and a trust-region method. The parallel platform of choice is the dynamic, heterogeneous, opportunistic platform provided by the Condor system. The algorithms are of master-worker type (with the workers being used to solve second-stage problems), and the MW runtime support library (which supports master-worker computations) is key to the implementation. Computational results are presented on large sample-average approximations of problems from the literature.
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.
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.
Mixed-Integer Nonconvex Quadratic Optimization Relaxations and Performance Analysis
2015-09-14
problem as a cardinality constrained quadratic program and study its computational complexity. Furthermore, we develop novel semi - definite relaxation (SDR...each application scenario, we first characterize the computational complexity of the joint optimization problem, and then propose novel semi - definite ...cardinality constrained quadratic programs ( QP ) and the low rank matrix completion problems. The project addresses a fundamental question regarding the
Mixed-Integer Nonconvex Quadratic Optimization Relaxations and Performance Analysis
2016-10-11
constrained quadratic programs, and the matrix completion problems with non-convex regularity. The project addresses a fundamental question how to...efficiently solve these problems, such as to find a provably high quality approximate solution or to fast find a local solution with probable structure ...applications in optimal and dynamic resource management, cardinality constrained quadratic programs, and the matrix completion problems with non
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]…
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)
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)
Dynamic programming algorithms as quantum circuits: symmetric function realization
NASA Astrophysics Data System (ADS)
Maslov, Dmitri A.
2004-08-01
The work starts with a general idea of how to realize a dynamic programming algorithm as a quantum circuit. This realization is not tied to a specific design model, technology or a class of dynamic algorithms, it shows an approach for such synthesis. As an illustration of the efficiency of this approach, the class of all multiple-output symmetric functions is realized in a dynamic programming algorithm manner as a reversible circuit of Toffoli type elements (NOT, CNOT, and Toffoli gates). The garbage and quantum cost (found based on Barenco et al. paper) of the presented implementation are calculated and compared to the costs of previously described reversible synthesis methods. The summary of results of this comparison is as follows. The quantum cost of the proposed method is less than the quantum cost of any other reported systematic approach. The garbage is usually lower, except for comparison with the synthesis methods, whose primary goal is synthesis with theoretically minimal garbage. The presented algorithm application to the symmetric function synthesis results in circuits suitable for quantum technology realizations.
Projected sequential quadratic programming methods
Heinkenschloss, M.
1994-12-31
In this talk we investigate projected SQP methods for the solution of min f(y, u). s.t. c(y, u) = 0 a {<=} u {<=} b. These methods combine the ideas of (reduced) SQP methods and projected Newton methods. The problem formulation and the design of these solution methods is motivated by optimal control problems. In this case y and u are the state and the control, respectively, and c(y, u) = 0 represents the state equation. Projected SQP methods use the simple projection onto the set {l_brace}a {<=} u {<=} b{r_brace} and maintain feasibility with respect to the inequality constraints. In each iteration only linearized constraint equations need to be solved. Global convergence of the method is enforced using a constrained merit function and an Armijo-like line search. We discuss global and local convergence properties of these methods, the identification of active indices, and implementation details for optimal control problems. Numerical examples of projected SQP methods applied to optimal control problems are presented.
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.
EVOLVING RETRIEVAL ALGORITHMS WITH A GENETIC PROGRAMMING SCHEME
J. THEILER; ET AL
1999-06-01
The retrieval of scene properties (surface temperature, material type, vegetation health, etc.) from remotely sensed data is the ultimate goal of many earth observing satellites. The algorithms that have been developed for these retrievals are informed by physical models of how the raw data were generated. This includes models of radiation as emitted and/or rejected by the scene, propagated through the atmosphere, collected by the optics, detected by the sensor, and digitized by the electronics. To some extent, the retrieval is the inverse of this ''forward'' modeling problem. But in contrast to this forward modeling, the practical task of making inferences about the original scene usually requires some ad hoc assumptions, good physical intuition, and a healthy dose of trial and error. The standard MTI data processing pipeline will employ algorithms developed with this traditional approach. But we will discuss some preliminary research on the use of a genetic programming scheme to ''evolve'' retrieval algorithms. Such a scheme cannot compete with the physical intuition of a remote sensing scientist, but it may be able to automate some of the trial and error. In this scenario, a training set is used, which consists of multispectral image data and the associated ''ground truth;'' that is, a registered map of the desired retrieval quantity. The genetic programming scheme attempts to combine a core set of image processing primitives to produce an IDL (Interactive Data Language) program which estimates this retrieval quantity from the raw data.
Quadratic Gabor correlation filters for object detection
NASA Astrophysics Data System (ADS)
Weber, David; Casasent, David P.
1996-10-01
We present a new class of quadratic filters that are capable of creating spherical, elliptical, hyperbolic and linear decision surfaces which result in better detection and classification capabilities than the linear decision surfaces obtained from correlation filters. Each filter comprises of a number of separately designed linear basis filters. These filters are linearly combined into several macro filters; the output from these macro filters are passed through a magnitude square operation and are then linearly combined using real weights to achieve the quadratic decision surface. This nonlinear fusion algorithm is called the extended piecewise quadratic neural network (E-PQNN). For detection, the creation of macro filters allows for a substantial computational saving by reducing the number of correlation operations required. In this work, we consider the use of Gabor basis filters; the Gabor filter parameters are separately optimized; the fusion parameters to combine the Gabor filter outputs are optimized using the conjugate gradient method; they and the nonlinear combination of filter outputs are included in our E-PQNN algorithm. We demonstrate methods for selecting the number of macro Gabor filters, the filter parameters and the linear and nonlinear combination coefficients. We prove that our simple E-PQNN architecture is able to generate arbitrary piecewise quadratic decision surfaces. We present preliminary results obtained for an IR vehicle detection problem.
Quadratic Gabor correlation filters for object detection
NASA Astrophysics Data System (ADS)
Weber, David; Casasent, David P.
1997-04-01
We present a new class of quadratic filters that are capable of creating spherical, elliptical, hyperbolic and linear decision surfaces which result in better detection and classification capabilities than the linear decision surfaces obtained from correlation filters. Each filter comprises of a number of separately designed linear basis filters. These filters are linearly combined into several macro filters; the output from these macro filters are passed through a magnitude square operation and are then linearly combined using real weights to achieve the quadratic decision surface. This non-linear fusion algorithm is called the extended piecewise quadratic neural network (E-PQNN). For detection, the creation of macro filters allows for a substantial computational saving by reducing the number of correlation operations required. In this work, we consider the use of Gabor basis filters; the Gabor filter parameters are separately optimized; the fusion parameters to combine the Gabor filter outputs are optimized using the conjugate gradient method; they and the non-linear combination of filter outputs are included in our E-PQNN algorithm. We demonstrate methods for selecting the number of macro Gabor filters, the filter parameters and the linear and non-linear combination coefficients. We prove that our simple E-PQNN architecture is able to generate arbitrary piecewise quadratic decision surfaces. We present preliminary results obtained for an IR vehicle detection problem.
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.
Performance characterization of the dynamic programming obstacle detection algorithm.
Gandhi, Tarak; Yang, Mau-Tsuen; Kasturi, Rangachar; Camps, Octavia I; Coraor, Lee D; McCandless, Jeffrey
2006-05-01
A computer vision-based system using images from an airborne aircraft can increase flight safety by aiding the pilot to detect obstacles in the flight path so as to avoid mid-air collisions. Such a system fits naturally with the development of an external vision system proposed by NASA for use in high-speed civil transport aircraft with limited cockpit visibility. The detection techniques should provide high detection probability for obstacles that can vary from subpixels to a few pixels in size, while maintaining a low false alarm probability in the presence of noise and severe background clutter. Furthermore, the detection algorithms must be able to report such obstacles in a timely fashion, imposing severe constraints on their execution time. For this purpose, we have implemented a number of algorithms to detect airborne obstacles using image sequences obtained from a camera mounted on an aircraft. This paper describes the methodology used for characterizing the performance of the dynamic programming obstacle detection algorithm and its special cases. The experimental results were obtained using several types of image sequences, with simulated and real backgrounds. The approximate performance of the algorithm is also theoretically derived using principles of statistical analysis in terms of the signal-to-noise ration (SNR) required for the probabilities of false alarms and misdetections to be lower than prespecified values. The theoretical and experimental performance are compared in terms of the required SNR.
Performance of a community detection algorithm based on semidefinite programming
NASA Astrophysics Data System (ADS)
Ricci-Tersenghi, Federico; Javanmard, Adel; Montanari, Andrea
2016-03-01
The problem of detecting communities in a graph is maybe one the most studied inference problems, given its simplicity and widespread diffusion among several disciplines. A very common benchmark for this problem is the stochastic block model or planted partition problem, where a phase transition takes place in the detection of the planted partition by changing the signal-to-noise ratio. Optimal algorithms for the detection exist which are based on spectral methods, but we show these are extremely sensible to slight modification in the generative model. Recently Javanmard, Montanari and Ricci-Tersenghi [1] have used statistical physics arguments, and numerical simulations to show that finding communities in the stochastic block model via semidefinite programming is quasi optimal. Further, the resulting semidefinite relaxation can be solved efficiently, and is very robust with respect to changes in the generative model. In this paper we study in detail several practical aspects of this new algorithm based on semidefinite programming for the detection of the planted partition. The algorithm turns out to be very fast, allowing the solution of problems with O(105) variables in few second on a laptop computer.
Testing the race model inequality: an algorithm and computer programs.
Ulrich, Rolf; Miller, Jeff; Schröter, Hannes
2007-05-01
In divided-attention tasks, responses are faster when two target stimuli are presented, and thus one is redundant, than when only a single target stimulus is presented. Raab (1962) suggested an account of this redundant-targets effect in terms of a race model in which the response to redundant target stimuli is initiated by the faster of two separate target detection processes. Such models make a prediction about the probability distributions of reaction times that is often called the race model inequality, and it is often of interest to test this prediction. In this article, we describe a precise algorithm that can be used to test the race model inequality and present MATLAB routines and a Pascal program that implement this algorithm.
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 dynamic programming algorithm for binning microbial community profiles.
Ruan, Quansong; Steele, Joshua A; Schwalbach, Michael S; Fuhrman, Jed A; Sun, Fengzhu
2006-06-15
A number of community profiling approaches have been widely used to study the microbial community composition and its variations in environmental ecology. Automated Ribosomal Intergenic Spacer Analysis (ARISA) is one such technique. ARISA has been used to study microbial communities using 16S-23S rRNA intergenic spacer length heterogeneity at different times and places. Owing to errors in sampling, random mutations in PCR amplification, and probably mostly variations in readings from the equipment used to analyze fragment sizes, the data read directly from the fragment analyzer should not be used for down stream statistical analysis. No optimal data preprocessing methods are available. A commonly used approach is to bin the reading lengths of the 16S-23S intergenic spacer. We have developed a dynamic programming algorithm based binning method for ARISA data analysis which minimizes the overall differences between replicates from the same sampling location and time. In a test example from an ocean time series sampling program, data preprocessing identified several outliers which upon re-examination were found to be because of systematic errors. Clustering analysis of the ARISA from different times based on the dynamic programming algorithm binned data revealed important features of the biodiversity of the microbial communities.
Quadratic image destriping. [GOES photograph enhancement
NASA Technical Reports Server (NTRS)
Dalton, J. T.; Winkert, G. E.
1979-01-01
An algorithm for removing second-order detector banding effects (striping) from digital imagery is described. This quadratic destriping method is basically an extension of a linear method to one higher degree. It provides a nonlinear alternative between the two-parameter linear correction and a multilinear histogram equalization approach. The application of the proposed technique to GOES visible imagery is discussed, and its effectiveness is compared to existing methods.
An Algorithm for Solving Interval Linear Programming Problems
1974-11-01
34regularized" a lä Chames -Cooper so that infeasibility is determined at optimal solution if that is the case. If I(x*(v)) - 0 then x*(v) is an... Chames and Cooper J3]) may be used to compute the new inverse. Theorem 2 The algorithm described above terminates in a finite number of steps...I J 19- REFERENCES 1) A. Ben-Israel and A. Chames , "An Explicit Solution of A Special Class of Linear Programming Problems", Operations
Dynamic Programming and Graph Algorithms in Computer Vision*
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
Dynamic programming and graph algorithms in computer vision.
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.
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.
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%.
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…
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…
Award DE-FG02-04ER52655 Final Technical Report: Interior Point Algorithms for Optimization Problems
O'Leary, Dianne P.; Tits, Andre
2014-04-03
Over the period of this award we developed an algorithmic framework for constraint reduction in linear programming (LP) and convex quadratic programming (QP), proved convergence of our algorithms, and applied them to a variety of applications, including entropy-based moment closure in gas dynamics.
Algorithms and programming tools for image processing on the MPP, introduction. Thesis
NASA Technical Reports Server (NTRS)
1985-01-01
The programming tools and parallel algorithms created for the Massively Parallel Processor (MPP) located at the NASA Goddard Space Center are discussed. A user-friendly environment for high level language parallel algorithm development was developed. The issues involved in implementing certain algorithms on the MPP were researched. The expected results were compared with the actual results.
Nalbantoğlu, Ö Ufuk
2014-01-01
Independent scoring of the aligned sections to determine the quality of biological sequence alignments enables recursive definitions of the overall alignment score. This property is not only biologically meaningful but it also provides the opportunity to find the optimal alignments using dynamic programming-based algorithms. Dynamic programming is an efficient problem solving technique for a class of problems that can be solved by dividing into overlapping subproblems. Pairwise sequence alignment techniques such as Needleman-Wunsch and Smith-Waterman algorithms are applications of dynamic programming on pairwise sequence alignment problems. These algorithms offer polynomial time and space solutions. In this chapter, we introduce the basic dynamic programming solutions for global, semi-global, and local alignment problems. Algorithmic improvements offering quadratic-time and linear-space programs and approximate solutions with space-reduction and seeding heuristics are discussed. We finally introduce the application of these techniques on multiple sequence alignment briefly.
Optimal Approximation of Quadratic Interval Functions
NASA Technical Reports Server (NTRS)
Koshelev, Misha; Taillibert, Patrick
1997-01-01
Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones.
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.
Quadratic Generalized Scale Invariance
NASA Astrophysics Data System (ADS)
Lovejoy, S.; Schertzer, D.; Addor, J. B.
Nearly twenty years ago, two of us argued that in order to account for the scaling strat- ification of the atmosphere, that an anisotropic "unified scaling model" of the atmo- sphere was required with elliptical dimension 23/9=2.555... "in between" the standard 3-D (small scale) and 2-D large scale model. This model was based on the formal- ism of generalized scale invariance (GSI). Physically, GSI is justified by arguing that various conserved fluxes (energy, buoyancy force variance etc.) should define the ap- propriate notion of scale. In a recent large scale satellite cloud image analysis, we directly confirmed this model by studying the isotropic (angle averaged) horizontal cloud statistics. Mathematically, GSI is based on a a group of scale changing opera- tors and their generators but to date, both analyses (primarily of cloud images) and nu- merical (multifractal) simulations, have been limited to the special case of linear GSI. This has shown that cloud texture can plausibly be associated with local linearizations. However realistic morphologies involve spatially avarying textures; the full non linear GSI is clearly necessary. In this talk, we first show that the observed angle averaged (multi)scaling statistics only give a realtively weak constraint on the nonlinear gner- ator: that the latter can be expressed by self-similar (isotropic) part, and a deviatoric part described (in two dimensions) by an arbitrary scalar potential which contains all the information about the cloud morphology. We then show (using a theorem due to Poincaré) how to reduce nonlinear GSI to linear GSI plus a nonlinear coordinate trans- formation numerically, using this to take multifractal GSI modelling to the next level of approximation: quadratic GSI. We show many examples of the coresponding simu- lations which include transitions from various morphologies (including cyclones) and we discuss the results in relation to satellite cloud images.
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…
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…
Equivalence of quadratic performance criteria.
NASA Technical Reports Server (NTRS)
Martin, C.
1973-01-01
Necessary and sufficient conditions are derived in terms of system parameters and quadratic weighting matrices for two quadratic cost functionals that are defined to be equivalent if they generate the same optimal control law. The derived conditions lie between the conditions of Tanaka and Asai (1971) and those of Kreindler and Hedrick (1970). Sufficient conditions for a vector valued function to attain an infimum are stated.
Block clustering based on difference of convex functions (DC) programming and DC algorithms.
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.
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…
SSME structural computer program development: BOPACE theoretical manual, addendum. [algorithms
NASA Technical Reports Server (NTRS)
1975-01-01
An algorithm developed and incorporated into BOPACE for improving the convergence and accuracy of the inelastic stress-strain calculations is discussed. The implementation of separation of strains in the residual-force iterative procedure is defined. The elastic-plastic quantities used in the strain-space algorithm are defined and compared with previous quantities.
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…
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.
Algorithms and programming tools for image processing on the MPP
NASA Technical Reports Server (NTRS)
Reeves, A. P.
1985-01-01
Topics addressed include: data mapping and rotational algorithms for the Massively Parallel Processor (MPP); Parallel Pascal language; documentation for the Parallel Pascal Development system; and a description of the Parallel Pascal language used on the MPP.
Exact solutions to quadratic gravity
NASA Astrophysics Data System (ADS)
Pravda, V.; Pravdová, A.; Podolský, J.; Švarc, R.
2017-04-01
Since all Einstein spacetimes are vacuum solutions to quadratic gravity in four dimensions, in this paper we study various aspects of non-Einstein vacuum solutions to this theory. Most such known solutions are of traceless Ricci and Petrov type N with a constant Ricci scalar. Thus we assume the Ricci scalar to be constant which leads to a substantial simplification of the field equations. We prove that a vacuum solution to quadratic gravity with traceless Ricci tensor of type N and aligned Weyl tensor of any Petrov type is necessarily a Kundt spacetime. This will considerably simplify the search for new non-Einstein solutions. Similarly, a vacuum solution to quadratic gravity with traceless Ricci type III and aligned Weyl tensor of Petrov type II or more special is again necessarily a Kundt spacetime. Then we study the general role of conformal transformations in constructing vacuum solutions to quadratic gravity. We find that such solutions can be obtained by solving one nonlinear partial differential equation for a conformal factor on any Einstein spacetime or, more generally, on any background with vanishing Bach tensor. In particular, we show that all geometries conformal to Kundt are either Kundt or Robinson-Trautman, and we provide some explicit Kundt and Robinson-Trautman solutions to quadratic gravity by solving the above mentioned equation on certain Kundt backgrounds.
A Stereo Dual-Channel Dynamic Programming Algorithm for UAV Image Stitching.
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.
Students' understanding of quadratic equations
NASA Astrophysics Data System (ADS)
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-05-01
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 students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.
Solving the Quadratic Capacitated Facilities Location Problem by Computer.
ERIC Educational Resources Information Center
Cote, Leon C.; Smith, Wayland P.
Several computer programs were developed to solve various versions of the quadratic capacitated facilities location problem. Matrices, which represent various business costs, are defined for the factors of sites, facilities, customers, commodities, and production units. The objective of the program is to find an optimization matrix for the lowest…
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.
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…
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.
Computer program for fast Karhunen Loeve transform algorithm
NASA Technical Reports Server (NTRS)
Jain, A. K.
1976-01-01
The fast KL transform algorithm was applied for data compression of a set of four ERTS multispectral images and its performance was compared with other techniques previously studied on the same image data. The performance criteria used here are mean square error and signal to noise ratio. The results obtained show a superior performance of the fast KL transform coding algorithm on the data set used with respect to the above stated perfomance criteria. A summary of the results is given in Chapter I and details of comparisons and discussion on conclusions are given in Chapter IV.
Some basic data structures and algorithms for chemical generic programming.
Zhang, Wei; Hou, Tingjun; Qiao, Xuebin; Xu, Xiaojie
2004-01-01
Here, we report a template library used for molecular operation, the Molecular Handling Template Library (MHTL). The library includes some generic data structures and generic algorithms, and the two parts are associated with each other by two concepts: Properties and Molecule. The concept Properties describes the interface to access objects' properties, and the concept Molecule describes the minimum requirement for a molecular class. Data structures include seven models of Properties, each using a different method to access properties, and two models of molecular classes. Algorithms include molecular file manipulation subroutines, SMARTS language interpreter and matcher functions, and molecular OpenGL rendering functions.
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...
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...
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.
APL simulation of Grover's algorithm
NASA Astrophysics Data System (ADS)
Lipovaca, Samir
2012-02-01
Grover's algorithm is a fast quantum search algorithm. Classically, to solve the search problem for a search space of size N we need approximately N operations. Grover's algorithm offers a quadratic speedup. Since present quantum computers are not robust enough for code writing and execution, to experiment with Grover's algorithm, we will simulate it using the APL programming language. The APL programming language is especially suited for this task. For example, to compute Walsh-Hadamard transformation matrix for N quantum states via a tensor product of N Hadamard matrices we need to iterate N-1 times only one line of the code. Initial study indicates the quantum mechanical amplitude of the solution is almost independent of the search space size and rapidly reaches 0.999 values with slight variations at higher decimal places.
Concretising Factorisation of Quadratic Expressions
ERIC Educational Resources Information Center
Hoong, Leong Yew; Fwe, Yap Sook; Yvonne, Teo Mei Lin; Subramaniam, Thilagam d/o; Zaini, Irni Karen Bte Mohd; Chiew, Quek Eng; Karen, Tan Kang Ling
2010-01-01
The way quadratic factorisation was usually taught to students in Bukit View Secondary was through the familiar "cross-method." However, some teachers felt that a significant number of students could not use the method effectively even after careful demonstration through repeated examples. In addition, many secondary mathematics teachers…
Improved dynamic-programming-based algorithms for segmentation of masses in mammograms
Dominguez, Alfonso Rojas; Nandi, Asoke K.
2007-11-15
In this paper, two new boundary tracing algorithms for segmentation of breast masses are presented. These new algorithms are based on the dynamic programming-based boundary tracing (DPBT) algorithm proposed in Timp and Karssemeijer, [S. Timp and N. Karssemeijer, Med. Phys. 31, 958-971 (2004)] The DPBT algorithm contains two main steps: (1) construction of a local cost function, and (2) application of dynamic programming to the selection of the optimal boundary based on the local cost function. The validity of some assumptions used in the design of the DPBT algorithm is tested in this paper using a set of 349 mammographic images. Based on the results of the tests, modifications to the computation of the local cost function have been designed and have resulted in the Improved-DPBT (IDPBT) algorithm. A procedure for the dynamic selection of the strength of the components of the local cost function is presented that makes these parameters independent of the image dataset. Incorporation of this dynamic selection procedure has produced another new algorithm which we have called ID{sup 2}PBT. Methods for the determination of some other parameters of the DPBT algorithm that were not covered in the original paper are presented as well. The merits of the new IDPBT and ID{sup 2}PBT algorithms are demonstrated experimentally by comparison against the DPBT algorithm. The segmentation results are evaluated with base on the area overlap measure and other segmentation metrics. Both of the new algorithms outperform the original DPBT; the improvements in the algorithms performance are more noticeable around the values of the segmentation metrics corresponding to the highest segmentation accuracy, i.e., the new algorithms produce more optimally segmented regions, rather than a pronounced increase in the average quality of all the segmented regions.
NASA Technical Reports Server (NTRS)
Dupnick, E.
1973-01-01
Description of the development and operation of a vehicle-scheduling algorithm which has applications to the NASA problem of assigning payloads to space delivery vehicles. The algorithm is based on a discrete, integer-valued, nonserial, dynamic-programming solution to the classical problem of developing resource utilization plans with limited resources. The algorithm places special emphasis on incorporating interpayload (precedence) relationships; maintaining optimal alternate schedule definitions (a unique feature of dynamic programming) in the event of contingencies (namely, resource inventory changes) without problem resolution; and, by using a special information storage technique, reducing the computational complexity of solving realistic problems.
NASA Astrophysics Data System (ADS)
Liu, Fang
2011-06-01
Image segmentation remains one of the major challenges in image analysis and computer vision. Fuzzy clustering, as a soft segmentation method, has been widely studied and successfully applied in mage clustering and segmentation. The fuzzy c-means (FCM) algorithm is the most popular method used in mage segmentation. However, most clustering algorithms such as the k-means and the FCM clustering algorithms search for the final clusters values based on the predetermined initial centers. The FCM clustering algorithms does not consider the space information of pixels and is sensitive to noise. In the paper, presents a new fuzzy c-means (FCM) algorithm with adaptive evolutionary programming that provides image clustering. The features of this algorithm are: 1) firstly, it need not predetermined initial centers. Evolutionary programming will help FCM search for better center and escape bad centers at local minima. Secondly, the spatial distance and the Euclidean distance is also considered in the FCM clustering. So this algorithm is more robust to the noises. Thirdly, the adaptive evolutionary programming is proposed. The mutation rule is adaptively changed with learning the useful knowledge in the evolving process. Experiment results shows that the new image segmentation algorithm is effective. It is providing robustness to noisy images.
Programming Deep Brain Stimulation for Parkinson's Disease: The Toronto Western Hospital Algorithms.
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.
Research on Knowledge Based Programming and Algorithm Design.
1981-08-01
algorithm design results will also appear in Steve Tappel’s doctoral disser- tation. Beverly Kedzierski , of the University of Southwestern Louisiana, is...Tom Pressburger, Susan Angebranndt, Beverly Kedzierski , Bernard Mont-Reynaud, and Daniel Chapiro Systems Control, Inc. This section presents an...ideas. The authors would like to thank them, as well as Beverly Kedzierski , Jerry Feldman and Sue Angebranndt for very helpful comments on content and
A program and data base for evaluating SMMR algorithms
NASA Technical Reports Server (NTRS)
1979-01-01
A program (PARAM) is described which enables a user to compare the values of meteorological parameters derived from data obtained by the scanning multichannel microwave radiometer (SMMR) instrument on NIMBUS 7 with surface observations made over the ocean. The input to this program is a data base, also described, which contains the surface observations and coincident SMMR data. The evaluation of meteorological parameters using SMMR data is done by a user supplied subroutine. Instruments are given for executing the program and writing the subroutine.
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.
Programming and Proving Correctness of the Scanning Algorithm with Backtrack,
1980-09-19
order for us to be able to use the method of intermittent asser- tions, we must generally look through each cycle of the program at the validity of any...lemmas that describe the effect of that cycle and imply ( generally in combination with other ler as) the validity of the main theorem which explains...in the set of candidates A are explicitly given (we are not aware of the order or how they are generated ), the preceding program for universal
Application and implementation of transient algorithms in computer programs
NASA Technical Reports Server (NTRS)
Benson, David J.
1989-01-01
A brief introduction is given to the nonlinear finite element programs developed at Lawrence Livermore National Laboratory. The four programs are DYNA3D and DYNA2D, which are explicit hydrocodes, and NIKE3D and NIKE2D, which are implicit programs. The main emphasis is on DYNA3D with asides about the other programs. During the past year several new features were added to DYNA3D, and major improvements were made in the computational efficiency of the shell and beam elements. Most of these new features and improvements will eventually make their way into the other programs. The emphasis in the computational mechanics effort was always, and continues to be, efficiency. To get the most out of the supercomputers, all Crays, the programs were vectorized where possible. Several of the more interesting capabilities of DYNA3D will be described and the impact on efficiency will be discussed. Some of the recent work on NIKE3D and NIKE2D will also be presented. In the belief that a single example is worth a thousand equations, the theory is skipped entirely and the examples presented.
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.
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.
Radar Rainfall Estimation using a Quadratic Z-R equation
NASA Astrophysics Data System (ADS)
Hall, Will; Rico-Ramirez, Miguel Angel; Kramer, Stefan
2016-04-01
The aim of this work is to test a method that enables the input of event based drop size distributions to alter a quadratic reflectivity (Z) to rainfall (R) equation that is limited by fixed upper and lower points. Results will be compared to the Marshall-Palmer Z-R relation outputs and validated by a network of gauges and a single polarisation weather radar located close to Essen, Germany. The time window over which the drop size distribution measurements will be collected is varied to note any effect on the generated quadratic Z-R relation. The new quadratic algorithm shows some distinct improvement over the Marshall-Palmer relationship through multiple events. The inclusion of a minimum number of Z-R points helped to decrease the associated error by defaulting back to the Marshall-Palmer equation if the limit was not reached. More research will be done to discover why the quadratic performs poorly in some events as there appears to be little correlation between number of drops or mean rainfall amount and the associated error. In some cases it seems the spatial distribution of the disdrometers has a significant effect as a large percentage of the rain bands pass to the north of two of the three disdrometers, frequently in a slightly north-easterly direction. However during widespread precipitation events the new algorithm works very well with reductions compared to the Marshall-Palmer relation.
Genetic-program-based data mining for hybrid decision-theoretic algorithms and theories
NASA Astrophysics Data System (ADS)
Smith, James F., III
2005-03-01
A genetic program (GP) based data mining (DM) procedure has been developed that automatically creates decision theoretic algorithms. A GP is an algorithm that uses the theory of evolution to automatically evolve other computer programs or mathematical expressions. The output of the GP is a computer program or mathematical expression that is optimal in the sense that it maximizes a fitness function. The decision theoretic algorithms created by the DM algorithm are typically designed for making real-time decisions about the behavior of systems. The database that is mined by the DM typically consists of many scenarios characterized by sensor output and labeled by experts as to the status of the scenario. The DM procedure will call a GP as a data mining function. The GP incorporates the database and expert"s rules into its fitness function to evolve an optimal decision theoretic algorithm. A decision theoretic algorithm created through this process will be discussed as well as validation efforts showing the utility of the decision theoretic algorithm created by the DM process. GP based data mining to determine equations related to scientific theories and automatic simplification methods based on computer algebra will also be discussed.
Realization of texture synthesis algorithm based on mixed programming via COM
NASA Astrophysics Data System (ADS)
Qin, Rizhao; Pu, Yuanyuan; Xu, Dan; Chen, Hong
2011-12-01
This paper analyzes the respective characteristics of VS2005 and MATLAB and their performances and introduces several methods of mixed programming. Then, the paper discusses the advantages and great applications of texture synthesis from sample (TSFS) and Image Quilting algorithm which is a typical algorithm of TSFS. Further, the paper realizes the Image Quilting algorithm by using mixed programming between VS2005 and MATLAB2007a via COM. We can perceive that mixed programming via COM that is used in developing texture synthesis program can not only speeds up its efficiency and reliability, but also strengthen the convenience of operation and visualization. Finally, the paper summarizes the relationship between texture synthesis parameters and synthesis effects from the experiment.
Realization of texture synthesis algorithm based on mixed programming via COM
NASA Astrophysics Data System (ADS)
Qin, Rizhao; Pu, Yuanyuan; Xu, Dan; Chen, Hong
2012-01-01
This paper analyzes the respective characteristics of VS2005 and MATLAB and their performances and introduces several methods of mixed programming. Then, the paper discusses the advantages and great applications of texture synthesis from sample (TSFS) and Image Quilting algorithm which is a typical algorithm of TSFS. Further, the paper realizes the Image Quilting algorithm by using mixed programming between VS2005 and MATLAB2007a via COM. We can perceive that mixed programming via COM that is used in developing texture synthesis program can not only speeds up its efficiency and reliability, but also strengthen the convenience of operation and visualization. Finally, the paper summarizes the relationship between texture synthesis parameters and synthesis effects from the experiment.
Approximate Graph Edit Distance in Quadratic Time.
Riesen, Kaspar; Ferrer, Miquel; Bunke, Horst
2015-09-14
Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.
A generalized speckle tracking algorithm for ultrasonic strain imaging using dynamic programming.
Jiang, Jingfeng; Hall, Timothy J
2009-11-01
This study developed an improved motion estimation algorithm for ultrasonic strain imaging that employs a dynamic programming technique. In this article, we model the motion estimation task as an optimization problem. Since tissue motion under external mechanical stimuli often should be reasonably continuous, a set of cost functions combining correlation and various levels of motion continuity constraint were used to regularize the motion estimation. To solve the optimization problem with a reasonable computational load, a dynamic programming technique that does not require iterations was used to obtain displacement vectors in integer precision. Then, a subsample estimation algorithm was used to calculate local displacements in fractional precision. Two implementation schemes were investigated with in vivo ultrasound echo data sets. We found that the proposed algorithm provides more accurate displacement estimates than our previous algorithm for in vivo clinical data. In particular, the new algorithm is capable of tracking motion in more complex anatomy and increases strain image consistency in a sequence of images. Preliminary results also suggest that a significantly longer sequence of high contrast strain images could be obtained with the new algorithm compared with the previous algorithm. The new algorithm can also tolerate larger motion discontinuities (e.g., cavity in an anthropomorphic uterine phantom).
A Generalized Speckle Tracking Algorithm for Ultrasonic Strain Imaging Using Dynamic Programming
Jiang, Jingfeng; Hall, Timothy J.
2009-01-01
This study developed an improved motion estimation algorithm for ultrasonic strain imaging that employs a dynamic programming technique. In this paper, we model the motion estimation task as an optimization problem. Since tissue motion under external mechanical stimuli often should be reasonably continuous, a set of cost functions combining correlation and various levels of motion continuity constraint were used to regularize the motion estimation. To solve the optimization problem with a reasonable computational load, a dynamic programming technique that does not require iterations was used to obtain displacement vectors in integer precision. Then, a sub-sample estimation algorithm was used to calculate local displacements in fractional precision. Two implementation schemes were investigated with in vivo ultrasound echo data sets. We found that the proposed algorithm provides more accurate displacement estimates than our previous algorithm for in vivo clinical data. In particular, the new algorithm is capable of tracking motion in more complex anatomy and increases strain image consistency in a sequence of images. Preliminary results also suggest that a significantly longer sequence of high contrast strain images could be obtained with the new algorithm compared to the previous algorithm. The new algorithm can also tolerate larger motion discontinuities (e.g. cavity in an anthropomorphic uterine phantom). PMID:19682789
Implementing embedded artificial intelligence rules within algorithmic programming languages
NASA Technical Reports Server (NTRS)
Feyock, Stefan
1988-01-01
Most integrations of artificial intelligence (AI) capabilities with non-AI (usually FORTRAN-based) application programs require the latter to execute separately to run as a subprogram or, at best, as a coroutine, of the AI system. In many cases, this organization is unacceptable; instead, the requirement is for an AI facility that runs in embedded mode; i.e., is called as subprogram by the application program. The design and implementation of a Prolog-based AI capability that can be invoked in embedded mode are described. The significance of this system is twofold: Provision of Prolog-based symbol-manipulation and deduction facilities makes a powerful symbolic reasoning mechanism available to applications programs written in non-AI languages. The power of the deductive and non-procedural descriptive capabilities of Prolog, which allow the user to describe the problem to be solved, rather than the solution, is to a large extent vitiated by the absence of the standard control structures provided by other languages. Embedding invocations of Prolog rule bases in programs written in non-AI languages makes it possible to put Prolog calls inside DO loops and similar control constructs. The resulting merger of non-AI and AI languages thus results in a symbiotic system in which the advantages of both programming systems are retained, and their deficiencies largely remedied.
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.
Orthogonality preserving infinite dimensional quadratic stochastic operators
Akın, Hasan; Mukhamedov, Farrukh
2015-09-18
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.
Cockwell, K Y; Giles, I G
1989-07-01
Two programs, MOTIF and PATTERN, that scan sequences for matches to user-defined motifs and patterns of motifs based on identity and set membership are described. The programs use a simple and logical notation to define motifs, and may be used either interactively or by using command line parameters (suitable for batch processing). The two programs described also incorporate a simple, yet reliable, algorithm that automatically detects in which of six possible formats the sequence entry is written.
Investigation of the Computational Utility of Geometric Programming Formulation and Algorithms.
1981-01-01
Programming (GP) is a body of theoretical and algorithmic results concerned with constrained optimization problems involving a class of nonlinear ...South Wales, Australia, 1974. 17. M. Ratner, L.S. Lasdon, and A. Jain, "Solving Geometric Programs using GRG : Results and Comparisons", J. Optimization ...computational tests in the study will be performed using the leading specialized GP and GGP codes as well as a selection of general nonlinear programing codes
Dynamic Programming Algorithms and Analyses for Nonserial Networks. Part I.
1983-01-01
Journal of Mathematical Analysis and Applications , Vol...Multistage Systems," Journal of Mathematical Analysis and Applications , Vol. 21, 1968, pp. 426-430. 4. Bellman, R.E.,A.O. Esogbue, and I. Nabeshima...the Secondary Optimization Problem in Nonserial Dynamic Programming," Journal of Mathematical Analysis and Applications , Vol. 27, 1969, pp. 565-574.
A Heuristic Ceiling Point Algorithm for General Integer Linear Programming
1988-11-01
narrowly satisfies the il h constraint: taking a unit step from x toward the ilh constraining hyperplane in a direction parallel to some coordinate...Business, Stanford Univesity , Stanford, Calif., December 1964. Hillier, F., "Efficient Heuristic Procedures for Integer Linear Programming with an Inte- rior
Guo, Liyong; Yan, Zhiqiang; Zheng, Xiliang; Hu, Liang; Yang, Yongliang; Wang, Jin
2014-07-01
In protein-ligand docking, an optimization algorithm is used to find the best binding pose of a ligand against a protein target. This algorithm plays a vital role in determining the docking accuracy. To evaluate the relative performance of different optimization algorithms and provide guidance for real applications, we performed a comparative study on six efficient optimization algorithms, containing two evolutionary algorithm (EA)-based optimizers (LGA, DockDE) and four particle swarm optimization (PSO)-based optimizers (SODock, varCPSO, varCPSO-ls, FIPSDock), which were implemented into the protein-ligand docking program AutoDock. We unified the objective functions by applying the same scoring function, and built a new fitness accuracy as the evaluation criterion that incorporates optimization accuracy, robustness, and efficiency. The varCPSO and varCPSO-ls algorithms show high efficiency with fast convergence speed. However, their accuracy is not optimal, as they cannot reach very low energies. SODock has the highest accuracy and robustness. In addition, SODock shows good performance in efficiency when optimizing drug-like ligands with less than ten rotatable bonds. FIPSDock shows excellent robustness and is close to SODock in accuracy and efficiency. In general, the four PSO-based algorithms show superior performance than the two EA-based algorithms, especially for highly flexible ligands. Our method can be regarded as a reference for the validation of new optimization algorithms in protein-ligand docking.
Algorithm for obtaining angular fluxes in a cell for the LUCKY and LUCKY_C multiprocessor programs
NASA Astrophysics Data System (ADS)
Moryakov, A. V.
2012-12-01
Basic formulas for solving the transport equation in a cell are presented. The algorithm has been implemented in the LUCKY and LUCKY_C programs. The advantages of the proposed algorithm are described.
Moryakov, A. V.
2012-12-15
Basic formulas for solving the transport equation in a cell are presented. The algorithm has been implemented in the LUCKY and LUCKY{sub C} programs. The advantages of the proposed algorithm are described.
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.
Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs
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.
The design of efficient dynamic programming and transfer matrix enumeration algorithms
NASA Astrophysics Data System (ADS)
Conway, Andrew R.
2017-09-01
Many algorithms have been developed for enumerating various combinatorial objects in time exponentially less than the number of objects. Two common classes of algorithms are dynamic programming and the transfer matrix method. This paper covers the design and implementation of such algorithms. A host of general techniques for improving efficiency are described. Three quite different example problems are used for detailed examples: 1324 pattern avoiding permutations, three-dimensional polycubes (using a novel approach), and two-dimensional directed animals. Other examples from the literature are used when appropriate to describe applicability of various techniques, but the paper does not attempt to survey all applications.
NASA Astrophysics Data System (ADS)
Konno, Hiroshi; Gotoh, Jun-Ya; Uno, Takeaki; Yuki, Atsushi
2002-09-01
We will propose a new cutting plane algorithm for solving a class of semi-definite programming problems (SDP) with a small number of variables and a large number of constraints. Problems of this type appear when we try to classify a large number of multi-dimensional data into two groups by a hyper-ellipsoidal surface. Among such examples are cancer diagnosis, failure discrimination of enterprises. Also, a certain class of option pricing problems can be formulated as this type of problem. We will show that the cutting plane algorithm is much more efficient than the standard interior point algorithms for solving SDP.
Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs
Gade, Dinakar; Hackebeil, Gabriel; Ryan, Sarah M.; Watson, Jean -Paul; Wets, Roger J.-B.; Woodruff, David L.
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.
Properties of surjective real quadratic maps
NASA Astrophysics Data System (ADS)
Arutyunov, A. V.; Zhukovskiy, S. E.
2016-09-01
The properties of surjective real quadratic maps are investigated. Sufficient conditions for the property of surjectivity to be stable under various perturbations are obtained. Examples of surjective quadratic maps whose surjectivity breaks down after an arbitrarily small perturbation are constructed. Sufficient conditions for quadratic maps to have nontrivial zeros are obtained. For a smooth even map in a neighbourhood of the origin an inverse function theorem in terms of the degree of the corresponding quadratic map is obtained. A canonical form of surjective quadratic maps from {R}^3 to {R}^3 is constructed. Bibliography: 27 titles.
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.
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.
A Projection Neural Network for Constrained Quadratic Minimax Optimization.
Liu, Qingshan; Wang, Jun
2015-11-01
This paper presents a projection neural network described by a dynamic system for solving constrained quadratic minimax programming problems. Sufficient conditions based on a linear matrix inequality are provided for global convergence of the proposed neural network. Compared with some of the existing neural networks for quadratic minimax optimization, the proposed neural network in this paper is capable of solving more general constrained quadratic minimax optimization problems, and the designed neural network does not include any parameter. Moreover, the neural network has lower model complexities, the number of state variables of which is equal to that of the dimension of the optimization problems. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network.
The generalized quadratic knapsack problem. A neuronal network approach.
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.
AI-BL1.0: a program for automatic on-line beamline optimization using the evolutionary algorithm.
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.
Programming Deep Brain Stimulation for Tremor and Dystonia: The Toronto Western Hospital Algorithms.
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.
Linear quadratic regulator for laser beam shaping
NASA Astrophysics Data System (ADS)
Escárate, Pedro; Agüero, Juan C.; Zúñiga, Sebastián; Castro, Mario; Garcés, Javier
2017-07-01
The performance of an adaptive optics system depends on multiple factors, including the quality of the laser beam before being projected to the mesosphere. In general, cumbersome procedures are required to optimize the laser beam in terms of amplitude and phase. However, aberrations produced by the optics of the laser beam system are still detected during the operations due to, for example, uncertainty in the utilized models. In this paper we propose the use of feedback to overcome the presence of model uncertainty and disturbances. In particular we use a Linear Quadratic Regulator (LQR) for closed loop laser beam shaping using a setup of two deformable mirrors. The proposed method is studied and simulated to provide an automatic optimization of the Amplitude of the laser beam. The performance of the LQR control algorithm is evaluated via numerical simulations using the root mean square error (RMSE). The results show an effective amplitude correction of the laser system aberrations after 20 iterations of the algorithm, a RMSE less than 0.7 was obtained, with about 140 actuators per mirror and a separation of z=3 [m] among the mirrors.
Chimeric alignment by dynamic programming: Algorithm and biological uses
Komatsoulis, G.A.; Waterman, M.S.
1997-12-01
A new nearest-neighbor method for detecting chimeric 16S rRNA artifacts generated during PCR amplification from mixed populations has been developed. The method uses dynamic programming to generate an optimal chimeric alignment, defined as the highest scoring alignment between a query and a concatenation of a 5{prime} and a 3{prime} segment from two separate entries from a database of related sequences. Chimeras are detected by studying the scores and form of the chimeric and global sequence alignments. The chimeric alignment method was found to be marginally more effective than k-tuple based nearest-neighbor methods in simulation studies, but its most effective use is in concert with k-tuple methods. 15 refs., 3 figs., 1 tab.
Asymptotic Normality of Quadratic Estimators.
Robins, James; Li, Lingling; Tchetgen, Eric; van der Vaart, Aad
2016-12-01
We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations.
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.
A parallel dynamic programming algorithm for multi-reservoir system optimization
NASA Astrophysics Data System (ADS)
Li, Xiang; Wei, Jiahua; Li, Tiejian; Wang, Guangqian; Yeh, William W.-G.
2014-05-01
This paper develops a parallel dynamic programming algorithm to optimize the joint operation of a multi-reservoir system. First, a multi-dimensional dynamic programming (DP) model is formulated for a multi-reservoir system. Second, the DP algorithm is parallelized using a peer-to-peer parallel paradigm. The parallelization is based on the distributed memory architecture and the message passing interface (MPI) protocol. We consider both the distributed computing and distributed computer memory in the parallelization. The parallel paradigm aims at reducing the computation time as well as alleviating the computer memory requirement associated with running a multi-dimensional DP model. Next, we test the parallel DP algorithm on the classic, benchmark four-reservoir problem on a high-performance computing (HPC) system with up to 350 cores. Results indicate that the parallel DP algorithm exhibits good performance in parallel efficiency; the parallel DP algorithm is scalable and will not be restricted by the number of cores. Finally, the parallel DP algorithm is applied to a real-world, five-reservoir system in China. The results demonstrate the parallel efficiency and practical utility of the proposed methodology.
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.
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.
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.
Quadratic Dynamical Systems and Algebras
NASA Astrophysics Data System (ADS)
Kinyon, M. K.; Sagle, A. A.
1995-03-01
Quadratic dynamical systems come from differential or discrete systems of the form Ẋ = Q(X) or X(k+1)=Q(X(k)), where Q:Rn→Rn is homogeneous of degree 2; i.e., Q(αX) = α2Q(X) for all α∈R, X∈Rn. Defining a bilinear mapping β:Rn × Rn→Rn by β(X, Y) ≔ {1}/{2}[Q(X+Y)-Q(X)-Q(Y)], we view XY≡β(X, Y) as a multiplication, and thus consider A=(Rn, β) to be a commutative, nonassociative algebra. The quadratic systems are then studied with the general theme that the structure of the algebras helps determine the behavior of the solutions. For example, semisimple algebras give a decoupling of the original system into systems occurring in simple algebras, and solvable algebras give solutions to differential systems via linear differential equations; the general three-dimensional example of the latter phenomenon is described. There are many classical examples and the scope of quadratic systems is large; every polynomial system can be embedded into a higher dimensional quadratic system such that solutions of the original system are obtained from the quadratic system. For differential systems, nilpotents of index 2 (N2=0) are equilibria and idempotents (E2=E) give ray solutions. The origin is never asymptotically stable, and the existence of nonzero idempotents implies that the origin is actually unstable. Nonzero equilibria are not hyperbolic, but can be studied by standard algebra techniques using nondegenerate bilinear forms as Lyapunov functions. Periodic orbits lie on "cones." They cannot occur in dimension 2 or in power-associative algebras. No periodic orbit can be an attractor but "limit cycles" (invariant cones) can exist. Automorphisms of the algebra A leave equilibria, periodic orbits, and domains of attraction invariant. Also, explicit solutions can be given by the action of automorphisms on an initial point; the general three-dimensional example of this is described. Thus if there are sufficient automorphisms, Hilbert‧s sixteenth problem in R3 has
A Survey of Successful Evaluations of Program Visualization and Algorithm Animation Systems
ERIC Educational Resources Information Center
Urquiza-Fuentes, Jaime; Velazquez-Iturbide, J. Angel
2009-01-01
This article reviews successful educational experiences in using program and algorithm visualizations (PAVs). First, we survey a total of 18 PAV systems that were subject to 33 evaluations. We found that half of the systems have only been tested for usability, and those were shallow inspections. The rest were evaluated with respect to their…
A Survey of Successful Evaluations of Program Visualization and Algorithm Animation Systems
ERIC Educational Resources Information Center
Urquiza-Fuentes, Jaime; Velazquez-Iturbide, J. Angel
2009-01-01
This article reviews successful educational experiences in using program and algorithm visualizations (PAVs). First, we survey a total of 18 PAV systems that were subject to 33 evaluations. We found that half of the systems have only been tested for usability, and those were shallow inspections. The rest were evaluated with respect to their…
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.
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.
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.
Single-photon quadratic optomechanics
Liao, Jie-Qiao; Nori, Franco
2014-01-01
We present exact analytical solutions to study the coherent interaction between a single photon and the mechanical motion of a membrane in quadratic optomechanics. We consider single-photon emission and scattering when the photon is initially inside the cavity and in the fields outside the cavity, respectively. Using our solutions, we calculate the single-photon emission and scattering spectra, and find relations between the spectral features and the system's inherent parameters, such as: the optomechanical coupling strength, the mechanical frequency, and the cavity-field decay rate. In particular, we clarify the conditions for the phonon sidebands to be visible. We also study the photon-phonon entanglement for the long-time emission and scattering states. The linear entropy is employed to characterize this entanglement by treating it as a bipartite one between a single mode of phonons and a single photon. PMID:25200128
The Random Quadratic Assignment Problem
NASA Astrophysics Data System (ADS)
Paul, Gerald; Shao, Jia; Stanley, H. Eugene
2011-11-01
The quadratic assignment problem, QAP, is one of the most difficult of all combinatorial optimization problems. Here, we use an abbreviated application of the statistical mechanics replica method to study the asymptotic behavior of instances in which the entries of at least one of the two matrices that specify the problem are chosen from a random distribution P. Surprisingly, the QAP has not been studied before using the replica method despite the fact that the QAP was first proposed over 50 years ago and the replica method was developed over 30 years ago. We find simple forms for C min and C max , the costs of the minimal and maximum solutions respectively. Notable features of our results are the symmetry of the results for C min and C max and their dependence on P only through its mean and standard deviation, independent of the details of P.
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 Dynamic Programming Algorithm For (1,2)-Exemplar Breakpoint Distance.
Wei, Zhexue; Zhu, Daming; Wang, Lusheng
2015-07-01
The exemplar breakpoint distance problem is motivated by finding conserved sets of genes between two genomes. It asks to find respective exemplars in two genomes to minimize the breakpoint distance between them. If one genome has no repeated gene (called trivial genome) and the other has genes repeating at most twice, it is referred to as the (1, 2)-exemplar breakpoint distance problem, EBD(1, 2) for short. Little has been done on algorithm design for this problem by now. In this article, we propose a parameter to describe the maximum physical span between two copies of a gene in a genome, and based on it, design a fixed-parameter algorithm for EBD(1, 2). Using a dynamic programming approach, our algorithm can take O(4(s)n(2)) time and O(4(s)n) space to solve an EBD(1, 2) instance that has two genomes of n genes where the second genome has each two copies of a gene spanning at most s copies of the genes. Our algorithm can also be used to compute the maximum adjacencies between two genomes. The algorithm has been implemented in C++. Simulations on randomly generated data have verified the effectiveness of our algorithm. The software package is available from the authors.
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.
Applying new optimization algorithms to more predictive control
Wright, S.J.
1996-03-01
The connections between optimization and control theory have been explored by many researchers and optimization algorithms have been applied with success to optimal control. The rapid pace of developments in model predictive control has given rise to a host of new problems to which optimization has yet to be applied. Concurrently, developments in optimization, and especially in interior-point methods, have produced a new set of algorithms that may be especially helpful in this context. In this paper, we reexamine the relatively simple problem of control of linear processes subject to quadratic objectives and general linear constraints. We show how new algorithms for quadratic programming can be applied efficiently to this problem. The approach extends to several more general problems in straightforward ways.
Optimization with quadratic support functions in nonconvex smooth optimization
NASA Astrophysics Data System (ADS)
Khamisov, O. V.
2016-10-01
Problem of global minimization of twice continuously differentiable function with Lipschitz second derivatives over a polytope is considered. We suggest a branch and bound method with polytopes as partition elements. Due to the Lipschitz property of the objective function we can construct a quadratic support minorant at each point of the feasible set. Global minimum of of this minorant provides a lower bound of the objective over given partition subset. The main advantage of the suggested method consists in the following. First quadratic minorants usually are nonconvex and we have to solve auxiliary global optimization problem. This problem is reduced to a mixed 0-1 linear programming problem and can be solved by an advanced 0-1 solver. Then we show that the quadratic minorants are getting convex as soon as partition elements are getting smaller in diameter. Hence, at the final steps of the branch and bound method we solve convex auxiliary quadratic problems. Therefore, the method accelerates when we are close to the global minimum of the initial problem.
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…
On Quantization of Quadratic Poisson Structures
NASA Astrophysics Data System (ADS)
Manchon, D.; Masmoudi, M.; Roux, A.
Any classical r-matrix on the Lie algebra of linear operators on a real vector space V gives rise to a quadratic Poisson structure on V which admits a deformation quantization stemming from the construction of V. Drinfel'd [Dr], [Gr]. We exhibit in this article an example of quadratic Poisson structure which does not arise this way.
2011-06-01
minimax and min-max-min problems and their efficiency. Phd thesis , Naval Postgraduate School, Monterey, California, 2011. [25] J.H. Jung, D.P. O’Leary, and...California, USA. Corresponding author, email: joroyset@nps.edu ‡Principal Analyst, Operations Analysis and Simulation, Defence Science and Technology ...quadratic programming (SQP) algorithm in [11] and the Pshenichnyi-Pironneau-Polak ( PPP ) algorithm [8, Section 2.4] for solving finite minimax problems
Solving the Quadratic Assignment Problems using Parallel ACO with Symmetric Multi Processing
NASA Astrophysics Data System (ADS)
Tsutsui, Shigeyoshi
In this paper, we propose several types of parallel ant colony optimization algorithms with symmetric multi processing for solving the quadratic assignment problem (QAP). These models include the master-slave models and the island models. As a base ant colony optimization algorithm, we used the cunning Ant System (cAS) which showed promising performance our in previous studies. We evaluated each parallel algorithm with a condition that the run time for each parallel algorithm and the base sequential algorithm are the same. The results suggest that using the master-slave model with increased iteration of ant colony optimization algorithms is promising in solving quadratic assignment problems for real or real-like instances.
Class Notes: Programming Parallel Algorithms CS 15-840B (Fall 1992)
1993-02-01
840: Programming Parallel Algorithms Lecture #15 Scribe: Bob Wheeler Thursday, 6 Nov 92 Overview * Connected components (continued). * Minimum spanning...Sriram Sethuraman Singular value decomposition Ken Tew EEG analysis Eric Thayer Speech recognition Xuemei Wang & Bob Wheeler Matrix operations Matt...Computing, 14(4):862-874, 1985. [33] L. W. Tucker, C. R. Feynman , and D. M. Fritzsche. Object recognition using the Connection Machine. Proceedings CVPR
An Accelerated Covering Relaxation Algorithm for Solving 0-1 Positive Polynomial Programs.
1980-06-01
accelerated algorithm is a cutting -plane method in which each relaxed problem is a set covering problem and the cutting planes are linear covering constraints...However by contrast with other cutting -plane methods in integer programming (including our original method), we do not solve the relaxed problems to...optimality after the introduction of the cutting -plane constraints. Rather, we first solve each relaxed set-covering problem heuristically and only if
OpenACC programs of the Swendsen-Wang multi-cluster spin flip algorithm
NASA Astrophysics Data System (ADS)
Komura, Yukihiro
2015-12-01
We present sample OpenACC programs of the Swendsen-Wang multi-cluster spin flip algorithm. OpenACC is a directive-based programming model for accelerators without requiring modification to the underlying CPU code itself. In this paper, we deal with the classical spin models as with the sample CUDA programs (Komura and Okabe, 2014), that is, two-dimensional (2D) Ising model, three-dimensional (3D) Ising model, 2D Potts model, 3D Potts model, 2D XY model and 3D XY model. We explain the details of sample OpenACC programs and compare the performance of the present OpenACC implementations with that of the CUDA implementations for the 2D and 3D Ising models and the 2D and 3D XY models.
ALGORITHMS AND PROGRAMS FOR STRONG GRAVITATIONAL LENSING IN KERR SPACE-TIME INCLUDING POLARIZATION
Chen, Bin; Maddumage, Prasad; Kantowski, Ronald; Dai, Xinyu; Baron, Eddie
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 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.
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.
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.
Solving the quadratic assignment problem with clues from nature.
Nissen, V
1994-01-01
This paper describes a new evolutionary approach to solving quadratic assignment problems. The proposed technique is based loosely on a class of search and optimization algorithms known as evolution strategies (ES). These methods are inspired by the mechanics of biological evolution and have been applied successfully to a variety of difficult problems, particularly in continuous optimization. The combinatorial variant of ES presented here performs very well on the given test problems as compared with the standard 2-Opt heuristic and results with simulated annealing and tabu search. Extensions for practical applications in factory layout are described.
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.
NASA Technical Reports Server (NTRS)
Ng, Hok K.; Grabbe, Shon; Mukherjee, Avijit
2010-01-01
The optimization of traffic flows in congested airspace with varying convective weather is a challenging problem. One approach is to generate shortest routes between origins and destinations while meeting airspace capacity constraint in the presence of uncertainties, such as weather and airspace demand. This study focuses on development of an optimal flight path search algorithm that optimizes national airspace system throughput and efficiency in the presence of uncertainties. The algorithm is based on dynamic programming and utilizes the predicted probability that an aircraft will deviate around convective weather. It is shown that the running time of the algorithm increases linearly with the total number of links between all stages. The optimal routes minimize a combination of fuel cost and expected cost of route deviation due to convective weather. They are considered as alternatives to the set of coded departure routes which are predefined by FAA to reroute pre-departure flights around weather or air traffic constraints. A formula, which calculates predicted probability of deviation from a given flight path, is also derived. The predicted probability of deviation is calculated for all path candidates. Routes with the best probability are selected as optimal. The predicted probability of deviation serves as a computable measure of reliability in pre-departure rerouting. The algorithm can also be extended to automatically adjust its design parameters to satisfy the desired level of reliability.
A depth-first search algorithm to compute elementary flux modes by linear programming
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
A depth-first search algorithm to compute elementary flux modes by linear programming.
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.
NASA Astrophysics Data System (ADS)
Jordi, Antoni; Georgas, Nickitas; Blumberg, Alan
2017-05-01
This paper presents a new parallel domain decomposition algorithm based on integer linear programming (ILP), a mathematical optimization method. To minimize the computation time of coastal ocean circulation models, the ILP decomposition algorithm divides the global domain in local domains with balanced work load according to the number of processors and avoids computations over as many as land grid cells as possible. In addition, it maintains the use of logically rectangular local domains and achieves the exact same results as traditional domain decomposition algorithms (such as Cartesian decomposition). However, the ILP decomposition algorithm may not converge to an exact solution for relatively large domains. To overcome this problem, we developed two ILP decomposition formulations. The first one (complete formulation) has no additional restriction, although it is impractical for large global domains. The second one (feasible) imposes local domains with the same dimensions and looks for the feasibility of such decomposition, which allows much larger global domains. Parallel performance of both ILP formulations is compared to a base Cartesian decomposition by simulating two cases with the newly created parallel version of the Stevens Institute of Technology's Estuarine and Coastal Ocean Model (sECOM). Simulations with the ILP formulations run always faster than the ones with the base decomposition, and the complete formulation is better than the feasible one when it is applicable. In addition, parallel efficiency with the ILP decomposition may be greater than one.
NASA Technical Reports Server (NTRS)
Ng, Hok K.; Grabbe, Shon; Mukherjee, Avijit
2010-01-01
The optimization of traffic flows in congested airspace with varying convective weather is a challenging problem. One approach is to generate shortest routes between origins and destinations while meeting airspace capacity constraint in the presence of uncertainties, such as weather and airspace demand. This study focuses on development of an optimal flight path search algorithm that optimizes national airspace system throughput and efficiency in the presence of uncertainties. The algorithm is based on dynamic programming and utilizes the predicted probability that an aircraft will deviate around convective weather. It is shown that the running time of the algorithm increases linearly with the total number of links between all stages. The optimal routes minimize a combination of fuel cost and expected cost of route deviation due to convective weather. They are considered as alternatives to the set of coded departure routes which are predefined by FAA to reroute pre-departure flights around weather or air traffic constraints. A formula, which calculates predicted probability of deviation from a given flight path, is also derived. The predicted probability of deviation is calculated for all path candidates. Routes with the best probability are selected as optimal. The predicted probability of deviation serves as a computable measure of reliability in pre-departure rerouting. The algorithm can also be extended to automatically adjust its design parameters to satisfy the desired level of reliability.
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.
Wang, Jin; Fung, Richard Y K
2015-01-01
A well-developed appointment system can help increase the utilization of medical facilities in an outpatient department. This paper outlines the development of an appointment system that can make an outpatient department work more efficiently and improve patient satisfaction level. A Markov decision process model is proposed to schedule sequential appointments with the consideration of patient preferences in order to maximize the patient satisfaction level. Adaptive dynamic programming algorithms are developed to avoid the curse of dimensionality. These algorithms can dynamically capture patient preferences, update the value of being a state, and thus improve the appointment decisions. Experiments were conducted to investigate the performance of the algorithms. The convergence behaviors under different settings, including the number of iterations needed for convergence and the accuracy of results, were examined. Bias-adjusted Kalman filter step-sizes were found to lead to the best convergence behavior, which stabilized within 5000 iterations. As for the effects of exploration and exploitation, it resulted in the best convergence behavior when the probability of taking a myopically optimal action equaled 0.9. The performance of value function approximation algorithm was greatly affected by the combination of basis functions. Under different combinations, errors varied from 2.7% to 8.3%. More preferences resulted in faster convergence, but required longer computation time. System parameters are adaptively updated as bookings are confirmed. The proposed appointment scheduling system could certainly contribute to better patient satisfaction level during the booking periods. Copyright © 2014 Elsevier B.V. All rights reserved.
An interior point method for semidefinite programming
Helmberg, C.; Rendl, F.; Vanderbei, R.J.; Wolkowicz, H.
1994-12-31
Semidefinite programming is of rising importance in min-max eigenvalue problems and relaxations for NP-complete problems. We present a new interior point algorithm based on the linearization XZ {minus} {mu}I which is very successful in linear programming. We show that, although the original {Delta}X is not symmetric, by using the symmetric part of {Delta}X convergence can be guaranteed. The algorithm works for arbitrary combinations of equalities and inequalities and, contrary to linearizations such as XZ + ZX {minus} {mu}I, does not make use of Kronecker products. In numerical experiments the algorithm exhibits fast quadratic convergence.
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.
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.)
A Special Circle for Quadratic Equations.
ERIC Educational Resources Information Center
Patterson, Walter M.; Lubecke, Andre M.
1991-01-01
Discussed is a method of approximating the roots of a quadratic that allows the discovery of relationships between parabolas and circles and between the use of geometry and algebra. Included are the procedure and justification of the method. (KR)
Linear quadratic optimal control for symmetric systems
NASA Technical Reports Server (NTRS)
Lewis, J. H.; Martin, C. F.
1983-01-01
Special symmetries are present in many control problems. This paper addresses the problem of determining linear-quadratic optimal control problems whose solutions preserve the symmetry of the initial linear control system.
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.)
Gravitational energy in quadratic-curvature gravities.
Deser, S; Tekin, Bayram
2002-09-02
We define energy (E) and compute its values for gravitational systems involving terms quadratic in curvature. There are significant differences, both conceptually and concretely, from Einstein theory. For D=4, all purely quadratic models admit constant curvature vacua with arbitrary Lambda, and E is the "cosmological" Abbott-Deser (AD) expression; instead, E always vanishes in flat, Lambda=0, background. For combined Einstein-quadratic curvature systems without explicit Lambda-term vacuum must be flat space, and E has the usual Arnowitt-Deser-Misner form. A Lambda-term forces unique de Sitter vacuum, with E the sum of contributions from Einstein and quadratic parts to the AD form. We also discuss the effects on energy definition of higher curvature terms and of higher dimension.
Brown, C.
1990-04-11
This contract developed and disseminated papers, ideas, algorithms, analysis, software, applications, and implementations for parallel programming environments for computer vision and for vision applications. The work has been widely reported and highly influential. The most significant work centered on the Butterfly Parallel Processor, the MaxVideo pipelined parallel image processor, and the development of the real-time computer vision laboratory. For the Butterfly, the Psyche multi-model operating system was developed and the CONSUL autoparallelizing compiler was designed. Much basic and influential performance monitoring and debugging work was completed, resulting in working systems and novel algorithms. There was also significant research in systems and applications using other parallel architectures in the laboratory, such as the MaxVideo parallel pipelined image processor. The contract developed a heterogeneous parallel architecture involving pipelined and MIMD parallelism and integrated it with a robot head.
Bardsiri, Mahshid Khatibi; Eftekhari, Mahdi; Mousavi, Reza
2015-01-01
In this study the problem of protein fold recognition, that is a classification task, is solved via a hybrid of evolutionary algorithms namely multi-gene Genetic Programming (GP) and Genetic Algorithm (GA). Our proposed method consists of two main stages and is performed on three datasets taken from the literature. Each dataset contains different feature groups and classes. In the first step, multi-gene GP is used for producing binary classifiers based on various feature groups for each class. Then, different classifiers obtained for each class are combined via weighted voting so that the weights are determined through GA. At the end of the first step, there is a separate binary classifier for each class. In the second stage, the obtained binary classifiers are combined via GA weighting in order to generate the overall classifier. The final obtained classifier is superior to the previous works found in the literature in terms of classification accuracy.
Modified Cholesky factorizations in interior-point algorithms for linear programming.
Wright, S.; Mathematics and Computer Science
1999-01-01
We investigate a modified Cholesky algorithm typical of those used in most interior-point codes for linear programming. Cholesky-based interior-point codes are popular for three reasons: their implementation requires only minimal changes to standard sparse Cholesky algorithms (allowing us to take full advantage of software written by specialists in that area); they tend to be more efficient than competing approaches that use alternative factorizations; and they perform robustly on most practical problems, yielding good interior-point steps even when the coefficient matrix of the main linear system to be solved for the step components is ill conditioned. We investigate this surprisingly robust performance by using analytical tools from matrix perturbation theory and error analysis, illustrating our results with computational experiments. Finally, we point out the potential limitations of this approach.
Automatic construction of image inspection algorithm by using image processing network programming
NASA Astrophysics Data System (ADS)
Yoshimura, Yuichiro; Aoki, Kimiya
2017-03-01
In this paper, we discuss a method for automatic programming of inspection image processing. In the industrial field, automatic program generators or expert systems are expected to shorten a period required for developing a new appearance inspection system. So-called "image processing expert system" have been studied for over the nearly 30 years. We are convinced of the need to adopt a new idea. Recently, a novel type of evolutionary algorithms, called genetic network programming (GNP), has been proposed. In this study, we use GNP as a method to create an inspection image processing logic. GNP develops many directed graph structures, and shows excellent ability of formulating complex problems. We have converted this network program model to Image Processing Network Programming (IPNP). IPNP selects an appropriate image processing command based on some characteristics of input image data and processing log, and generates a visual inspection software with series of image processing commands. It is verified from experiments that the proposed method is able to create some inspection image processing programs. In the basic experiment with 200 test images, the success rate of detection of target region was 93.5%.
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.
Skil: An imperative language with algorithmic skeletons for efficient distributed programming
Botorog, G.H.; Kuchen, H.
1996-12-31
In this paper we present Skil, an imperative language enhanced with higher-order functions and currying, as well as with a polymorphic type system. The high level of Skil allows the integration of algorithmic skeletons, i.e. of higher-order functions representing parallel computation patterns. At the same time, the language can be efficiently implemented. After describing a series of skeletons which work with distributed arrays, we give two examples of parallel programs implemented on the basis of skeletons, namely shortest paths in graphs and Gaussian elimination. Runtime measurements show that we approach the efficiency of message-passing C up to a factor between 1 and 2.5.
Duarte, Belmiro P M; Wong, Weng Kee; Atkinson, Anthony C
2015-03-01
T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We propose a potentially more systematic and general way for finding T-optimal designs using a Semi-Infinite Programming (SIP) approach. The strategy requires that we first reformulate the original minimax or maximin optimization problem into an equivalent semi-infinite program and solve it using an exchange-based method where lower and upper bounds produced by solving the outer and the inner programs, are iterated to convergence. A global Nonlinear Programming (NLP) solver is used to handle the subproblems, thus finding the optimal design and the least favorable parametric configuration that minimizes the residual sum of squares from the alternative or test models. We also use a nonlinear program to check the global optimality of the SIP-generated design and automate the construction of globally optimal designs. The algorithm is successfully used to produce results that coincide with several T-optimal designs reported in the literature for various types of model discrimination problems with normally distributed errors. However, our method is more general, merely requiring that the parameters of the model be estimated by a numerical optimization.
Duarte, Belmiro P.M.; Wong, Weng Kee; Atkinson, Anthony C.
2016-01-01
T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We propose a potentially more systematic and general way for finding T-optimal designs using a Semi-Infinite Programming (SIP) approach. The strategy requires that we first reformulate the original minimax or maximin optimization problem into an equivalent semi-infinite program and solve it using an exchange-based method where lower and upper bounds produced by solving the outer and the inner programs, are iterated to convergence. A global Nonlinear Programming (NLP) solver is used to handle the subproblems, thus finding the optimal design and the least favorable parametric configuration that minimizes the residual sum of squares from the alternative or test models. We also use a nonlinear program to check the global optimality of the SIP-generated design and automate the construction of globally optimal designs. The algorithm is successfully used to produce results that coincide with several T-optimal designs reported in the literature for various types of model discrimination problems with normally distributed errors. However, our method is more general, merely requiring that the parameters of the model be estimated by a numerical optimization. PMID:27330230
Penalty Dynamic Programming Algorithm for Dim Targets Detection in Sensor Systems
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
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.
Inversion of oceanic constituents in case I and II waters with genetic programming algorithms.
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.
The RAIDER program: Radio Algorithms for Integration and Design of Engineering Requirements
NASA Astrophysics Data System (ADS)
Rothschild, Susan L.; Farrow, Joseph E.
1991-04-01
The Radio Algorithm for Integration and Design of Engineering Requirements (RAIDER) program consists of a set of modules which provide an easy to use and precise approach to the complete design and documentation of terrestrial radio links operating in the frequency range of 1 to 30 GHz. The program allows the engineer to design both analog and digital line-of-sight links and analog beyond line-of-sight links. Tabular and graphical outputs are developed which may be rendered to the screen or as hard copy at the request of the operator. The input variables can be easily changed and new outputs calculated to enable 'what if' studies to be performed. The operator is prompted to input all required values so calculations can proceed, and each user input is compared with a range of acceptable values to ensure accurate and complete calculations.
NASA Technical Reports Server (NTRS)
Bauman, William H., III
2014-01-01
NASAs LSP customers and the future SLS program rely on observations of upper-level winds for steering, loads, and trajectory calculations for the launch vehicles flight. On the day of launch, the 45th Weather Squadron (45 WS) Launch Weather Officers (LWOs) monitor the upper-level winds and provide forecasts to the launch team via the AMU-developed LSP Upper Winds tool for launches at Kennedy Space Center (KSC) and Cape Canaveral Air Force Station. This tool displays wind speed and direction profiles from rawinsondes released during launch operations, the 45th Space Wing 915-MHz Doppler Radar Wind Profilers (DRWPs) and KSC 50-MHz DRWP, and output from numerical weather prediction models.The goal of this task was to splice the wind speed and direction profiles from the 45th Space Wing (45 SW) 915-MHz Doppler radar Wind Profilers (DRWPs) and KSC 50-MHz DRWP at altitudes where the wind profiles overlap to create a smooth profile. In the first version of the LSP Upper Winds tool, the top of the 915-MHz DRWP wind profile and the bottom of the 50-MHz DRWP were not spliced, sometimes creating a discontinuity in the profile. The Marshall Space Flight Center (MSFC) Natural Environments Branch (NE) created algorithms to splice the wind profiles from the two sensors to generate an archive of vertically complete wind profiles for the SLS program. The AMU worked with MSFC NE personnel to implement these algorithms in the LSP Upper Winds tool to provide a continuous spliced wind profile.The AMU transitioned the MSFC NE algorithms to interpolate and fill data gaps in the data, implement a Gaussian weighting function to produce 50-m altitude intervals in each sensor, and splice the data together from both DRWPs. They did so by porting the MSFC NE code written with MATLAB software into Microsoft Excel Visual Basic for Applications (VBA). After testing the new algorithms in stand-alone VBA modules, the AMU replaced the existing VBA code in the LSP Upper Winds tool with the new
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,…
Khan, Mohammad Ibrahim; Kamal, Md Sarwar
2015-03-01
Markov Chain is very effective in prediction basically in long data set. In DNA sequencing it is always very important to find the existence of certain nucleotides based on the previous history of the data set. We imposed the Chapman Kolmogorov equation to accomplish the task of Markov Chain. Chapman Kolmogorov equation is the key to help the address the proper places of the DNA chain and this is very powerful tools in mathematics as well as in any other prediction based research. It incorporates the score of DNA sequences calculated by various techniques. Our research utilize the fundamentals of Warshall Algorithm (WA) and Dynamic Programming (DP) to measures the score of DNA segments. The outcomes of the experiment are that Warshall Algorithm is good for small DNA sequences on the other hand Dynamic Programming are good for long DNA sequences. On the top of above findings, it is very important to measure the risk factors of local sequencing during the matching of local sequence alignments whatever the length.
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.
Detection of spatial variations in temporal trends with a quadratic function.
Moraga, Paula; Kulldorff, Martin
2016-08-01
Methods for the assessment of spatial variations in temporal trends (SVTT) are important tools for disease surveillance, which can help governments to formulate programs to prevent diseases, and measure the progress, impact, and efficacy of preventive efforts already in operation. The linear SVTT method is designed to detect areas with unusual different disease linear trends. In some situations, however, its estimation trend procedure can lead to wrong conclusions. In this article, the quadratic SVTT method is proposed as alternative of the linear SVTT method. The quadratic method provides better estimates of the real trends, and increases the power of detection in situations where the linear SVTT method fails. A performance comparison between the linear and quadratic methods is provided to help illustrate their respective properties. The quadratic method is applied to detect unusual different cervical cancer trends in white women in the United States, over the period 1969 to 1995.
NASA Astrophysics Data System (ADS)
Swaidan, Waleeda; Hussin, Amran
2015-10-01
Most direct methods solve finite time horizon optimal control problems with nonlinear programming solver. In this paper, we propose a numerical method for solving nonlinear optimal control problem with state and control inequality constraints. This method used quasilinearization technique and Haar wavelet operational matrix to convert the nonlinear optimal control problem into a quadratic programming problem. The linear inequality constraints for trajectories variables are converted to quadratic programming constraint by using Haar wavelet collocation method. The proposed method has been applied to solve Optimal Control of Multi-Item Inventory Model. The accuracy of the states, controls and cost can be improved by increasing the Haar wavelet resolution.
NASA Astrophysics Data System (ADS)
Montoya Villena, Rafael
According to its title, the general objective of the Thesis consists in developing a clear, simple and systematic methodology for programming type PLC devices. With this aim in mind, we will use the following elements: Codification of all variables types. This section is very important since it allows us working with little information. The necessary rules are given to codify all type of phrases produced in industrial processes. An algorithm that describes process evolution and that has been called process D.F. This is one of the most important contributions, since it will allow us, together with information codification, representing the process evolution in a graphic way and with any design theory used. Theory selection. Evidently, the use of some kind of design method is necessary to obtain logic equations. For this particular case, we will use binodal theory, an ideal theory for wired technologies, since it can obtain highly reduced schemas for relatively simple automatisms, which means a minimum number of components used. User program outline algorithm (D.F.P.). This is another necessary contribution and perhaps the most important one, since logic equations resulting from binodal theory are compatible with process evolution if wired technology is used, whether it is electric, electronic, pneumatic, etc. On the other hand, PLC devices performance characteristics force the program instructions order to validate or not the automatism, as we have proven in different articles and lectures at congresses both national and international. Therefore, we will codify any information concerning the automating process, graphically represent its temporal evolution and, applying binodal theory and D.F.P (previously adapted), succeed in making logic equations compatible with the process to be automated and the device in which they will be implemented (PLC in our case)
Limit cycles near hyperbolas in quadratic systems
NASA Astrophysics Data System (ADS)
Artés, Joan C.; Dumortier, Freddy; Llibre, Jaume
In this paper we introduce the notion of infinity strip and strip of hyperbolas as organizing centers of limit cycles in polynomial differential systems on the plane. We study a strip of hyperbolas occurring in some quadratic systems. We deal with the cyclicity of the degenerate graphics DI2a from the programme, set up in [F. Dumortier, R. Roussarie, C. Rousseau, Hilbert's 16th problem for quadratic vector fields, J. Differential Equations 110 (1994) 86-133], to solve the finiteness part of Hilbert's 16th problem for quadratic systems. Techniques from geometric singular perturbation theory are combined with the use of the Bautin ideal. We also rely on the theory of Darboux integrability.
A Branch and Bound Based Heuristic for Solving the Quadratic Assignment Problem,
1981-10-01
the Quadratic Assignment Problem M. S. Bazaraa and 0. Kirca FDRC-81-13 V Contract N~o. N00014-8O-k-0709 A Branch and Bound Based Heuristic for...Solving the Quadratic Assignment Problem M. S. Bazaraa and 0. Kirca Abstract I\\ .... In this paper a branch and bound algorithm is proposed for solving the...concept of branch and bound or im- plicit enumeration, as in the works of Gilmore (1962), Lawler (1963), Craves and Whinston (1970), Bazaraa and Elshafei
Linear Quadratic Gaussian-Based Closed-Loop Control of Type 1 Diabetes
Patek, Stephen D.; Breton, Marc D.; Chen, Yuanda; Solomon, Chad; Kovatchev, Boris
2007-01-01
Background We investigated the applicability of linear quadratic Gaussian (LQG) methodology to the subcutaneous blood glucose regulation problem. We designed an LQG-based feedback control algorithm using linearization of a previously published metabolic model of type 1 diabetes. A key feature of the controller is a Kalman filter used to estimate metabolic states of the patient based on continuous glucose monitoring. Insulin infusion is computed from linear quadratic regulator feedback gains applied to these estimates, generally seeking to minimize squared deviations from a target glucose concentration and basal insulin rate. We evaluated in silico subject-specific LQG control and compared it to preexisting proportional-integral-derivative control. PMID:19756210
Rational quadratic Bézier curve fitting by simulated annealing technique
NASA Astrophysics Data System (ADS)
Mohamed, Najihah; Abd Majid, Ahmad; Mt Piah, Abd Rahni
2013-04-01
A metaheuristic algorithm, which is an approximation method called simulated annealing is implemented in order to have the best rational quadratic Bézier curve from a given data points. This technique is used to minimize sum squared errors in order to improve the middle control point position and the value of weight. As a result, best fitted rational quadratic Bézier curve and its mathematical function that represents all the given data points is obtained. Numerical and graphical examples are also presented to demonstrate the effectiveness and robustness of the proposed method.
Quintessence with quadratic coupling to dark matter
Boehmer, Christian G.; Chan, Nyein; Caldera-Cabral, Gabriela; Lazkoz, Ruth; Maartens, Roy
2010-04-15
We introduce a new form of coupling between dark energy and dark matter that is quadratic in their energy densities. Then we investigate the background dynamics when dark energy is in the form of exponential quintessence. The three types of quadratic coupling all admit late-time accelerating critical points, but these are not scaling solutions. We also show that two types of coupling allow for a suitable matter era at early times and acceleration at late times, while the third type of coupling does not admit a suitable matter era.
Limit Cycles of Planar Quadratic Differential Equations,
1982-05-01
A120 71g LIMIT CYCLES OF PLANAR QUADRATIC DIFFERENTIAL EQUATIONS i/i (U) VALE UNIV NEW~ HAVEN CT CENTER FOR SYSTEMS SCIENCE D E KODITSCHE( ET AL...MICROCOPY RESOLUTION TEST CHART ""OftAI IIMEA OF WSTMAIhSIItg0s3a NATIONA BUREAU OF -TANDtMAROga / - -w w w ~ S S S S S S S S LIMIT CYCLES OF PLANAR...pubta rolb=% DW*5UMato UnlIhd ... a.. . . . . . . . . .......- .lu uo . ,aK Limit Cycles of Planar Quadratic Differential Equations D. E. Koditschek
On orthogonality preserving quadratic stochastic operators
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.
Guises and disguises of quadratic divergences
NASA Astrophysics Data System (ADS)
Cherchiglia, A. L.; Vieira, A. R.; Hiller, Brigitte; Baêta Scarpelli, A. P.; Sampaio, Marcos
2014-12-01
In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.
Guises and disguises of quadratic divergences
Cherchiglia, A.L.; Vieira, A.R.; Hiller, Brigitte; Baêta Scarpelli, A.P.; Sampaio, Marcos
2014-12-15
In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.
2002-01-01
Background Covariance models (CMs) are probabilistic models of RNA secondary structure, analogous to profile hidden Markov models of linear sequence. The dynamic programming algorithm for aligning a CM to an RNA sequence of length N is O(N3) in memory. This is only practical for small RNAs. Results I describe a divide and conquer variant of the alignment algorithm that is analogous to memory-efficient Myers/Miller dynamic programming algorithms for linear sequence alignment. The new algorithm has an O(N2 log N) memory complexity, at the expense of a small constant factor in time. Conclusions Optimal ribosomal RNA structural alignments that previously required up to 150 GB of memory now require less than 270 MB. PMID:12095421
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.
Mehrotra, Sanjay; Papp, Dávid
2014-01-01
We present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. Moments of arbitrary order, as well as nonpolynomial moments, can be included in the formulation. We show that this gives rise to a hierarchy of optimization problems with decreasing levels of risk-aversion, with classic robust optimization at one end of the spectrum and stochastic programming at the other. Although our primary motivation is to solve distributionally robustmore » optimization problems with moment uncertainty, the cutting surface method for general semi-infinite convex programs is also of independent interest. The proposed method is applicable to problems with nondifferentiable semi-infinite constraints indexed by an infinite dimensional index set. Examples comparing the cutting surface algorithm to the central cutting plane algorithm of Kortanek and No demonstrate the potential of our algorithm even in the solution of traditional semi-infinite convex programming problems, whose constraints are differentiable, and are indexed by an index set of low dimension. After the rate of convergence analysis of the cutting surface algorithm, we extend the authors' moment matching scenario generation algorithm to a probabilistic algorithm that finds optimal probability distributions subject to moment constraints. The combination of this distribution optimization method and the central cutting surface algorithm yields a solution to a family of distributionally robust optimization problems that are considerably more general than the ones proposed to date.« less
Mehrotra, Sanjay; Papp, Dávid
2014-01-01
We present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. Moments of arbitrary order, as well as nonpolynomial moments, can be included in the formulation. We show that this gives rise to a hierarchy of optimization problems with decreasing levels of risk-aversion, with classic robust optimization at one end of the spectrum and stochastic programming at the other. Although our primary motivation is to solve distributionally robust optimization problems with moment uncertainty, the cutting surface method for general semi-infinite convex programs is also of independent interest. The proposed method is applicable to problems with nondifferentiable semi-infinite constraints indexed by an infinite dimensional index set. Examples comparing the cutting surface algorithm to the central cutting plane algorithm of Kortanek and No demonstrate the potential of our algorithm even in the solution of traditional semi-infinite convex programming problems, whose constraints are differentiable, and are indexed by an index set of low dimension. After the rate of convergence analysis of the cutting surface algorithm, we extend the authors' moment matching scenario generation algorithm to a probabilistic algorithm that finds optimal probability distributions subject to moment constraints. The combination of this distribution optimization method and the central cutting surface algorithm yields a solution to a family of distributionally robust optimization problems that are considerably more general than the ones proposed to date.
Efficient dynamic programming algorithm with prior knowledge for protein β-strand alignment.
Sabzekar, Mostafa; Naghibzadeh, Mahmoud; Sadri, Javad
2017-03-21
One of the main tasks towards the prediction of protein β-sheet structure is to predict the native alignment of β-strands. The alignment of two β-strands defines similar regions that may reflect functional, structural, or evolutionary relationships between them. Therefore, any improvement in β-strands alignment not only reduces the computational search space but also improves β-sheet structure prediction accuracy. To define the alignment scores, previous studies utilized predicted residue-residue contacts (contact maps). However, there are two serious problems using them. First, the precision of contact map prediction techniques, especially for long-range contacts (i.e., β-residues), is still not satisfactory. Second, the residue-residue contact predictors usually utilize general properties of amino acids and disregard the structural features of β-residues. In this paper, we consider β-structure information, which is estimated from protein β-sheet data sets, as alignment scores. However, the predicted contact maps are used as a prior knowledge about residues. They are used for strengthening or weakening the alignment scores in our algorithm. Thus, we can utilize both β-residues and β-structure information in alignment of β-strands. The structure of dynamic programming of the alignment algorithm is changed in order to work with our prior knowledge. Moreover, the Four Russians method is applied to the proposed alignment algorithm in order to reduce the time complexity of the problem. For evaluating the proposed method, we applied it to the state-of-the-art β-sheet structure prediction methods. The experimental results on the BetaSheet916 data set showed significant improvements in the execution time, the accuracy of β-strands' alignment and consequently β-sheet structure prediction accuracy. The results are available at http://conceptsgate.com/BetaSheet.
NASA Astrophysics Data System (ADS)
Itoh, Yoshiaki; Tanaka, Kazuyo
2004-08-01
Word frequency in a document has often been utilized in text searching and summarization. Similarly, identifying frequent words or phrases in a speech data set for searching and summarization would also be meaningful. However, obtaining word frequency in a speech data set is difficult, because frequent words are often special terms in the speech and cannot be recognized by a general speech recognizer. This paper proposes another approach that is effective for automatic extraction of such frequent word sections in a speech data set. The proposed method is applicable to any domain of monologue speech, because no language models or specific terms are required in advance. The extracted sections can be regarded as speech labels of some kind or a digest of the speech presentation. The frequent word sections are determined by detecting similar sections, which are sections of audio data that represent the same word or phrase. The similar sections are detected by an efficient algorithm, called Shift Continuous Dynamic Programming (Shift CDP), which realizes fast matching between arbitrary sections in the reference speech pattern and those in the input speech, and enables frame-synchronous extraction of similar sections. In experiments, the algorithm is applied to extract the repeated sections in oral presentation speeches recorded in academic conferences in Japan. The results show that Shift CDP successfully detects similar sections and identifies the frequent word sections in individual presentation speeches, without prior domain knowledge, such as language models and terms.
Efficient linear programming algorithm to generate the densest lattice sphere packings.
Marcotte, Étienne; Torquato, Salvatore
2013-06-01
Finding the densest sphere packing in d-dimensional Euclidean space R(d) is an outstanding fundamental problem with relevance in many fields, including the ground states of molecular systems, colloidal crystal structures, coding theory, discrete geometry, number theory, and biological systems. Numerically generating the densest sphere packings becomes very challenging in high dimensions due to an exponentially increasing number of possible sphere contacts and sphere configurations, even for the restricted problem of finding the densest lattice sphere packings. In this paper we apply the Torquato-Jiao packing algorithm, which is a method based on solving a sequence of linear programs, to robustly reproduce the densest known lattice sphere packings for dimensions 2 through 19. We show that the TJ algorithm is appreciably more efficient at solving these problems than previously published methods. Indeed, in some dimensions, the former procedure can be as much as three orders of magnitude faster at finding the optimal solutions than earlier ones. We also study the suboptimal local density-maxima solutions (inherent structures or "extreme" lattices) to gain insight about the nature of the topography of the "density" landscape.
Osser, David N; Roudsari, Mohsen Jalali; Manschreck, Theo
2013-01-01
This article is an update of the algorithm for schizophrenia from the Psychopharmacology Algorithm Project at the Harvard South Shore Program. A literature review was conducted focusing on new data since the last published version (1999-2001). The first-line treatment recommendation for new-onset schizophrenia is with amisulpride, aripiprazole, risperidone, or ziprasidone for four to six weeks. In some settings the trial could be shorter, considering that evidence of clear improvement with antipsychotics usually occurs within the first two weeks. If the trial of the first antipsychotic cannot be completed due to intolerance, try another until one of the four is tolerated and given an adequate trial. There should be evidence of bioavailability. If the response to this adequate trial is unsatisfactory, try a second monotherapy. If the response to this second adequate trial is also unsatisfactory, and if at least one of the first two trials was with risperidone, olanzapine, or a first-generation (typical) antipsychotic, then clozapine is recommended for the third trial. If neither trial was with any these three options, a third trial prior to clozapine should occur, using one of those three. If the response to monotherapy with clozapine (with dose adjusted by using plasma levels) is unsatisfactory, consider adding risperidone, lamotrigine, or ECT. Beyond that point, there is little solid evidence to support further psychopharmacological treatment choices, though we do review possible options.
Branching process deconvolution algorithm reveals a detailed cell-cycle transcription program.
Guo, Xin; Bernard, Allister; Orlando, David A; Haase, Steven B; Hartemink, Alexander J
2013-03-05
Due to cell-to-cell variability and asymmetric cell division, cells in a synchronized population lose synchrony over time. As a result, time-series measurements from synchronized cell populations do not reflect the underlying dynamics of cell-cycle processes. Here, we present a branching process deconvolution algorithm that learns a more accurate view of dynamic cell-cycle processes, free from the convolution effects associated with imperfect cell synchronization. Through wavelet-basis regularization, our method sharpens signal without sharpening noise and can remarkably increase both the dynamic range and the temporal resolution of time-series data. Although applicable to any such data, we demonstrate the utility of our method by applying it to a recent cell-cycle transcription time course in the eukaryote Saccharomyces cerevisiae. Our method more sensitively detects cell-cycle-regulated transcription and reveals subtle timing differences that are masked in the original population measurements. Our algorithm also explicitly learns distinct transcription programs for mother and daughter cells, enabling us to identify 82 genes transcribed almost entirely in early G1 in a daughter-specific manner.
Liu Zhongyi Sun, Wenyu Tian Fangbao
2009-10-15
This paper proposes an infeasible interior-point algorithm with full-Newton step for linear programming, which is an extension of the work of Roos (SIAM J. Optim. 16(4):1110-1136, 2006). The main iteration of the algorithm consists of a feasibility step and several centrality steps. We introduce a kernel function in the algorithm to induce the feasibility step. For parameter p element of [0,1], the polynomial complexity can be proved and the result coincides with the best result for infeasible interior-point methods, that is, O(nlog n/{epsilon})
Advances in methods and algorithms in a modern quantum chemistry program package.
Shao, Yihan; Molnar, Laszlo Fusti; Jung, Yousung; Kussmann, Jörg; Ochsenfeld, Christian; Brown, Shawn T; Gilbert, Andrew T B; Slipchenko, Lyudmila V; Levchenko, Sergey V; O'Neill, Darragh P; DiStasio, Robert A; Lochan, Rohini C; Wang, Tao; Beran, Gregory J O; Besley, Nicholas A; Herbert, John M; Lin, Ching Yeh; Van Voorhis, Troy; Chien, Siu Hung; Sodt, Alex; Steele, Ryan P; Rassolov, Vitaly A; Maslen, Paul E; Korambath, Prakashan P; Adamson, Ross D; Austin, Brian; Baker, Jon; Byrd, Edward F C; Dachsel, Holger; Doerksen, Robert J; Dreuw, Andreas; Dunietz, Barry D; Dutoi, Anthony D; Furlani, Thomas R; Gwaltney, Steven R; Heyden, Andreas; Hirata, So; Hsu, Chao-Ping; Kedziora, Gary; Khalliulin, Rustam Z; Klunzinger, Phil; Lee, Aaron M; Lee, Michael S; Liang, Wanzhen; Lotan, Itay; Nair, Nikhil; Peters, Baron; Proynov, Emil I; Pieniazek, Piotr A; Rhee, Young Min; Ritchie, Jim; Rosta, Edina; Sherrill, C David; Simmonett, Andrew C; Subotnik, Joseph E; Woodcock, H Lee; Zhang, Weimin; Bell, Alexis T; Chakraborty, Arup K; Chipman, Daniel M; Keil, Frerich J; Warshel, Arieh; Hehre, Warren J; Schaefer, Henry F; Kong, Jing; Krylov, Anna I; Gill, Peter M W; Head-Gordon, Martin
2006-07-21
Advances in theory and algorithms for electronic structure calculations must be incorporated into program packages to enable them to become routinely used by the broader chemical community. This work reviews advances made over the past five years or so that constitute the major improvements contained in a new release of the Q-Chem quantum chemistry package, together with illustrative timings and applications. Specific developments discussed include fast methods for density functional theory calculations, linear scaling evaluation of energies, NMR chemical shifts and electric properties, fast auxiliary basis function methods for correlated energies and gradients, equation-of-motion coupled cluster methods for ground and excited states, geminal wavefunctions, embedding methods and techniques for exploring potential energy surfaces.
Hart, W.E.
1999-02-10
Evolutionary programs (EPs) and evolutionary pattern search algorithms (EPSAS) are two general classes of evolutionary methods for optimizing on continuous domains. The relative performance of these methods has been evaluated on standard global optimization test functions, and these results suggest that EPSAs more robustly converge to near-optimal solutions than EPs. In this paper we evaluate the relative performance of EPSAs and EPs on a real-world application: flexible ligand binding in the Autodock docking software. We compare the performance of these methods on a suite of docking test problems. Our results confirm that EPSAs and EPs have comparable performance, and they suggest that EPSAs may be more robust on larger, more complex problems.
Streppa, Joanna; Schneidman, Valerie; Biron, Alain D
2014-01-01
Crowding is extremely problematic in Canada, as the emergency department (ED) utilization is considerably higher than in any other country. Consequently, an increase has been noted in waiting times for patients who present with injuries of lesser acuity such as wrist injuries. Wrist fractures are the most common broken bone in patients younger than 65 years. Many nurses employed within EDs are requesting wrist radiographs for patients who present with wrist complaints as a norm within their working practice. Significant potential advantages can ensue if EDs adopt a triage nurse-requested radiographic protocol; patients can benefit from a significant time-saving of 36% in ED length of stay (M. Lindley-Jones & B. J Finlayson, 2000)— when nurses initiated radiographs in triage. In addition, the literature suggests that increased rates of patient and staff satisfaction may be achieved, without compromising quality of radiographic request or quality of service (W. Parris,S. McCarthy, A. M. Kelly, & S. Richardson, 1997). Studies have shown that nurses are capable of requesting appropriate radiographs on the basis of a preset protocol. As there are no standardized set of rules for assessing patients, presenting with suspected wrist fractures, a training program as well as a diagnostic algorithm was developed to prepare emergency nurses to appropriately request wrist radiographs. The triage nurse-specific training program includes the following topics: wrist anatomy and physiology, commonly occurring wrist injuries, mechanisms of injury, physical assessment techniques, and types of radiographic images required. The triage nurse algorithm includes the clinical decision-making process. Providing triage nurses with up-to-date evidence-based educational material not only allowed triage nurses to independently assess and request wrist radiographs for patients with potential wrist fractures but also strengthening the link between competent nursing care and better patient
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.
Target manifold formation using a quadratic SDF
NASA Astrophysics Data System (ADS)
Hester, Charles F.; Risko, Kelly K. D.
2013-05-01
Synthetic Discriminant Function (SDF) formulation of correlation filters provides constraints for forming target subspaces for a target set. In this paper we extend the SDF formulation to include quadratic constraints and use this solution to form nonlinear manifolds in the target space. The theory for forming these manifolds will be developed and demonstrated with data.
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…
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…
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.
Bôcher and Abstract Contractions of 2nd Order Quadratic Algebras
NASA Astrophysics Data System (ADS)
Escobar-Ruiz, Mauricio A.; Kalnins, Ernest G.; Miller, Willar, Jr.; Subag, Eyal
2017-03-01
Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. Distinct superintegrable systems and their quadratic algebras can be related by geometric contractions, induced by Bôcher contractions of the conformal Lie algebra {so}(4,C) to itself. In this paper we give a precise definition of Bôcher contractions and show how they can be classified. They subsume well known contractions of {e}(2,C) and {so}(3,C) and have important physical and geometric meanings, such as the derivation of the Askey scheme for obtaining all hypergeometric orthogonal polynomials as limits of Racah/Wilson polynomials. We also classify abstract nondegenerate quadratic algebras in terms of an invariant that we call a canonical form. We describe an algorithm for finding the canonical form of such algebras. We calculate explicitly all canonical forms arising from quadratic algebras of 2D nondegenerate superintegrable systems on constant curvature spaces and Darboux spaces. We further discuss contraction of quadratic algebras, focusing on those coming from superintegrable systems.
A combined strategy for solving quadratic assignment problem
NASA Astrophysics Data System (ADS)
Ahyaningsih, Faiz
2017-08-01
The quadratic assignment problem is a combinatorial problem of deciding the placement of facilities in specified locations in such a way as to minimize a nonconvex objective function expressed in terms of flow between facilities, and distance between location. Due to the non-convexity nature of the problem, therefore to get a `good' starting point is necessary in order to obtain a better optimal solution. In this paper we propose a combined strategy (random point strategy to get initial starting point and then use forward exchange strategy and backward exchange strategy to get `optimal' solution). As a computational experience we've solved the problem of Esc 16b, Esc 16c and Esc 16h from QAPLIB. Finally, we present a comparative study between Combined Strategy and Data -Guided Lexisearch Algorithm. The computational study shows the effectiveness of our proposed combined strategy.
Quadratic trigonometric B-spline for image interpolation using GA
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
Discriminative learning quadratic discriminant function for handwriting recognition.
Liu, Cheng-Lin; Sako, Hiroshi; Fujisawa, Hiromichi
2004-03-01
In character string recognition integrating segmentation and classification, high classification accuracy and resistance to noncharacters are desired to the underlying classifier. In a previous evaluation study, the modified quadratic discriminant function (MQDF) proposed by Kimura et al. was shown to be superior in noncharacter resistance but inferior in classification accuracy to neural networks. This paper proposes a discriminative learning algorithm to optimize the parameters of MQDF with aim to improve the classification accuracy while preserving the superior noncharacter resistance. We refer to the resulting classifier as discriminative learning QDF (DLQDF). The parameters of DLQDF adhere to the structure of MQDF under the Gaussian density assumption and are optimized under the minimum classification error (MCE) criterion. The promise of DLQDF is justified in handwritten digit recognition and numeral string recognition, where the performance of DLQDF is comparable to or superior to that of neural classifiers. The results are also competitive to the best ones reported in the literature.
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)
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)
Profile-Following Entry Guidance Using Linear Quadratic Regulator Theory
NASA Technical Reports Server (NTRS)
Dukeman, Greg A.; Fogle, Frank (Technical Monitor)
2002-01-01
This paper describes one of the entry guidance concepts that is currently being tested as part of Marshall Space Flight Center's Advance Guidance and Control Project. The algorithm is of the reference profile tracking type. The reference profile consists of the reference states, range-to-go, altitude, and flight path angle, and reference controls, bank angle and angle of attack, versus energy. A linear control law using state feedback is used with energy-scheduled gains. The gains are obtained offline using Matlab's steady state linear quadratic regulator function. Lateral trajectory control is effected by performing periodic bank sign reversals based on a heading error corridor. A description and results of the AG&C test cases on which it has been tested are given. Although it is not anticipated that the algorithm will be quite as robust as algorithms with onboard trajectory re-generation capability, the results nevertheless show it to be very robust with respect to varying initial conditions and works satisfactorily even for entries from widely different orbits than that of the reference profile. Moreover, the commanded bank and angle of attack histories are very smooth, making it easier for the attitude control system to implement the guidance commands. Finally, results indicate that the guidance gains are more or less trajectory-independent which is a potentially useful property.
Dennis, J.E. Jr.; Tapia, R.A.
1995-12-19
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.
CAMPBELL, PHILIP L.
1999-08-01
This report presents an implementation of the Berlekamp-Massey linear feedback shift-register (LFSR) synthesis algorithm in the C programming language. Two pseudo-code versions of the code are given, the operation of LFSRs is explained, C-version of the pseudo-code versions is presented, and the output of the code, when run on two input samples, is shown.
New approaches to linear and nonlinear programming
Murray, W.; Saunders, M.A.
1990-03-01
During the last twelve months, research has concentrated on barrier- function methods for linear programming (LP) and quadratic programming (QP). Some ground-work for the application of barrier methods to nonlinearly constrained problems has also begun. In our previous progress report we drew attention to the difficulty of developing robust implementations of barrier methods for LP. We have continued to refine both the primal algorithm and the dual algorithm. We still do not claim that the barrier algorithms are as robust as the simplex method; however, the dual algorithm has solved all the problems in our extensive test set. We have also gained some experience with using the algorithms to solve aircrew scheduling problems.
1987-05-01
Laboratory •U The Equivmluce of Dentig’$ Self-Dual Parametric Algorithm for Linemr Progame to Lems Ngorithm fur Lse Cemllusemtawt Problems Appled to Umer...agement Science 11, pp. 681-689. Lemke, C.E. (1970). "Recent results on complementarity problems," in Nonlinear pro- gramming (J.B. Rosen, O.L
Use of quadratic components for buckling calculations
Dohrmann, C.R.; Segalman, D.J.
1996-12-31
A buckling calculation procedure based on the method of quadratic components is presented. Recently developed for simulating the motion of rotating flexible structures, the method of quadratic components is shown to be applicable to buckling problems with either conservative or nonconservative loads. For conservative loads, stability follows from the positive definiteness of the system`s stiffness matrix. For nonconservative loads, stability is determined by solving a nonsymmetric eigenvalue problem, which depends on both the stiffness and mass distribution of the system. Buckling calculations presented for a cantilevered beam are shown to compare favorably with classical results. Although the example problem is fairly simple and well-understood, the procedure can be used in conjunction with a general-purpose finite element code for buckling calculations of more complex systems.
Linear quadratic output tracking and disturbance rejection
NASA Astrophysics Data System (ADS)
Karimi-Ghartemani, Masoud; Khajehoddin, S. Ali; Jain, Praveen; Bakhshai, Alireza
2011-08-01
This article introduces the problem of linear quadratic tracking (LQT) where the objective is to design a closed-loop control scheme such that the output signal of the system optimally tracks a given reference signal and rejects a given disturbance. Different performance indices that have been used to address the tracking problem are discussed and an appropriate new form is introduced. It is shown that a solution to the proposed optimality index exists under very mild conditions of stabilisability and detectability of the plant state-space equations. The solution is formulated based on converting the LQT problem to a standard linear quadratic regulation problem. The method is applied to two examples, a first-order plant and a third-order plant, and their simulation results are presented and discussed.
Bifurcations in biparametric quadratic potentials. II.
Lanchares, V.; Elipe, A.
1995-09-01
Quadratic Hamiltonians with the phase space on the S (2) sphere represent numerous dynamical systems. There are only two classes of quadratic Hamiltonians depending on two parameters. We analyze the occurrence of bifurcations and we obtain the bifurcation lines in the parameter plane for one of these classes, thus complementing the work done in a previous paper where the other class was analyzed. As the parameters evolve, the appearance-disappearance of homoclinic orbits in the phase portrait is governed by four types of bifurcations: namely the pitchfork, the butterfly, the oyster and the pentadent bifurcations. We find also values where the system is degenerate, that is, there are nonisolated equilibria. (c) 1995 American Institute of Physics.
NASA Technical Reports Server (NTRS)
Soeder, J. F.
1983-01-01
As turbofan engines become more complex, the development of controls necessitate the use of multivariable control techniques. A control developed for the F100-PW-100(3) turbofan engine by using linear quadratic regulator theory and other modern multivariable control synthesis techniques is described. The assembly language implementation of this control on an SEL 810B minicomputer is described. This implementation was then evaluated by using a real-time hybrid simulation of the engine. The control software was modified to run with a real engine. These modifications, in the form of sensor and actuator failure checks and control executive sequencing, are discussed. Finally recommendations for control software implementations are presented.
Graphical Solution of the Monic Quadratic Equation with Complex Coefficients
ERIC Educational Resources Information Center
Laine, A. D.
2015-01-01
There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…
THE EFFECTIVENESS OF QUADRATS FOR MEASURING VASCULAR PLANT DIVERSITY
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...
Graphical Solution of the Monic Quadratic Equation with Complex Coefficients
ERIC Educational Resources Information Center
Laine, A. D.
2015-01-01
There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…
THE EFFECTIVENESS OF QUADRATS FOR MEASURING VASCULAR PLANT DIVERSITY
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...
Monotone and convex quadratic spline interpolation
NASA Technical Reports Server (NTRS)
Lam, Maria H.
1990-01-01
A method for producing interpolants that preserve the monotonicity and convexity of discrete data is described. It utilizes the quadratic spline proposed by Schumaker (1983) which was subsequently characterized by De Vore and Yan (1986). The selection of first order derivatives at the given data points is essential to this spline. An observation made by De Vore and Yan is generalized, and an improved method to select these derivatives is proposed. The resulting spline is completely local, efficient, and simple to implement.
Communications circuit including a linear quadratic estimator
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.
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.
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.
Stochastic Linear Quadratic Optimal Control Problems
Chen, S.; Yong, J.
2001-07-01
This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well.
Quadratic optimization in ill-posed problems
NASA Astrophysics Data System (ADS)
Ben Belgacem, F.; Kaber, S.-M.
2008-10-01
Ill-posed quadratic optimization frequently occurs in control and inverse problems and is not covered by the Lax-Milgram-Riesz theory. Typically, small changes in the input data can produce very large oscillations on the output. We investigate the conditions under which the minimum value of the cost function is finite and we explore the 'hidden connection' between the optimization problem and the least-squares method. Eventually, we address some examples coming from optimal control and data completion, showing how relevant our contribution is in the knowledge of what happens for various ill-posed problems. The results we state bring a substantial improvement to the analysis of the regularization methods applied to the ill-posed quadratic optimization problems. Indeed, for the cost quadratic functions bounded from below the Lavrentiev method is just the Tikhonov regularization for the 'hidden least-squares' problem. As a straightforward result, Lavrentiev's regularization exhibits better regularization and convergence results than expected at first glance.
Quadratic Gabor filters for object detection.
Weber, D M; Casasent, D P
2001-01-01
We present a new class of quadratic filters that are capable of creating spherical, elliptical, hyperbolic and linear decision surfaces which result in better detection and classification capabilities than the linear decision surfaces obtained from correlation filters. Each filter comprises of a number of separately designed linear basis filters. These filters are linearly combined into several macro filters; the output from these macro filters are passed through a magnitude square operation and are then linearly combined using real weights to achieve the quadratic decision surface. For detection, the creation of macro filters (linear combinations of multiple single filters) allows for a substantial computational saving by reducing the number of correlation operations required. In this work, we consider the use of Gabor basis filters; the Gabor filter parameters are separately optimized. The fusion parameters to combine the Gabor filter outputs are optimized using an extended piecewise quadratic neural network (E-PQNN). We demonstrate methods for selecting the number of macro Gabor filters, the filter parameters and the linear and nonlinear combination coefficients. We present preliminary results obtained for an infrared (IR) vehicle detection problem.
Strout, Michelle
2015-08-15
Programming parallel machines is fraught with difficulties: the obfuscation of algorithms due to implementation details such as communication and synchronization, the need for transparency between language constructs and performance, the difficulty of performing program analysis to enable automatic parallelization techniques, and the existence of important "dusty deck" codes. The SAIMI project developed abstractions that enable the orthogonal specification of algorithms and implementation details within the context of existing DOE applications. The main idea is to enable the injection of small programming models such as expressions involving transcendental functions, polyhedral iteration spaces with sparse constraints, and task graphs into full programs through the use of pragmas. These smaller, more restricted programming models enable orthogonal specification of many implementation details such as how to map the computation on to parallel processors, how to schedule the computation, and how to allocation storage for the computation. At the same time, these small programming models enable the expression of the most computationally intense and communication heavy portions in many scientific simulations. The ability to orthogonally manipulate the implementation for such computations will significantly ease performance programming efforts and expose transformation possibilities and parameter to automated approaches such as autotuning. At Colorado State University, the SAIMI project was supported through DOE grant DE-SC3956 from April 2010 through August 2015. The SAIMI project has contributed a number of important results to programming abstractions that enable the orthogonal specification of implementation details in scientific codes. This final report summarizes the research that was funded by the SAIMI project.
Optimal Path Planning Program for Autonomous Speed Sprayer in Orchard Using Order-Picking Algorithm
NASA Astrophysics Data System (ADS)
Park, T. S.; Park, S. J.; Hwang, K. Y.; Cho, S. I.
This study was conducted to develop a software program which computes optimal path for autonomous navigation in orchard, especially for speed sprayer. Possibilities of autonomous navigation in orchard were shown by other researches which have minimized distance error between planned path and performed path. But, research of planning an optimal path for speed sprayer in orchard is hardly founded. In this study, a digital map and a database for orchard which contains GPS coordinate information (coordinates of trees and boundary of orchard) and entity information (heights and widths of trees, radius of main stem of trees, disease of trees) was designed. An orderpicking algorithm which has been used for management of warehouse was used to calculate optimum path based on the digital map. Database for digital map was created by using Microsoft Access and graphic interface for database was made by using Microsoft Visual C++ 6.0. It was possible to search and display information about boundary of an orchard, locations of trees, daily plan for scattering chemicals and plan optimal path on different orchard based on digital map, on each circumstance (starting speed sprayer in different location, scattering chemicals for only selected trees).
Fuzzy bilevel programming with multiple non-cooperative followers: model, algorithm and application
NASA Astrophysics Data System (ADS)
Ke, Hua; Huang, Hu; Ralescu, Dan A.; Wang, Lei
2016-04-01
In centralized decision problems, it is not complicated for decision-makers to make modelling technique selections under uncertainty. When a decentralized decision problem is considered, however, choosing appropriate models is no longer easy due to the difficulty in estimating the other decision-makers' inconclusive decision criteria. These decision criteria may vary with different decision-makers because of their special risk tolerances and management requirements. Considering the general differences among the decision-makers in decentralized systems, we propose a general framework of fuzzy bilevel programming including hybrid models (integrated with different modelling methods in different levels). Specially, we discuss two of these models which may have wide applications in many fields. Furthermore, we apply the proposed two models to formulate a pricing decision problem in a decentralized supply chain with fuzzy coefficients. In order to solve these models, a hybrid intelligent algorithm integrating fuzzy simulation, neural network and particle swarm optimization based on penalty function approach is designed. Some suggestions on the applications of these models are also presented.
Optimization of Water Distribution and Water Quality by Genetic Algorithm and Nonlinear Programming
NASA Astrophysics Data System (ADS)
Tu, M.; Tsai, F. T.; Yeh, W. W.
2001-12-01
When managing a regional water distribution system, it is not only important to optimize water allocation but also to meet the desired water quality requirements. This paper develops a multicommodity flow model that can be used to optimize water distribution and water quality in a regional water supply system. Waters from different sources with different quality are considered as distinct commodities, which concurrently share a single water distribution system. Volumetric water blend is used to represent water quality in the proposed model. The multicommodity model is capable of handling two-way flow pipes, as represented undirectional arcs, and the perfect mixing condition. Additionally, blending requirements are specified at certain control nodes within the water distribution system to ensure that downstream users receive the desired water quality. The developed multicommodity flow model is imbedded in a nonlinear optimization model. To reduce nonlinearity and to improve convergence, GA is combined with a gradient-based-algorithm to solve the nonlinearly constrained optimization model in that GA is used to search for the optimal direction for all undirectional arcs in the system and iteratively linked with a nonlinear programming solver. The proposed methodology was first tested and verified on a simplified hypothetical system and then applied to the regional water distribution system of the Metropolitan Water District of Southern California. The results obtained indicate that the optimization model can efficiently allocate waters from different sources with different quality to satisfy the blending requirements, the perfect mixing and two-way flow conditions.
NASA Astrophysics Data System (ADS)
Biswas, Papun; Chakraborti, Debjani
2010-10-01
This paper describes how the genetic algorithms (GAs) can be efficiently used to fuzzy goal programming (FGP) formulation of optimal power flow problems having multiple objectives. In the proposed approach, the different constraints, various relationships of optimal power flow calculations are fuzzily described. In the model formulation of the problem, the membership functions of the defined fuzzy goals are characterized first for measuring the degree of achievement of the aspiration levels of the goals specified in the decision making context. Then, the achievement function for minimizing the regret for under-deviations from the highest membership value (unity) of the defined membership goals to the extent possible on the basis of priorities is constructed for optimal power flow problems. In the solution process, the GA method is employed to the FGP formulation of the problem for achievement of the highest membership value (unity) of the defined membership functions to the extent possible in the decision making environment. In the GA based solution search process, the conventional Roulette wheel selection scheme, arithmetic crossover and random mutation are taken into consideration to reach a satisfactory decision. The developed method has been tested on IEEE 6-generator 30-bus System. Numerical results show that this method is promising for handling uncertain constraints in practical power systems.
Method of expanding hyperspheres - an interior algorithm for linear programming problems
Chandrupatla, T.
1994-12-31
A new interior algorithm using some properties of hyperspheres is proposed for the solution of linear programming problems with inequality constraints: maximize c{sup T} x subject to Ax {<=} b where c and rows of A are normalized in the Euclidean sense such that {parallel} c {parallel} = {radical}c{sup T}c = 1 {parallel} a{sub i} {parallel} {radical} A{sub i}A{sub i}{sup T} = 1 for i = 1 to m. The feasible region in the polytope bounded by the constraint planes. We start from an interior point. We pass a plane normal to c until it touches a constraint plane. Then the sphere is expanded so that it keeps contact with the previously touched planes and the expansion proceeds till it touches another plane. The procedure is continued till the sphere touches the c-plane and n constraint planes. We move to the center of the sphere and repeat the process. The interior maximum is reached when the radius of the expanded sphere is less than a critical value say {epsilon}. Problems of direction finding, determination of incoming constraint, sphere jamming, and evaluation of the initial feasible point are discussed.
Policy iteration adaptive dynamic programming algorithm for discrete-time nonlinear systems.
Liu, Derong; Wei, Qinglai
2014-03-01
This paper is concerned with a new discrete-time policy iteration adaptive dynamic programming (ADP) method for solving the infinite horizon optimal control problem of nonlinear systems. The idea is to use an iterative ADP technique to obtain the iterative control law, which optimizes the iterative performance index function. The main contribution of this paper is to analyze the convergence and stability properties of policy iteration method for discrete-time nonlinear systems for the first time. It shows that the iterative performance index function is nonincreasingly convergent to the optimal solution of the Hamilton-Jacobi-Bellman equation. It is also proven that any of the iterative control laws can stabilize the nonlinear systems. Neural networks are used to approximate the performance index function and compute the optimal control law, respectively, for facilitating the implementation of the iterative ADP algorithm, where the convergence of the weight matrices is analyzed. Finally, the numerical results and analysis are presented to illustrate the performance of the developed method.
NASA Technical Reports Server (NTRS)
Lansing, F. L.; Strain, D. M.; Chai, V. W.; Higgins, S.
1979-01-01
The energy Comsumption Computer Program was developed to simulate building heating and cooling loads and compute thermal and electric energy consumption and cost. This article reports on the new additional algorithms and modifications made in an effort to widen the areas of application. The program structure was rewritten accordingly to refine and advance the building model and to further reduce the processing time and cost. The program is noted for its very low cost and ease of use compared to other available codes. The accuracy of computations is not sacrificed however, since the results are expected to lie within + or - 10% of actual energy meter readings.
NASA Technical Reports Server (NTRS)
Lansing, F. L.; Strain, D. M.; Chai, V. W.; Higgins, S.
1979-01-01
The energy Comsumption Computer Program was developed to simulate building heating and cooling loads and compute thermal and electric energy consumption and cost. This article reports on the new additional algorithms and modifications made in an effort to widen the areas of application. The program structure was rewritten accordingly to refine and advance the building model and to further reduce the processing time and cost. The program is noted for its very low cost and ease of use compared to other available codes. The accuracy of computations is not sacrificed however, since the results are expected to lie within + or - 10% of actual energy meter readings.
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.
A Path Algorithm for Constrained Estimation
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
Utkin, Lev V; Chekh, Anatoly I; Zhuk, Yulia A
2016-08-01
Classification algorithms based on different forms of support vector machines (SVMs) for dealing with interval-valued training data are proposed in the paper. L2-norm and L∞-norm SVMs are used for constructing the algorithms. The main idea allowing us to represent the complex optimization problems as a set of simple linear or quadratic programming problems is to approximate the Gaussian kernel by the well-known triangular and Epanechnikov kernels. The minimax strategy is used to choose an optimal probability distribution from the set and to construct optimal separating functions. Numerical experiments illustrate the algorithms. Copyright © 2016 Elsevier Ltd. All rights reserved.
Finite Element Simulation of Articular Contact Mechanics with Quadratic Tetrahedral Elements
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.
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.
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.
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 L1 norm or even sub-linear potentials corresponding to quasinorms Lp (0
algorithms (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.
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.
Fabrellas, Núria; Sánchez, Carmen; Juvé, Eulàlia; Aurin, Eva; Monserrat, Dolors; Casanovas, Esther; Urrea, Magali
2013-05-16
Attention to patients with acute minor-illnesses requesting same-day consultation represents a major burden in primary care. The workload is assumed by general practitioners in many countries. A number of reports suggest that care to these patients may be provided, at in least in part, by nurses. However, there is scarce information with respect to the applicability of a program of nurse management for adult patients with acute minor-illnesses in large areas. The aim of this study is to assess the effectiveness of a program of nurse algorithm-guided care for adult patients with acute minor illnesses requesting same-day consultation in primary care in a largely populated area. A cross-sectional study of all adult patients seeking same day consultation for 16 common acute minor illnesses in a large geographical area with 284 primary care practices. Patients were included in a program of nurse case management using management algorithms. The main outcome measure was case resolution, defined as completion of the algorithm by the nurse without need of referral of the patient to the general practitioner. The secondary outcome measure was return to consultation, defined as requirement of new consultation for the same reason as the first one, in primary care within a 7-day period. During a two year period (April 2009-April 2011), a total of 1,209,669 consultations were performed in the program. Case resolution was achieved by nurses in 62.5% of consultations. The remaining cases were referred to a general practitioner. Resolution rates ranged from 94.2% in patients with burns to 42% in patients with upper respiratory symptoms. None of the 16 minor illnesses had a resolution rate below 40%. Return to consultation during a 7-day period was low, only 4.6%. A program of algorithms-guided care is effective for nurse case management of patients requesting same day consultation for minor illnesses in primary care.
Shan, Xiao; Connor, J N L
2012-11-26
A previous paper by Shan and Connor (Phys. Chem. Chem. Phys. 2011, 13, 8392) reported the surprising result that four simple parametrized S matrices can reproduce the forward-angle glory scattering of the H + D(2)(v(i)=0,j(i)=0) → HD(v(f)=3,j(f)=0) + D reaction, whose differential cross section (DCS) had been computed in a state-of-the-art scattering calculation for a state-of-the-art potential energy surface. Here, v and j are vibrational and rotational quantum numbers, respectively, and the translational energy is 1.81 eV. This paper asks the question: Can we replace the analytic functions (of class C(ω)) used by Shan-Connor with simpler mathematical functions and still reproduce the forward-angle glory scattering? We first construct S matrix elements (of class C(0)) using a quadratic phase and a piecewise-continuous pre-exponential factor consisting of three pieces. Two of the pieces are constants, with one taking the value N (a real normalization constant) at small values of the total angular momentum number, J; the other piece has the value 0 at large J. These two pieces are joined at intermediate values of J by either a straight line, giving rise to the linear parametrization (denoted param L), or a quadratic curve, which defines the quadratic parametrization (param Q). We find that both param L and param Q can reproduce the glory scattering for center-of-mass reactive scattering angles, θ(R) ≲ 30°. Second, we use a piecewise-discontinuous pre-exponential factor and a quadratic phase, giving rise to a step-function parametrization (param SF) and a top-hat parametrization (param TH). We find that both param SF and param TH can reproduce the forward-angle scattering, even though these class C(-1) parametrizations are usually considered too simplistic to be useful for calculations of DCSs. We find that an ultrasimplistic param THz, which is param TH with a phase of zero, can also reproduce the glory scattering at forward angles. The S matrix elements for
Zhang, Huaguang; Jiang, He; Luo, Chaomin; Xiao, Geyang
2016-10-03
In this paper, we investigate the nonzero-sum games for a class of discrete-time (DT) nonlinear systems by using a novel policy iteration (PI) adaptive dynamic programming (ADP) method. The main idea of our proposed PI scheme is to utilize the iterative ADP algorithm to obtain the iterative control policies, which not only ensure the system to achieve stability but also minimize the performance index function for each player. This paper integrates game theory, optimal control theory, and reinforcement learning technique to formulate and handle the DT nonzero-sum games for multiplayer. First, we design three actor-critic algorithms, an offline one and two online ones, for the PI scheme. Subsequently, neural networks are employed to implement these algorithms and the corresponding stability analysis is also provided via the Lyapunov theory. Finally, a numerical simulation example is presented to demonstrate the effectiveness of our proposed approach.
NASA Astrophysics Data System (ADS)
Singh, Vikas; Xu, Jinhui; Hoffmann, Kenneth R.; Noël, Peter B.; Walczak, Alan M.
2006-03-01
Multi-view imaging is the primary modality for high-spatial-resolution imaging of the vasculature. The 3D vascular structure can be reconstructed if the imaging geometries are determined using known corresponding point-pairs (or k-tuples) in two or more images. Because the accuracy improves with more input corresponding point-pairs, we propose a new technique to automatically determine corresponding point-pairs in multi-view (k-view) images, from 2D vessel image centerlines. We formulate the problem, first as a multi-partite graph-matching problem. Each 2D centerline point is a vertex; each individual graph contains all vessel-points (vertices) in an image. The weight ('cost') of the edges between vertices (in different graphs) is the shortest distance between the points' respective projection-lines. Using this construction, a universe of mappings (k-tuples) is created, each k-tuple having k vertices (one from each image). A k-tuple's weight is the sum of pair-wise 'costs' of its members. Ideally, a set of such mappings is desired that preserves the ordering of points along the vessel and minimizes an appropriate global cost function, such that all vertices (in all graphs) participate in at least one mapping. We formulate this problem as a special case of the well-studied Set-Cover problem with additional constraints. Then, the equivalent linear program is solved, and randomized-rounding techniques are used to yield a feasible set of mappings. Our algorithm is efficient and yields a theoretical quality guarantee. In simulations, the correct matching is achieved in ~98% cases, even with high input error. In clinical data, apparently correct matching is achieved in >90% cases. This method should provide the basis for improving the calculated 3D vasculature from multi-view data-sets.
Quadratic finite elements and incompressible viscous flows.
Dohrmann, Clark R.; Gartling, David K.
2005-01-01
Pressure stabilization methods are applied to higher-order velocity finite elements for application to viscous incompressible flows. Both a standard pressure stabilizing Petrov-Galerkin (PSPG) method and a new polynomial pressure projection stabilization (PPPS) method have been implemented and tested for various quadratic elements in two dimensions. A preconditioner based on relaxing the incompressibility constraint is also tested for the iterative solution of saddle point problems arising from mixed Galerkin finite element approximations to the Navier-Stokes equations. The preconditioner is demonstrated for BB stable elements with discontinuous pressure approximations in two and three dimensions.
Constrained neural approaches to quadratic assignment problems.
Ishii, S; Sato, M
1998-08-01
In this paper, we discuss analog neural approaches to the quadratic assignment problem (QAP). These approaches employ a hard constraints scheme to restrict the domain space, and are able to obtain much improved solutions over conventional neural approaches. Since only a few strong heuristics for QAP have been known to date, our approaches are good alternatives, capable of obtaining fairly good solutions in a short period of time. Some of them can also be applied to large-scale problems, say of size N>/=300.
A quadratic analog-to-digital converter
NASA Technical Reports Server (NTRS)
Harrison, D. C.; Staples, M. H.
1980-01-01
An analog-to-digital converter with a square root transfer function has been developed for use with a pair of CCD imaging detectors in the White Light Coronagraph/X-ray XUV Telescope experiment to be flown as part of the Internal Solar Polar Mission. It is shown that in background-noise-limited instrumentation systems a quadratic analog-to-digital converter will allow a maximum dynamic range with a fixed number of data bits. Low power dissipation, moderately fast conversion time, and reliability are achieved in the proposed design using standard components and avoiding nonlinear elements.
A quadratic analog-to-digital converter
NASA Technical Reports Server (NTRS)
Harrison, D. C.; Staples, M. H.
1980-01-01
An analog-to-digital converter with a square root transfer function has been developed for use with a pair of CCD imaging detectors in the White Light Coronagraph/X-ray XUV Telescope experiment to be flown as part of the Internal Solar Polar Mission. It is shown that in background-noise-limited instrumentation systems a quadratic analog-to-digital converter will allow a maximum dynamic range with a fixed number of data bits. Low power dissipation, moderately fast conversion time, and reliability are achieved in the proposed design using standard components and avoiding nonlinear elements.
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.
Approximate algorithms for fast optimal attitude computation
NASA Technical Reports Server (NTRS)
Shuster, M. D.
1978-01-01
Fast accurate algorithms are presented for computing an optimal attitude which minimizes a quadratic loss function. These algorithms compute an optimal rotation which carries a set of reference vectors into a set of corresponding observation vectors. Simplifications of these algorithms are obtained for the case of small rotation angles. Applications to the Magsat mission are discussed.
Using quadratic simplicial elements for hierarchical approximation and visualization
NASA Astrophysics Data System (ADS)
Wiley, David F.; Childs, Henry R.; Hamann, Bernd; Joy, Kenneth I.; Max, Nelson
2002-03-01
Best quadratic simplicial spline approximations can be computed, using quadratic Bernstein-Bezier basis functions, by identifying and bisecting simplicial elements with largest errors. Our method begins with an initial triangulation of the domain; a best quadratic spline approximation is computed; errors are computed for all simplices; and simplices of maximal error are subdivided. This process is repeated until a user-specified global error tolerance is met. The initial approximations for the unit square and cube are given by two quadratic triangles and five quadratic tetrahedra, respectively. Our more complex triangulation and approximation method that respects field discontinuities and geometrical features allows us to better approximate data. Data is visualized by using the hierarchy of increasingly better quadratic approximations generated by this process. Many visualization problems arise for quadratic elements. First tessellating quadratic elements with smaller linear ones and then rendering the smaller linear elements is one way to visualize quadratic elements. Our results show a significant reduction in the number of simplices required to approximate data sets when using quadratic elements as compared to using linear elements.
Prompt critical control of the ACRR using a linear quadratic regulator design
Gilkey, J.C.
1992-09-01
This paper describes the application of linear control design techniques to the problem of nuclear reactor control. The control algorithm consists of generating a nominal trajectory within the control authority of the reactor rod drives, and then following this trajectory with a gain scheduled linear quadratic regulator (LQR). A controller based on this algorithm has generated power pulses up to 100 MW on Sandia`s Annular Core Research Reactor (ACRR). Prompt critical control at $1.02 net reactivity and controlled start up rates over 350 DPM have also been demonstrated using tills controller.
Prompt critical control of the ACRR using a linear quadratic regulator design
Gilkey, J.C.
1992-01-01
This paper describes the application of linear control design techniques to the problem of nuclear reactor control. The control algorithm consists of generating a nominal trajectory within the control authority of the reactor rod drives, and then following this trajectory with a gain scheduled linear quadratic regulator (LQR). A controller based on this algorithm has generated power pulses up to 100 MW on Sandia's Annular Core Research Reactor (ACRR). Prompt critical control at $1.02 net reactivity and controlled start up rates over 350 DPM have also been demonstrated using tills controller.
Prompt critical control of the ACRR using a linear quadratic regulator design
Gilkey, J.C. )
1993-01-20
This paper describes the application of Modern Control'' design techniques to the problem of nuclear reactor control. The control algorithm consists of generating a nominal trajectory within the control authority of the reactor rod drives, and then following this trajectory with a gain scheduled linear quadratic regulator (LQR). A controller based on this algorithm has generated power pulses up to 100 mW on Sandia's Annular Core Research Reactor (ACRR). Prompt critical control at $1.02 net reactivity and at start-up rates over 350 decades per minute (DPM) has also been demonstrated using this controller.
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.
Victor, Jonathan D; Goldberg, David H; Gardner, Daniel
2007-04-15
Cost-based metrics formalize notions of distance, or dissimilarity, between two spike trains, and are applicable to single- and multineuronal responses. As such, these metrics have been used to characterize neural variability and neural coding. By examining the structure of an efficient algorithm [Aronov D, 2003. Fast algorithm for the metric-space analysis of simultaneous responses of multiple single neurons. J Neurosci Methods 124(2), 175-79] implementing a metric for multineuronal responses, we determine criteria for its generalization, and identify additional efficiencies that are applicable when related dissimilarity measures are computed in parallel. The generalized algorithm provides the means to test a wide range of coding hypotheses.
Status report: Data management program algorithm evaluation activity at Marshall Space Flight Center
NASA Technical Reports Server (NTRS)
Jayroe, R. R., Jr.
1977-01-01
An algorithm evaluation activity was initiated to study the problems associated with image processing by assessing the independent and interdependent effects of registration, compression, and classification techniques on LANDSAT data for several discipline applications. The objective of the activity was to make recommendations on selected applicable image processing algorithms in terms of accuracy, cost, and timeliness or to propose alternative ways of processing the data. As a means of accomplishing this objective, an Image Coding Panel was established. The conduct of the algorithm evaluation is described.
NASA Astrophysics Data System (ADS)
Chang, L.; Chen, Y.; Pan, C.
2009-12-01
Surface water resources are strongly influenced by hydrological conditions, and using only surface water resources as water supplies may have higher shortage risk than before because of the climate change caused by the global warming. Conjunctive use of surface and subsurface water is one of the most effective water resource practices to increase water supply reliability with minimal cost and environmental impact. Therefore, this paper presents a novel stepwise optimization model for optimizing the conjunctive use of surface and subsurface water resources management. At each time step, a two level decomposition approach was proposed to divide the nonlinear optimal conjunctive use problem into a linear surface water subproblem and a nonlinear groundwater subproblem. Because of the two level decomposition approach, a hybrid framework is used for the implementation of the conjunctive use model. In the hybrid framework, evolution algorithms, Genetic Algorithm (GA) and Artificial Neural Network (ANN), and Linear Programming (LP) are used for model solving. GA and LP are respectively used for determining the optimal pumping quantities and reservoir allocation, and ANN is used for the groundwater simulation. In the groundwater simulation, this study uses an ANN to simulate groundwater response and greatly reduce computational loading for unconfined aquifers, unlike conventional “response matrix method” or “embedding method”. Because of the very high performance of LP, the usage of LP for the linear surface water subproblem can significantly decrease the computational burden of entire model. In this study, four cases have been demonstrated. Case #1 is a pure surface water case and others are conjunctive use cases. In Case #2, “surface water supply firstly” is the supply principle between surface water. In Case #3 and #4, the “Index Balance” theory is the supply principle and different operation curves used in different cases respectively. The case result
Programming Non-Trivial Algorithms in the Measurement Based Quantum Computation Model
Alsing, Paul; Fanto, Michael; Lott, Capt. Gordon; Tison, Christoper C.
2014-01-01
We provide a set of prescriptions for implementing a quantum circuit model algorithm as measurement based quantum computing (MBQC) algorithm1, 2 via a large cluster state. As means of illustration we draw upon our numerical modeling experience to describe a large graph state capable of searching a logical 8 element list (a non-trivial version of Grover's algorithm3 with feedforward). We develop several prescriptions based on analytic evaluation of cluster states and graph state equations which can be generalized into any circuit model operations. Such a resulting cluster state will be able to carry out the desired operation with appropriate measurements and feed forward error correction. We also discuss the physical implementation and the analysis of the principal 3-qubit entangling gate (Toffoli) required for a non-trivial feedforward realization of an 8-element Grover search algorithm.
Algorithmic Bricks: A Tangible Robot Programming Tool for Elementary School Students
ERIC Educational Resources Information Center
Kwon, D.-Y.; Kim, H.-S.; Shim, J.-K.; Lee, W.-G.
2012-01-01
Tangible programming tools enable children to easily learn the programming process, previously considered to be difficult for them. While various tangible programming tools have been developed, there is still a lack of available tools to help students experience the general programming process. This study therefore developed a tool called…
Algorithmic Bricks: A Tangible Robot Programming Tool for Elementary School Students
ERIC Educational Resources Information Center
Kwon, D.-Y.; Kim, H.-S.; Shim, J.-K.; Lee, W.-G.
2012-01-01
Tangible programming tools enable children to easily learn the programming process, previously considered to be difficult for them. While various tangible programming tools have been developed, there is still a lack of available tools to help students experience the general programming process. This study therefore developed a tool called…
Unai, Shinya; Tanaka, Daizo; Ruggiero, Nicholas; Hirose, Hitoshi; Cavarocchi, Nicholas C
2016-03-01
Extracorporeal membrane oxygenation (ECMO) in our institution resulted in near total mortality prior to the establishment of an algorithm-based program in July 2010. We hypothesized that an algorithm-based ECMO program improves the outcome of patients with acute myocardial infarction complicated with cardiogenic shock. Between March 2003 and July 2013, 29 patients underwent emergent catheterization for acute myocardial infarction due to left main or proximal left anterior descending artery occlusion complicated with cardiogenic shock (defined as systolic blood pressure <90 mm Hg despite multiple inotropes, with or without intra-aortic balloon pump, lactic acidosis). Of 29 patients, 15 patients were treated before July 2010 (Group 1, old program), and 14 patients were treated after July 2010 (Group 2, new program). There were no significant differences in the baseline characteristics, including age, sex, coronary risk factors, and left ventricular ejection fraction between the two groups. Cardiopulmonary resuscitation prior to ECMO was performed in two cases (13%) in Group 1 and four cases (29%) in Group 2. ECMO support was performed in one case (6.7%) in Group 1 and six cases (43%) in Group 2. The 30-day survival of Group 1 versus Group 2 was 40 versus 79% (P = 0.03), and 1-year survival rate was 20 versus 56% (P = 0.01). The survival rate for patients who underwent ECMO was 0% in Group 1 versus 83% in Group 2 (P = 0.09). In Group 2, the mean duration on ECMO was 9.8 ± 5.9 days. Of the six patients who required ECMO in Group 2, 100% were successfully weaned off ECMO or were bridged to ventricular assist device implantation. Initiation of an algorithm-based ECMO program improved the outcomes in patients with acute myocardial infarction complicated by cardiogenic shock.
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
Some Aspects of Quadratic Generalized White Noise Functionals
NASA Astrophysics Data System (ADS)
Si, Si; Hida, Takeyuki
2009-02-01
We shall discuss some particular roles of quadratic generalized white noise functionals. First observation is made from the viewpoint of the so-called "la passage du fini à l'infini". We then come to a dual pairing of spaces formed by quadratic generalized white noise functionals. In this line, we can further discuss quadratic forms of differential operators acting on the space of white noise functionals.
A quadratic pulse height analyzer for space applications.
NASA Technical Reports Server (NTRS)
Burtis, D. W.; Aalami, D.; Evelyn-Veere, R. H.; Sarkady, A. A.
1972-01-01
A flight-worthy pulse height analyzer that has a quadratic transfer function is described. This quadratic function permits optimum usage of the entire PHA dynamic range due to the quadratic nature of the gamma ray spectrometer's resolution vs energy. After the theoretical design discussion, the implementation of the design is examined and test results described. The analyzer is part of the University of New Hampshire gamma ray monitor for OSO-H.
ERIC Educational Resources Information Center
Olmstead, Eugene
1995-01-01
Explores quadratic functions using the graphing calculator. Discoveries are made graphically whereas hypotheses are proven algebraically. Includes traditional quadratics, other algebraic quadratics, nonpolynomial quadratics, transcendental quadratics, and proofs. (MKR)
Steller Structure Treatment of Quadratic Gravity
NASA Astrophysics Data System (ADS)
Chen, Y.; Shao, C.; Chen, X.
2001-07-01
A scheme for considering stellar structure by taking advantage of the quadratic theory of gravitation in four-dimensions is proposed, citing the fact that the possible deviation of gravity in astrophysical systems from the Newtonian inverse square law can be explained through the use of this theory. A modified Lane-Emden equation is derived by making use of the linearized static field equation of quadratic gravity and the polytropic equation of state for a fluid. The influence on stellar structure of the additional force included in quadratic gravity is investigated. It is shown that the additional force can be treated as a perturbation of a bound system by solutions of the modified Lane-Emden equation and an order-of-magnitude analysis. %ZY. Fujii, Nature (London) 234 (1971), 5; Phys. Rev. D9 (1974), 874. D. R. Long, Phys. Rev. D 9 (1974), 850. J. O'Hanlon, Phys. Rev. Lett. 29 (1972), 137. D. R. Mikkelson and M. J. Newman, Phys. Rev. D 16 (1977), 919. R. V. Wagoner, Phys. Rev. D 1 (1970), 3209. J. Z. Xu and Y. H. Chen, Gen. Relat. Gravit. J. 23 (1991), 169. K. S. Stelle, Gen. Relat. Gravit. J. 8 (1978), 631. C. Xu and G. F. R. Ellis, Class. Quant. Grav. 8 (1991), 1747. A. Eddington, The Mathematical Theory of Relativity, 2nd ed. (Cambridge University Press, Cambridge, 1924). W. Pauli, Theory of Relativity (Pergamon Press, New York, 1921). H. A. Buchdahl, Proc. Edinburgh Math. Soc. 8 (1948), 89. J. D. Barrow and A. C. Ottewill, J. of Phys. A 16 (1983), 2757. M. B. Mijic, M. S. Morris and W. M. Suen, Phys. Rev. D 34 (1986), 2934. A. L. Berkin, Phys. Rev. D 42 (1990), 1017. N. D. Birrell and P. C. W. Davies, Quantum Field in Curved Space (Cambridge University Press, 1982). E. T. Tomboulis, Quantum Theory of Gravity, ed. S. M. Christensen (Bristol: Adam Hilger 1984). H. J. Treder, Ann. der Phys. 32 (1975), 383. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York 1972). E. N. Glass and G. Szamosi
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.
Polarization Nonlinear Optics of Quadratically Nonlinear Azopolymers
Konorov, S.O.; Akimov, D.A.; Ivanov, A.A.; Petrov, A.N.; Alfimov, M.V.; Yakimanskii, A.V.; Smirnov, N.N.; Ivanova, V.N.; Kudryavtsev, V.V.; Podshivalov, A.A.; Sokolova, I.M.; Zheltikov, A.M.
2005-07-15
The polarization properties of second harmonic and sum-frequency signals generated by femtosecond laser pulses in films of polymers containing covalent groups of an azobenzothiazole chromophore polarized by an external electric field are investigated. It is shown that the methods of polarization nonlinear optics make it possible to determine the structure of oriented molecular dipoles and reveal important properties of the motion of collectivized {pi}electrons in organic molecules with strong optical nonlinearities. The polarization measurements show that the tensor of quadratic nonlinear optical susceptibility of chromophore fragments oriented by an external field in macromolecules of the noted azopolymers has a degenerate form. This is indicative of a predominantly one-dimensional character of motion of collectivized {pi} electrons along an extended group of atoms in such molecules.
Forced oscillations in quadratically damped systems
NASA Technical Reports Server (NTRS)
Bayliss, A.
1978-01-01
Bayliss (1975) has studied the question whether in the case of linear differential equations the relationship between the stability of the homogeneous equations and the existence of almost periodic solutions to the inhomogeneous equation is preserved by finite difference approximations. In the current investigation analogous properties are considered for the case in which the damping is quadratic rather than linear. The properties of the considered equation for arbitrary forcing terms are examined and the validity is proved of a theorem concerning the characteristics of the unique solution. By using the Lipschitz continuity of the mapping and the contracting mapping principle, almost periodic solutions can be found for perturbations of the considered equation. Attention is also given to the Lipschitz continuity of the solution operator and the results of numerical tests which have been conducted to test the discussed theory.
Compact stars with quadratic equation of state
NASA Astrophysics Data System (ADS)
Ngubelanga, Sifiso A.; Maharaj, Sunil D.; Ray, Subharthi
2015-05-01
We provide new exact solutions to the Einstein-Maxwell system of equations for matter configurations with anisotropy and charge. The spacetime is static and spherically symmetric. A quadratic equation of state is utilised for the matter distribution. By specifying a particular form for one of the gravitational potentials and the electric field intensity we obtain new exact solutions in isotropic coordinates. In our general class of models, an earlier model with a linear equation of state is regained. For particular choices of parameters we regain the masses of the stars PSR J1614-2230, 4U 1608-52, PSR J1903+0327, EXO 1745-248 and SAX J1808.4-3658. A comprehensive physical analysis for the star PSR J1903+0327 reveals that our model is reasonable.
On Coupled Rate Equations with Quadratic Nonlinearities
Montroll, Elliott W.
1972-01-01
Rate equations with quadratic nonlinearities appear in many fields, such as chemical kinetics, population dynamics, transport theory, hydrodynamics, etc. Such equations, which may arise from basic principles or which may be phenomenological, are generally solved by linearization and application of perturbation theory. Here, a somewhat different strategy is emphasized. Alternative nonlinear models that can be solved exactly and whose solutions have the qualitative character expected from the original equations are first searched for. Then, the original equations are treated as perturbations of those of the solvable model. Hence, the function of the perturbation theory is to improve numerical accuracy of solutions, rather than to furnish the basic qualitative behavior of the solutions of the equations. PMID:16592013
Mammogram enhancement using alpha weighted quadratic filter.
Zhou, Yicong; Panetta, Karen; Agaian, Sos
2009-01-01
Mammograms are widely used to detect breast cancer in women. The quality of the image may suffer from poor resolution or low contrast due to the limitations of the X-ray hardware systems. Image enhancement is a powerful tool to improve the visual quality of mammograms. This paper introduces a new powerful nonlinear filter called the alpha weighted quadratic filter for mammogram enhancement. The user has the flexibility to design the filter by selecting all of the parameters manually or using an existing quantitative measure to select the optimal enhancement parameters. Computer simulations show that excellent enhancement results can be obtained with no apriori knowledge of the mammogram contents. The filter can also be used for automatic segmentation.
An optimal approach for the critical node problem using semidefinite programming
NASA Astrophysics Data System (ADS)
Jiang, Cheng; Liu, Zhonghua; Wang, Juyun; Yu, Hua; Guo, Xiaoling
2017-04-01
Detecting critical nodes in complex networks (CNP) has great theoretical and practical significance in many disciplines. The existing formulations for CNP are mostly, as we know, based on the integer linear programming model. However, we observed that, these formulations only considered the sizes but neglected the cohesiveness properties of the connected components in the induced network. To solve the problem and improve the performance of CNP solutions, we construct a novel nonconvex quadratically constrained quadratic programming (QCQP) model and derive its approximation solutions via semidefinite programming (SDP) technique and heuristic algorithms. Various types of synthesized and real-world networks, in the context of different connectivity patterns, are used to validate and verify the effectiveness of the proposed model and algorithm. Experimental results show that our method improved the state of the art of the CNP.
Learning control for minimizing a quadratic cost during repetitions of a task
NASA Technical Reports Server (NTRS)
Longman, Richard W.; Chang, Chi-Kuang
1990-01-01
In many applications, control systems are asked to perform the same task repeatedly. Learning control laws have been developed over the last few years that allow the controller to improve its performance each repetition, and to converge to zero error in tracking a desired trajectory. This paper generates a new type of learning control law that learns to minimize a quadratic cost function for tracking. Besides being of interest in its own right, this objective alleviates the need to specify a desired trajectory that can actually be performed by the system. The approach used here is to adapt appropriate methods from numerical optimization theory in order to produce learning control algorithms that adjust the system command from repetition to repetition in order to converge to the quadratic cost optimal trajectory.
Learning control for minimizing a quadratic cost during repetitions of a task
NASA Technical Reports Server (NTRS)
Longman, Richard W.; Chang, Chi-Kuang
1990-01-01
In many applications, control systems are asked to perform the same task repeatedly. Learning control laws have been developed over the last few years that allow the controller to improve its performance each repetition, and to converge to zero error in tracking a desired trajectory. This paper generates a new type of learning control law that learns to minimize a quadratic cost function for tracking. Besides being of interest in its own right, this objective alleviates the need to specify a desired trajectory that can actually be performed by the system. The approach used here is to adapt appropriate methods from numerical optimization theory in order to produce learning control algorithms that adjust the system command from repetition to repetition in order to converge to the quadratic cost optimal trajectory.
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.
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.
Genetic algorithms and MCML program for recovery of optical properties of homogeneous turbid media
Morales Cruzado, Beatriz; y Montiel, Sergio Vázquez; Atencio, José Alberto Delgado
2013-01-01
In this paper, we present and validate a new method for optical properties recovery of turbid media with slab geometry. This method is an iterative method that compares diffuse reflectance and transmittance, measured using integrating spheres, with those obtained using the known algorithm MCML. The search procedure is based in the evolution of a population due to selection of the best individual, i.e., using a genetic algorithm. This new method includes several corrections such as non-linear effects in integrating spheres measurements and loss of light due to the finite size of the sample. As a potential application and proof-of-principle experiment of this new method, we use this new algorithm in the recovery of optical properties of blood samples at different degrees of coagulation. PMID:23504404
Genetic algorithms and MCML program for recovery of optical properties of homogeneous turbid media.
Morales Cruzado, Beatriz; Y Montiel, Sergio Vázquez; Atencio, José Alberto Delgado
2013-03-01
In this paper, we present and validate a new method for optical properties recovery of turbid media with slab geometry. This method is an iterative method that compares diffuse reflectance and transmittance, measured using integrating spheres, with those obtained using the known algorithm MCML. The search procedure is based in the evolution of a population due to selection of the best individual, i.e., using a genetic algorithm. This new method includes several corrections such as non-linear effects in integrating spheres measurements and loss of light due to the finite size of the sample. As a potential application and proof-of-principle experiment of this new method, we use this new algorithm in the recovery of optical properties of blood samples at different degrees of coagulation.
Solution of transient optimization problems by using an algorithm based on nonlinear programming
NASA Technical Reports Server (NTRS)
Teren, F.
1977-01-01
A new algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.
Solution of transient optimization problems by using an algorithm based on nonlinear programming
NASA Technical Reports Server (NTRS)
Teren, F.
1977-01-01
An algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.
Solution of transient optimization problems by using an algorithm based on nonlinear programming
NASA Technical Reports Server (NTRS)
Teren, F.
1977-01-01
A new algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.
Biswas, Abhishek; Ranjan, Desh; Zubair, Mohammad; He, Jing
2015-09-01
The determination of secondary structure topology is a critical step in deriving the atomic structures from the protein density maps obtained from electron cryomicroscopy technique. This step often relies on matching the secondary structure traces detected from the protein density map to the secondary structure sequence segments predicted from the amino acid sequence. Due to inaccuracies in both sources of information, a pool of possible secondary structure positions needs to be sampled. One way to approach the problem is to first derive a small number of possible topologies using existing matching algorithms, and then find the optimal placement for each possible topology. We present a dynamic programming method of Θ(Nq(2)h) to find the optimal placement for a secondary structure topology. We show that our algorithm requires significantly less computational time than the brute force method that is in the order of Θ(q(N) h).
Pillió, Zoltán; Tajti, Attila; Szalay, Péter G
2012-09-11
A new algorithm is presented for the calculation of the ladder-type term of the coupled cluster singles and doubles (CCSD) equations using two-electron integrals in atomic orbital (AO) basis. The method is based on an orbital grouping scheme, which results in an optimal partitioning of the AO integral matrix into sparse and dense blocks allowing efficient matrix multiplication. Carefully chosen numerical tests have been performed to analyze the performance of all aspects of the new algorithm. It is shown that the suggested scheme allows an efficient utilization of modern highly parallel architectures and devices in CCSD calculations. Details of the implementation in the development version of CFOUR quantum chemical program package are also presented.
Evaluation of a particle swarm algorithm for biomechanical optimization.
Schutte, Jaco F; Koh, Byung-Il; Reinbolt, Jeffrey A; Haftka, Raphael T; George, Alan D; Fregly, Benjamin J
2005-06-01
Optimization is frequently employed in biomechanics research to solve system identification problems, predict human movement, or estimate muscle or other internal forces that cannot be measured directly. Unfortunately, biomechanical optimization problems often possess multiple local minima, making it difficult to find the best solution. Furthermore, convergence in gradient-based algorithms can be affected by scaling to account for design variables with different length scales or units. In this study we evaluate a recently-developed version of the particle swarm optimization (PSO) algorithm to address these problems. The algorithm's global search capabilities were investigated using a suite of difficult analytical test problems, while its scale-independent nature was proven mathematically and verified using a biomechanical test problem. For comparison, all test problems were also solved with three off-the-shelf optimization algorithms--a global genetic algorithm (GA) and multistart gradient-based sequential quadratic programming (SQP) and quasi-Newton (BFGS) algorithms. For the analytical test problems, only the PSO algorithm was successful on the majority of the problems. When compared to previously published results for the same problems, PSO was more robust than a global simulated annealing algorithm but less robust than a different, more complex genetic algorithm. For the biomechanical test problem, only the PSO algorithm was insensitive to design variable scaling, with the GA algorithm being mildly sensitive and the SQP and BFGS algorithms being highly sensitive. The proposed PSO algorithm provides a new off-the-shelf global optimization option for difficult biomechanical problems, especially those utilizing design variables with different length scales or units.
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
Ament, D; Ho, J; Loute, E; Remmelswaal, M
1980-06-01
Nested decomposition of linear programs is the result of a multilevel, hierarchical application of the Dantzig-Wolfe decomposition principle. The general structure is called lower block-triangular, and permits direct accounting of long-term effects of investment, service life, etc. LIFT, an algorithm for solving lower block triangular linear programs, is based on state-of-the-art modular LP software. The algorithmic and software aspects of LIFT are outlined, and computational results are presented. 5 figures, 6 tables. (RWR)
NASA Astrophysics Data System (ADS)
Paino, A.; Keller, J.; Popescu, M.; Stone, K.
2014-06-01
In this paper we present an approach that uses Genetic Programming (GP) to evolve novel feature extraction algorithms for greyscale images. Our motivation is to create an automated method of building new feature extraction algorithms for images that are competitive with commonly used human-engineered features, such as Local Binary Pattern (LBP) and Histogram of Oriented Gradients (HOG). The evolved feature extraction algorithms are functions defined over the image space, and each produces a real-valued feature vector of variable length. Each evolved feature extractor breaks up the given image into a set of cells centered on every pixel, performs evolved operations on each cell, and then combines the results of those operations for every cell using an evolved operator. Using this method, the algorithm is flexible enough to reproduce both LBP and HOG features. The dataset we use to train and test our approach consists of a large number of pre-segmented image "chips" taken from a Forward Looking Infrared Imagery (FLIR) camera mounted on the hood of a moving vehicle. The goal is to classify each image chip as either containing or not containing a buried object. To this end, we define the fitness of a candidate solution as the cross-fold validation accuracy of the features generated by said candidate solution when used in conjunction with a Support Vector Machine (SVM) classifier. In order to validate our approach, we compare the classification accuracy of an SVM trained using our evolved features with the accuracy of an SVM trained using mainstream feature extraction algorithms, including LBP and HOG.
Machnes, S.; Sander, U.; Glaser, S. J.; Schulte-Herbrueggen, T.; Fouquieres, P. de; Gruslys, A.; Schirmer, S.
2011-08-15
For paving the way to novel applications in quantum simulation, computation, and technology, increasingly large quantum systems have to be steered with high precision. It is a typical task amenable to numerical optimal control to turn the time course of pulses, i.e., piecewise constant control amplitudes, iteratively into an optimized shape. Here, we present a comparative study of optimal-control algorithms for a wide range of finite-dimensional applications. We focus on the most commonly used algorithms: GRAPE methods which update all controls concurrently, and Krotov-type methods which do so sequentially. Guidelines for their use are given and open research questions are pointed out. Moreover, we introduce a unifying algorithmic framework, DYNAMO (dynamic optimization platform), designed to provide the quantum-technology community with a convenient matlab-based tool set for optimal control. In addition, it gives researchers in optimal-control techniques a framework for benchmarking and comparing newly proposed algorithms with the state of the art. It allows a mix-and-match approach with various types of gradients, update and step-size methods as well as subspace choices. Open-source code including examples is made available at http://qlib.info.
Gonçalves, Cristina P; Mohallem, José R
2004-11-15
We report the development of a simple algorithm to modify quantum chemistry codes based on the LCAO procedure, to account for the isotope problem in electronic structure calculations. No extra computations are required compared to standard Born-Oppenheimer calculations. An upgrade of the Gamess package called ISOTOPE is presented, and its applicability is demonstrated in some examples.
An Extension of CART's Pruning Algorithm. Program Statistics Research Technical Report No. 91-11.
ERIC Educational Resources Information Center
Kim, Sung-Ho
Among the computer-based methods used for the construction of trees such as AID, THAID, CART, and FACT, the only one that uses an algorithm that first grows a tree and then prunes the tree is CART. The pruning component of CART is analogous in spirit to the backward elimination approach in regression analysis. This idea provides a tool in…
Effect of Algorithms' Multiple Representations in the Context of Programming Education
ERIC Educational Resources Information Center
Siozou, Stefania; Tselios, Nikolaos; Komis, Vassilis
2008-01-01
Purpose: The purpose of this paper is to compare the effect of different representations while teaching basic algorithmic concepts to novice programmers. Design/methodology/approach: A learning activity was designed and mediated with two conceptually different learning environments, each one used by a different group. The first group used the…
Effect of Algorithms' Multiple Representations in the Context of Programming Education
ERIC Educational Resources Information Center
Siozou, Stefania; Tselios, Nikolaos; Komis, Vassilis
2008-01-01
Purpose: The purpose of this paper is to compare the effect of different representations while teaching basic algorithmic concepts to novice programmers. Design/methodology/approach: A learning activity was designed and mediated with two conceptually different learning environments, each one used by a different group. The first group used the…
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…
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…
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…
Convexity preserving C2 rational quadratic trigonometric spline
NASA Astrophysics Data System (ADS)
Dube, Mridula; Tiwari, Preeti
2012-09-01
A C2 rational quadratic trigonometric spline interpolation has been studied using two kind of rational quadratic trigonometric splines. It is shown that under some natural conditions the solution of the problem exits and is unique. The necessary and sufficient condition that constrain the interpolation curves to be convex in the interpolating interval or subinterval are derived.
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.)
Geometric quadratic stochastic operator on countable infinite set
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.
A Constructive Transition from Linear to Quadratic Functions.
ERIC Educational Resources Information Center
Movshovitz-Hadar, Nitsa
1993-01-01
Presents an approach to quadratic functions that draws upon knowledge of linear functions by looking at the product of two linear functions. Then considers the quadratic function as the sum of three monomials. Potential advantages of each approach are discussed. (Contains 17 references.) (MDH)
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.)
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…
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…
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…
SPARSE REPRESENTATIONS WITH DATA FIDELITY TERM VIA AN ITERATIVELY REWEIGHTED LEAST SQUARES ALGORITHM
WOHLBERG, BRENDT; RODRIGUEZ, PAUL
2007-01-08
Basis Pursuit and Basis Pursuit Denoising, well established techniques for computing sparse representations, minimize an {ell}{sup 2} data fidelity term subject to an {ell}{sup 1} sparsity constraint or regularization term on the solution by mapping the problem to a linear or quadratic program. Basis Pursuit Denoising with an {ell}{sup 1} data fidelity term has recently been proposed, also implemented via a mapping to a linear program. They introduce an alternative approach via an iteratively Reweighted Least Squares algorithm, providing greater flexibility in the choice of data fidelity term norm, and computational advantages in certain circumstances.
Quadratic algebras for three-dimensional superintegrable systems
Daskaloyannis, C. Tanoudis, Y.
2010-02-15
The three-dimensional superintegrable systems with quadratic integrals of motion have five functionally independent integrals, one among them is the Hamiltonian. Kalnins, Kress, and Miller have proved that in the case of nondegenerate potentials with quadratic integrals of motion there is a sixth quadratic integral, which is linearly independent of the other integrals. The existence of this sixth integral implies that the integrals of motion form a ternary parafermionic-like quadratic Poisson algebra with five generators. In this contribution we investigate the structure of this algebra. We show that in all the nondegenerate cases there is at least one subalgebra of three integrals having a Poisson quadratic algebra structure, which is similar to the two-dimensional case.
NASA Astrophysics Data System (ADS)
Qiu, J. P.; Niu, D. X.
Micro-grid is one of the key technologies of the future energy supplies. Take economic planning. reliability, and environmental protection of micro grid as a basis for the analysis of multi-strategy objective programming problems for micro grid which contains wind power, solar power, and battery and micro gas turbine. Establish the mathematical model of each power generation characteristics and energy dissipation. and change micro grid planning multi-objective function under different operating strategies to a single objective model based on AHP method. Example analysis shows that in combination with dynamic ant mixed genetic algorithm can get the optimal power output of this model.
Sadeghi, Mehdi; Parto, Sahar; Arab, Shahriar; Ranjbar, Bijan
2005-06-20
We have used a statistical approach for protein secondary structure prediction based on information theory and simultaneously taking into consideration pairwise residue types and conformational states. Since the prediction of residue secondary structure by one residue window sliding make ambiguity in state prediction, we used a dynamic programming algorithm to find the path with maximum score. A score system for residue pairs in particular conformations is derived for adjacent neighbors up to ten residue apart in sequence. The three state overall per-residue accuracy, Q3, of this method in a jackknife test with dataset created from PDBSELECT is more than 70%.
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.
1991-10-31
Problems, Mathematical Programming Studies, 48:1, 1-18. R. E. Marsten, 1989. User’s Manual for: OB1/XMP, Interior Point Methods for Linear Programming. R. E...Industrial Dr. Istvan Maros E.T.S. Ingenieros Industriales Computer and Automation Institute Jose Gutierrez Abascal, 2 Hungarian Academy of Sciences E
NASA Technical Reports Server (NTRS)
Cochran, D. R.; Ishikawa, M. K.; Paulson, R. E.; Ramsey, H. R.
1975-01-01
A user guide for the Programming Language for Allocation and Network Scheduling (PLANS) is presented. Information is included for the construction of PLANS programs. The basic philosophy of PLANS is discussed, and access and update reference techniques are described along with the use of tree structures.
Multi-Core Programming Design Patterns: Stream Processing Algorithms for Dynamic Scene Perceptions
2014-05-01
reads are dashed lines , writes are solid lines . . . . . . . . . . . . . . 18 15 Performance of the cross-weave (a,b,c,d) and wavefront scan (e,f,g,h...Tools (E2AT) and Next Generation Wide Area Motion Imagery (WAMI). An initial implementation of the 3D spatiotemporal median filter for background...extended the integral histogram approach to design and implement an initial version of the 3D spatiotemporal median filter algorithm for fast motion
Research on an augmented Lagrangian penalty function algorithm for nonlinear programming
NASA Technical Reports Server (NTRS)
Frair, L.
1978-01-01
The augmented Lagrangian (ALAG) Penalty Function Algorithm for optimizing nonlinear mathematical models is discussed. The mathematical models of interest are deterministic in nature and finite dimensional optimization is assumed. A detailed review of penalty function techniques in general and the ALAG technique in particular is presented. Numerical experiments are conducted utilizing a number of nonlinear optimization problems to identify an efficient ALAG Penalty Function Technique for computer implementation.
Validation Data for Mechanical System Algorithms Used in Building Energy Analysis Programs.
1982-02-01
Wae Date Entered) i!I I imr! A4Zr iT Fn SZCURiTY CLASIFICATION OF THIS PAGE(Whia Data 3.iRe. When gathering data to validate the algorithms which...tation in mind , the OES components were chosen as follows: 1. The cooling coil was a six-row coil with a face dimension of 33 X 55 in. (0.84 x 1.4 m). It
Jihong, Qu
2014-01-01
Wind-hydrothermal power system dispatching has received intensive attention in recent years because it can help develop various reasonable plans to schedule the power generation efficiency. But future data such as wind power output and power load would not be accurately predicted and the nonlinear nature involved in the complex multiobjective scheduling model; therefore, to achieve accurate solution to such complex problem is a very difficult task. This paper presents an interval programming model with 2-step optimization algorithm to solve multiobjective dispatching. Initially, we represented the future data into interval numbers and simplified the object function to a linear programming problem to search the feasible and preliminary solutions to construct the Pareto set. Then the simulated annealing method was used to search the optimal solution of initial model. Thorough experimental results suggest that the proposed method performed reasonably well in terms of both operating efficiency and precision. PMID:24895663
Ren, Kun; Jihong, Qu
2014-01-01
Wind-hydrothermal power system dispatching has received intensive attention in recent years because it can help develop various reasonable plans to schedule the power generation efficiency. But future data such as wind power output and power load would not be accurately predicted and the nonlinear nature involved in the complex multiobjective scheduling model; therefore, to achieve accurate solution to such complex problem is a very difficult task. This paper presents an interval programming model with 2-step optimization algorithm to solve multiobjective dispatching. Initially, we represented the future data into interval numbers and simplified the object function to a linear programming problem to search the feasible and preliminary solutions to construct the Pareto set. Then the simulated annealing method was used to search the optimal solution of initial model. Thorough experimental results suggest that the proposed method performed reasonably well in terms of both operating efficiency and precision.
Extremal Optimization for Quadratic Unconstrained Binary Problems
NASA Astrophysics Data System (ADS)
Boettcher, S.
We present an implementation of τ-EO for quadratic unconstrained binary optimization (QUBO) problems. To this end, we transform modify QUBO from its conventional Boolean presentation into a spin glass with a random external field on each site. These fields tend to be rather large compared to the typical coupling, presenting EO with a challenging two-scale problem, exploring smaller differences in couplings effectively while sufficiently aligning with those strong external fields. However, we also find a simple solution to that problem that indicates that those external fields apparently tilt the energy landscape to a such a degree such that global minima become more easy to find than those of spin glasses without (or very small) fields. We explore the impact of the weight distribution of the QUBO formulation in the operations research literature and analyze their meaning in a spin-glass language. This is significant because QUBO problems are considered among the main contenders for NP-hard problems that could be solved efficiently on a quantum computer such as D-Wave.
A Quadratic Closure for Compressible Turbulence
Futterman, J A
2008-09-16
We have investigated a one-point closure model for compressible turbulence based on third- and higher order cumulant discard for systems undergoing rapid deformation, such as might occur downstream of a shock or other discontinuity. In so doing, we find the lowest order contributions of turbulence to the mean flow, which lead to criteria for Adaptive Mesh Refinement. Rapid distortion theory (RDT) as originally applied by Herring closes the turbulence hierarchy of moment equations by discarding third order and higher cumulants. This is similar to the fourth-order cumulant discard hypothesis of Millionshchikov, except that the Millionshchikov hypothesis was taken to apply to incompressible homogeneous isotropic turbulence generally, whereas RDT is applied only to fluids undergoing a distortion that is 'rapid' in the sense that the interaction of the mean flow with the turbulence overwhelms the interaction of the turbulence with itself. It is also similar to Gaussian closure, in which both second and fourth-order cumulants are retained. Motivated by RDT, we develop a quadratic one-point closure for rapidly distorting compressible turbulence, without regard to homogeneity or isotropy, and make contact with two equation turbulence models, especially the K-{var_epsilon} and K-L models, and with linear instability growth. In the end, we arrive at criteria for Adaptive Mesh Refinement in Finite Volume simulations.
NASA Astrophysics Data System (ADS)
Hachmann, Johannes; Cardoen, Wim; Chan, Garnet Kin-Lic
2006-10-01
We have devised a local ab initio density matrix renormalization group algorithm to describe multireference correlations in large systems. For long molecules that are extended in one of their spatial dimensions, we can obtain an exact characterization of correlation, in the given basis, with a cost that scales only quadratically with the size of the system. The reduced scaling is achieved solely through integral screening and without the construction of correlation domains. We demonstrate the scaling, convergence, and robustness of the algorithm in polyenes and hydrogen chains. We converge to exact correlation energies (in the sense of full configuration interaction, with 1-10μEh precision) in all cases and correlate up to 100 electrons in 100 active orbitals. We further use our algorithm to obtain exact energies for the metal-insulator transition in hydrogen chains and compare and contrast our results with those from conventional quantum chemical methods.
Optimization algorithm performance in determining optimal controls in human movement analyses.
Neptune, R R
1999-04-01
The objective of this study was to evaluate the performance of different multivariate optimization algorithms by solving a "tracking" problem using a forward dynamic model of pedaling. The tracking problem was defined as solving for the muscle controls (muscle stimulation onset, offset, and magnitude) that minimized the error between experimentally collected kinetic and kinematic data and the simulation results of pedaling at 90 rpm and 250 W. Three different algorithms were evaluated: a downhill simplex method, a gradient-based sequential quadratic programming algorithm, and a simulated annealing global optimization routine. The results showed that the simulated annealing algorithm performed for superior to the conventional routines by converging more rapidly and avoiding local minima.
Nagurney, A.; Kim, D.S.
1989-01-01
The authors have applied parallel and serial variational inequality (VI) diagonal decomposition algorithms to large-scale multicommodity market equilibrium problems. These decomposition algorithms resolve the VI problems into single commodity problems, which are then solved as quadratic programming problems. The algorithms are implemented on an IBM 3090-600E, and randomly generated linear and nonlinear problems with as many as 100 markets and 12 commodities are solved. The computational results demonstrate that the parallel diagonal decomposition scheme is amenable to parallelization. This is the first time that multicommodity equilibrium problems of this scale and level of generality have been solved. Furthermore, this is the first study to compare the efficiencies of parallel and serial VI decomposition algorithms. Although the authors have selected as a prototype an equilibrium problem in economics, virtually any equilibrium problem can be formulated and studied as a variational inequality problem. Hence, their results are not limited to applications in economics and operations research.
NASA Technical Reports Server (NTRS)
Lien, T.
1981-01-01
The programming and analysis methods to support the development of a thermal model of the Earth's surface from detailed analysis of day/night registered data sets from the Heat Capacity Mapping Mission satellite are briefly described.
Algorithmic Approximation of Optimal Value Differential Stability Bounds in Nonlinear Programming,
1981-08-01
NCLASSIFIED RANO/PA6659 N IN *~4 112.0.0 ~11111,.. I32 111 IIIII 111111.25 MICROCOPY RESOLUTION TESI CHART NATIOt AL BJRLAU Of SIANDARD 1964 A * LEVEL 00 o pm...Sensitivity Analysis in Parametric Nonlinear Programming, Doctoral Dissertation, School of Engineering and Applied Science, The George Washington University...Differential Stability of the Optimal Value Function in Constrained Nonlinear Programing, Doctoral Disser- tation, School of Engineering and Applied
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…
Sequential quadratic programming with step control using the Lagrange function
Danilin, Yu.M.
1995-01-01
This article examines some methods of solving the problem min f (x), x {epsilon} S {contained_in} E{sup n}, S = (x:g{sub j}(x) = O,j = 1,...,t). These methods construct the iterative sequence x{sub k}+1 = x{sub k} + {alpha}{sub k}p{sub k}, k = 0, 1,..., where the vector p{sub k} is the solution of the problem min [
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.
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.
ORACLS - A linear-quadratic-Gaussian computer-aided design package
NASA Technical Reports Server (NTRS)
Armstrong, E. S.
1982-01-01
ORACLS, an acronym denoting Optimal Regular Algorithms for the Control of Linear Systems, is a collection of FORTRAN coded subroutines dedicated to the formulation and solution of the Linear-Quadratic-Gaussian (LQG) design problem modeled in both continuous and discrete form. The ORACLS system is under continuous development at the NASA Langley Research Center, Hampton, Virginia, and is widely used by universities and industry within the U.S.A. The current (operational) ORACLS version as well as new software under development is described.
Ray-tracing simulation method using piecewise quadratic interpolant for aspheric optical systems.
Morita, Shin-Ya; Nishidate, Yohei; Nagata, Takashi; Yamagata, Yutaka; Teodosiu, Cristian
2010-06-20
We present a new method for precise ray-tracing simulation considering form errors in the fabrication process of aspheric lenses. The Nagata patch, a quadratic interpolant for surface meshes using normal vectors, is adopted for representing the lens geometry with mid-spectral frequencies of surface profile errors. Several improvements in the ray-patch intersection calculation and its acceleration technique are also proposed. The developed algorithm is applied to ray-tracing simulation of optical disk pick-up aspheric objectives, and this technique requires 10(5) to 10(9) times fewer patches than a polygonal approximation. The simulation takes only several seconds on a standard PC.
HOW DO YOU SOLVE A QUADRATIC EQUATION
The nature of the floating - point number system of digital computers is explained to a reader whose university mathematical background is very limited...The possibly large errors in using mathematical algorithms blindly with floating - point computation are illustrated by the formula for solving a
Models and Algorithms Involving Very Large Scale Stochastic Mixed-Integer Programs
2011-02-28
give rise to a non - convex and discontinuous recourse function that may be difficult to optimize . As a result of this project, there have been... convex , the master problem in (3.1.6)-(3.1.9) is a non - convex mixed-integer program, and as indicated in [C.1], this approach is not scalable without...the first stage would result in a Benders’ master program which is non - convex , leading to a problem that is not any easier than (3.1.5). Nevertheless
Graph Modeling for Quadratic Assignment Problems Associated with the Hypercube
NASA Astrophysics Data System (ADS)
Mittelmann, Hans; Peng, Jiming; Wu, Xiaolin
2009-07-01
In the paper we consider the quadratic assignment problem arising from channel coding in communications where one coefficient matrix is the adjacency matrix of a hypercube in a finite dimensional space. By using the geometric structure of the hypercube, we first show that there exist at least n different optimal solutions to the underlying QAPs. Moreover, the inherent symmetries in the associated hypercube allow us to obtain partial information regarding the optimal solutions and thus shrink the search space and improve all the existing QAP solvers for the underlying QAPs. Secondly, we use graph modeling technique to derive a new integer linear program (ILP) models for the underlying QAPs. The new ILP model has n(n-1) binary variables and O(n3 log(n)) linear constraints. This yields the smallest known number of binary variables for the ILP reformulation of QAPs. Various relaxations of the new ILP model are obtained based on the graphical characterization of the hypercube, and the lower bounds provided by the LP relaxations of the new model are analyzed and compared with what provided by several classical LP relaxations of QAPs in the literature.
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
An inertia-free filter line-search algorithm for large-scale nonlinear programming
Chiang, Nai-Yuan; Zavala, Victor M.
2016-02-15
We present a filter line-search algorithm that does not require inertia information of the linear system. This feature enables the use of a wide range of linear algebra strategies and libraries, which is essential to tackle large-scale problems on modern computing architectures. The proposed approach performs curvature tests along the search step to detect negative curvature and to trigger convexification. We prove that the approach is globally convergent and we implement the approach within a parallel interior-point framework to solve large-scale and highly nonlinear problems. Our numerical tests demonstrate that the inertia-free approach is as efficient as inertia detection via symmetric indefinite factorizations. We also demonstrate that the inertia-free approach can lead to reductions in solution time because it reduces the amount of convexification needed.
A decentralized linear quadratic control design method for flexible structures
NASA Technical Reports Server (NTRS)
Su, Tzu-Jeng; Craig, Roy R., Jr.
1990-01-01
A decentralized suboptimal linear quadratic control design procedure which combines substructural synthesis, model reduction, decentralized control design, subcontroller synthesis, and controller reduction is proposed for the design of reduced-order controllers for flexible structures. The procedure starts with a definition of the continuum structure to be controlled. An evaluation model of finite dimension is obtained by the finite element method. Then, the finite element model is decomposed into several substructures by using a natural decomposition called substructuring decomposition. Each substructure, at this point, still has too large a dimension and must be reduced to a size that is Riccati-solvable. Model reduction of each substructure can be performed by using any existing model reduction method, e.g., modal truncation, balanced reduction, Krylov model reduction, or mixed-mode method. Then, based on the reduced substructure model, a subcontroller is designed by an LQ optimal control method for each substructure independently. After all subcontrollers are designed, a controller synthesis method called substructural controller synthesis is employed to synthesize all subcontrollers into a global controller. The assembling scheme used is the same as that employed for the structure matrices. Finally, a controller reduction scheme, called the equivalent impulse response energy controller (EIREC) reduction algorithm, is used to reduce the global controller to a reasonable size for implementation. The EIREC reduced controller preserves the impulse response energy of the full-order controller and has the property of matching low-frequency moments and low-frequency power moments. An advantage of the substructural controller synthesis method is that it relieves the computational burden associated with dimensionality. Besides that, the SCS design scheme is also a highly adaptable controller synthesis method for structures with varying configuration, or varying mass
Solving mixed integer nonlinear programming problems using spiral dynamics optimization algorithm
NASA Astrophysics Data System (ADS)
Kania, Adhe; Sidarto, Kuntjoro Adji
2016-02-01
Many engineering and practical problem can be modeled by mixed integer nonlinear programming. This paper proposes to solve the problem with modified spiral dynamics inspired optimization method of Tamura and Yasuda. Four test cases have been examined, including problem in engineering and sport. This method succeeds in obtaining the optimal result in all test cases.
Geometric structure of pseudo-plane quadratic flows
NASA Astrophysics Data System (ADS)
Sun, Che
2017-03-01
Quadratic flows have the unique property of uniform strain and are commonly used in turbulence modeling and hydrodynamic analysis. While previous applications focused on two-dimensional homogeneous fluid, this study examines the geometric structure of three-dimensional quadratic flows in stratified fluid by solving a steady-state pseudo-plane flow model. The complete set of exact solutions reveals that steady quadratic flows have an invariant conic type in the non-rotating frame and a non-rotatory vertical structure in the rotating frame. Three baroclinic solutions with vertically non-aligned formulation disprove an earlier conjecture. All elliptic and hyperbolic solutions, except for the inertial ones, exhibit vertical concentricity. The rich geometry of quadratic flows stands in contrast to the depleted geometry of high-degree polynomial flows. A paradox in the steady solutions of shallow-water reduced-gravity models is also explained.
Linearly convergent inexact proximal point algorithm for minimization. Revision 1
Zhu, C.
1993-08-01
In this paper, we propose a linearly convergent inexact PPA for minimization, where the inner loop stops when the relative reduction on the residue (defined as the objective value minus the optimal value) of the inner loop subproblem meets some preassigned constant. This inner loop stopping criterion can be achieved in a fixed number of iterations if the inner loop algorithm has a linear rate on the regularized subproblems. Therefore the algorithm is able to avoid the computationally expensive process of solving the inner loop subproblems exactly or asymptotically accurately; a process required by most of the other linearly convergent PPAs. As applications of this inexact PPA, we develop linearly convergent iteration schemes for minimizing functions with singular Hessian matrices, and for solving hemiquadratic extended linear-quadratic programming problems. We also prove that Correa-Lemarechal`s ``implementable form`` of PPA converges linearly under mild conditions.
Quadratic bulk viscosity and the topology of space time.
NASA Astrophysics Data System (ADS)
Wolf, C.
1997-12-01
By considering a homogeneous isotropic universe admitting quadratic bulk viscosity the author shows that if the bulk viscosity coefficient is large the effective topology of space time attains an antiintuitive interpretation in the sense that a positive curvature space time is ever-expanding. This is true for all cosmologies studied except in the case of small quadratic bulk viscosity (3γ+1-kβ ≥ 0, 3γ+1 > 0).
Quadratic function approaching method for magnetotelluric soundingdata inversion
Liangjun, Yan; Wenbao, Hu; Zhang, Keni
2004-04-05
The quadratic function approaching method (QFAM) is introduced for magnetotelluric sounding (MT) data inversion. The method takes the advantage of that quadratic function has single extreme value, which avoids leading to an inversion solution for local minimum and ensures the solution for global minimization of an objective function. The method does not need calculation of sensitivity matrix and not require a strict initial earth model. Examples for synthetic data and field measurement data indicate that the proposed inversion method is effective.
Chaos synchronization based on quadratic optimum regulation and control
NASA Astrophysics Data System (ADS)
Gong, Lihua
2005-03-01
Based on the method of the quadratic optimum control, a quadratic optimal regulator used for synchronizing chaotic systems is constructed to realize chaos synchronization. The synchronization method can maintain the least error with less control energy, and then realize the optimization on both sides of energy and error synthetically. In addition, the control cost can also be reduced by using this method intermittently. The simulation results of the chaotic Chua's circuit and the Rossler chaos system prove that the method is effective.
AdS waves as exact solutions to quadratic gravity
Guellue, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram; Guerses, Metin
2011-04-15
We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane-fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity. A subset of the solutions change the asymptotic structure of the anti-de Sitter space due to their logarithmic behavior.
Algorithm Animation with Galant.
Stallmann, Matthias F
2017-01-01
Although surveys suggest positive student attitudes toward the use of algorithm animations, it is not clear that they improve learning outcomes. The Graph Algorithm Animation Tool, or Galant, challenges and motivates students to engage more deeply with algorithm concepts, without distracting them with programming language details or GUIs. Even though Galant is specifically designed for graph algorithms, it has also been used to animate other algorithms, most notably sorting algorithms.
QUADrATiC: scalable gene expression connectivity mapping for repurposing FDA-approved therapeutics.
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
JUDGE, LAWRENCE W.; BELLAR, DAVID; THRASHER, ASHLEY B.; SIMON, LAURA; HINDAWI, OMAR S.; WANLESS, ELIZABETH
2013-01-01
The purpose of this pilot study was to examine the quadratic nature of the relationship between the strength and throwing distance in the shot put. A survey was sent to throws coaches with Master Coach or USA Track and Field Level III distinction to examine fifty-three collegiate and elite throwers (24 male, 29 female). The coaches reported the thrower’s personal best shot put distance and preseason weight room 1RM for bench press, power clean, and squat exercises. Relationship between distance and 1RM was determined via general linear model polynomial contrast analysis and regression. Data analysis showed significant linear and quadratic trends for distance and 1RM power clean for both male (linear: p≤0.001, quadratic: p≤0.003) and female (linear: p≤0.001, quadratic: p=0.001) elite and collegiate shot put athletes. Analysis also provided a quadratic equation to compare personal best distance and 1RM power clean. The power clean was found to be more closely related to shot put distance as compared with squat and also with bench press, which is the least related. Based on the results of this investigation, in addition to strength exercises such as the squat and bench press, power exercises such as the power clean should also be incorporated into strength and conditioning programs of shot put athletes for optimal performance. PMID:28638500