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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Gu, Xuejun; Kim, Hyun K.; Masciotti, James; Hielscher, Andreas H.
2009-02-01
Computational speed and available memory size on a single processor are two limiting factors when using the frequency-domain equation of radiative transport (FD-ERT) as a forward and inverse model to reconstruct three-dimensional (3D) tomographic images. In this work, we report on a parallel, multiprocessor reducedspace sequential quadratic programming (RSQP) approach to improve computational speed and reduce memory requirement. To evaluate and quantify the performance of the code, we performed simulation studies employing a 3D numerical mouse model. Furthermore, we tested the algorithm with experimental data obtained from tumor bearing mice.
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.
Consensus-ADMM for General Quadratically Constrained Quadratic Programming
NASA Astrophysics Data System (ADS)
Huang, Kejun; Sidiropoulos, Nicholas D.
2016-10-01
Non-convex quadratically constrained quadratic programming (QCQP) problems have numerous applications in signal processing, machine learning, and wireless communications, albeit the general QCQP is NP-hard, and several interesting special cases are NP-hard as well. This paper proposes a new algorithm for general QCQP. The problem is first reformulated in consensus optimization form, to which the alternating direction method of multipliers (ADMM) can be applied. The reformulation is done in such a way that each of the sub-problems is a QCQP with only one constraint (QCQP-1), which is efficiently solvable irrespective of (non-)convexity. The core components are carefully designed to make the overall algorithm more scalable, including efficient methods for solving QCQP-1, memory efficient implementation, parallel/distributed implementation, and smart initialization. The proposed algorithm is then tested in two applications: multicast beamforming and phase retrieval. The results indicate superior performance over prior state-of-the-art methods.
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.
Factorization using the quadratic sieve algorithm
Davis, J.A.; Holdridge, D.B.
1983-12-01
Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories to determine as sharply as possible the current state-of-the-art in factoring. Because all viable attacks on RSA thus far proposed are equivalent to factorization of the modulus, sharper bounds on the computational difficulty of factoring permit improved estimates for the size of RSA parameters needed for given levels of cryptosecurity. Analysis of the Quadratic Sieve indicates that it may be faster than any previously published general purpose algorithm for factoring large integers. The high speed of the CRAY I coupled with the capability of the CRAY to pipeline certain vectorized operations make this algorithm (and code) the front runner in current factoring techniques.
Factorization using the quadratic sieve algorithm
Davis, J.A.; Holdridge, D.B.
1983-01-01
Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories to determine as sharply as possible the current state-of-the-art in factoring. Because all viable attacks on RSA thus far proposed are equivalent to factorization of the modulus, sharper bounds on the computational difficulty of factoring permit improved estimates for the size of RSA parameters needed for given levels of cryptosecurity. Analysis of the Quadratic Sieve indicates that it may be faster than any previously published general purpose algorithm for factoring large integers. The high speed of the CRAY I coupled with the capability of the CRAY to pipeline certain vectorized operations make this algorithm (and code) the front runner in current factoring techniques.
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
Optimal power flow using sequential quadratic programming
NASA Astrophysics Data System (ADS)
Nejdawi, Imad M.
1999-11-01
Optimal power flow (OPF) is an operational as well as a planning tool used by electric utilities to help them operate their network in the most economic and secure mode of operation. Various algorithms to solve the OPF problem evolved over the past three decades; linear programming (LP) techniques were among the major mathematical programming methods utilized. The linear models of the objective function and the linearization of the constraints are the main features of these techniques. The main advantages of the LP approach are simplicity and speed. Nonlinear programming techniques have been applied to OPF solution. The major drawback is the expensive solution of large sparse systems of equations. This research is concerned with the development of a new OPF solution algorithm using sequential quadratic programming (SQP). In this formulation, a small dense system the size of which is equal to the number of control variables is solved in an inner loop. The Jacobian and Hessian terms are calculated in an outer loop. The total number of outer loop iterations is comparable to those in an ordinary load flow in contrast to 20--30 iterations in other nonlinear methods. In addition, the total number of floating point operations is less than that encountered in direct methods by two orders of magnitude. We also model dispatch over a twenty four-hour time horizon in a transmission constrained power network that includes price-responsive loads where large energy customers can operate their loads in time intervals with lowest spot prices.
Phase recovery based on quadratic programming
NASA Astrophysics Data System (ADS)
Zhang, Quan Bing; Ge, Xiao Juan; Cheng, Ya Dong; Ni, Na
2014-11-01
Most of the information of optical wavefront is encoded in the phase which includes more details of the object. Conventional optical measuring apparatus is relatively easy to record the intensity of light, but can not measure the phase of light directly. Thus it is important to recovery the phase from the intensity measurements of the object. In recent years, the methods based on quadratic programming such as PhaseLift and PhaseCut can recover the phase of general signal exactly for overdetermined system. To retrieve the phase of sparse signal, the Compressive Phase Retrieval (CPR) algorithm combines the l1-minimization in Compressive Sensing (CS) with low-rank matrix completion problem in PhaseLift, but the result is unsatisfied. This paper focus on the recovery of the phase of sparse signal and propose a new method called the Compressive Phase Cut Retrieval (CPCR) by combining the CPR algorithm with the PhaseCut algorithm. To ensure the sparsity of the recovered signal, we use CPR method to solve a semi-definite programming problem firstly. Then apply linear transformation to the recovered signal, and set the phase of the result as the initial value of the PhaseCut problem. We use TFOCS (a library of Matlab-files) to implement the proposed CPCR algorithm in order to improve the recovered results of the CPR algorithm. Experimental results show that the proposed method can improve the accuracy of the CPR algorithm, and overcome the shortcoming of the PhaseCut method that it can not recover the sparse signal effectively.
Nios II hardware acceleration of the epsilon quadratic sieve algorithm
NASA Astrophysics Data System (ADS)
Meyer-Bäse, Uwe; Botella, Guillermo; Castillo, Encarnacion; García, Antonio
2010-04-01
The quadratic sieve (QS) algorithm is one of the most powerful algorithms to factor large composite primes used to break RSA cryptographic systems. The hardware structure of the QS algorithm seems to be a good fit for FPGA acceleration. Our new ɛ-QS algorithm further simplifies the hardware architecture making it an even better candidate for C2H acceleration. This paper shows our design results in FPGA resource and performance when implementing very long arithmetic on the Nios microprocessor platform with C2H acceleration for different libraries (GMP, LIP, FLINT, NRMP) and QS architecture choices for factoring 32-2048 bit RSA numbers.
A path-following interior-point algorithm for linear and quadratic problems
Wright, S.J.
1993-12-01
We describe an algorithm for the monotone linear complementarity problem that converges for many positive, not necessarily feasible, starting point and exhibits polynomial complexity if some additional assumptions are made on the starting point. If the problem has a strictly complementary solution, the method converges subquadratically. We show that the algorithm and its convergence extend readily to the mixed monotone linear complementarity problem and, hence, to all the usual formulations of the linear programming and convex quadratic programming problems.
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.
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.
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.
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.
Tableau-based protein substructure search using quadratic programming
Stivala, Alex; Wirth, Anthony; Stuckey, Peter J
2009-01-01
Background Searching for proteins that contain similar substructures is an important task in structural biology. The exact solution of most formulations of this problem, including a recently published method based on tableaux, is too slow for practical use in scanning a large database. Results We developed an improved method for detecting substructural similarities in proteins using tableaux. Tableaux are compared efficiently by solving the quadratic program (QP) corresponding to the quadratic integer program (QIP) formulation of the extraction of maximally-similar tableaux. We compare the accuracy of the method in classifying protein folds with some existing techniques. Conclusion We find that including constraints based on the separation of secondary structure elements increases the accuracy of protein structure search using maximally-similar subtableau extraction, to a level where it has comparable or superior accuracy to existing techniques. We demonstrate that our implementation is able to search a structural database in a matter of hours on a standard PC. PMID:19450287
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.
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.
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. PMID:27639239
A reduced successive quadratic programming strategy for errors-in-variables estimation.
Tjoa, I.-B.; Biegler, L. T.; Carnegie-Mellon Univ.
1992-01-01
Parameter estimation problems in process engineering represent a special class of nonlinear optimization problems, because the maximum likelihood structure of the objective function can be exploited. Within this class, the errors in variables method (EVM) is particularly interesting. Here we seek a weighted least-squares fit to the measurements with an underdetermined process model. Thus, both the number of variables and degrees of freedom available for optimization increase linearly with the number of data sets. Large optimization problems of this type can be particularly challenging and expensive to solve because, for general-purpose nonlinear programming (NLP) algorithms, the computational effort increases at least quadratically with problem size. In this study we develop a tailored NLP strategy for EVM problems. The method is based on a reduced Hessian approach to successive quadratic programming (SQP), but with the decomposition performed separately for each data set. This leads to the elimination of all variables but the model parameters, which are determined by a QP coordination step. In this way the computational effort remains linear in the number of data sets. Moreover, unlike previous approaches to the EVM problem, global and superlinear properties of the SQP algorithm apply naturally. Also, the method directly incorporates inequality constraints on the model parameters (although not on the fitted variables). This approach is demonstrated on five example problems with up to 102 degrees of freedom. Compared to general-purpose NLP algorithms, large improvements in computational performance are observed.
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.
Airborne gravimetry data sparse reconstruction via L1-norm convex quadratic programming
NASA Astrophysics Data System (ADS)
Yang, Ya-Peng; Wu, Mei-Ping; Tang, Gang
2015-06-01
In practice, airborne gravimetry is a sub-Nyquist sampling method because of the restrictions imposed by national boundaries, financial cost, and database size. In this study, we analyze the sparsity of airborne gravimetry data by using the discrete Fourier transform and propose a reconstruction method based on the theory of compressed sensing for large-scale gravity anomaly data. Consequently, the reconstruction of the gravity anomaly data is transformed to a L1-norm convex quadratic programming problem. We combine the preconditioned conjugate gradient algorithm (PCG) and the improved interior-point method (IPM) to solve the convex quadratic programming problem. Furthermore, a flight test was carried out with the homegrown strapdown airborne gravimeter SGA-WZ. Subsequently, we reconstructed the gravity anomaly data of the flight test, and then, we compared the proposed method with the linear interpolation method, which is commonly used in airborne gravimetry. The test results show that the PCG-IPM algorithm can be used to reconstruct large-scale gravity anomaly data with higher accuracy and more effectiveness than the linear interpolation method.
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.
Quadratically convergent algorithm for fractional occupation numbers in density functional theory
NASA Astrophysics Data System (ADS)
Cancès, Eric; Kudin, Konstantin N.; Scuseria, Gustavo E.; Turinici, Gabriel
2003-03-01
The numerical solution of the electronic structure problem in Kohn-Sham density functional theory may in certain cases yield fractional occupancy of the single-particle orbitals. In this paper, we propose a quadratically convergent approach for simultaneous optimization of orbitals and occupancies in systems with fractional occupation numbers (FONs). The starting guess for orbitals and FONs is obtained via the relaxed constraint algorithm. Numerical results are presented for benchmark cases.
NASA Astrophysics Data System (ADS)
Son, Kyungchan; Lim, Sung-Yong; Lee, Jae-seong; Jeong, Wooyoung; Yang, Hyunseok
2016-09-01
In holographic data storage, tilt is one of the critical disturbances. There are two types of tilt: tangential and radial. In real systems, tangential and radial tilt occur simultaneously. Thus, it is difficult to measure and compensate for tilt. In this study, using a quadratic window, which compares the intensity of a certain area, a tilt error signal was generated and compensated for with the proposed algorithm. The compensated image obtained satisfied a 0.3 dB tolerance.
NASA Astrophysics Data System (ADS)
Diwakar, S. V.; Das, Sarit K.; Sundararajan, T.
2009-12-01
A new Quadratic Spline based Interface (QUASI) reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature. The fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous PLIC approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves. The conversion is achieved by a sequence of predictor-corrector operations enforcing function ( C0) and derivative ( C1) continuity at the cell boundaries using simple analytical expressions for the continuity requirements. The efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations. These benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature. Quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes; only in situations where the interface geometry is primarily flat, the rate of convergence becomes linear with the mesh size. The flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location. As a consequence, it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface. This has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium. Finally, the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water.
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
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…
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.
An inner-outer nonlinear programming approach for constrained quadratic matrix model updating
NASA Astrophysics Data System (ADS)
Andretta, M.; Birgin, E. G.; Raydan, M.
2016-01-01
The Quadratic Finite Element Model Updating Problem (QFEMUP) concerns with updating a symmetric second-order finite element model so that it remains symmetric and the updated model reproduces a given set of desired eigenvalues and eigenvectors by replacing the corresponding ones from the original model. Taking advantage of the special structure of the constraint set, it is first shown that the QFEMUP can be formulated as a suitable constrained nonlinear programming problem. Using this formulation, a method based on successive optimizations is then proposed and analyzed. To avoid that spurious modes (eigenvectors) appear in the frequency range of interest (eigenvalues) after the model has been updated, additional constraints based on a quadratic Rayleigh quotient are dynamically included in the constraint set. A distinct practical feature of the proposed method is that it can be implemented by computing only a few eigenvalues and eigenvectors of the associated quadratic matrix pencil.
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
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.
Constraint identification and algorithm stabilization for degenerate nonlinear programs.
Wright, S. J.; Mathematics and Computer Science
2003-01-01
In the vicinity of a solution of a nonlinear programming problem at which both strict complementarity and linear independence of the active constraints may fail to hold, we describe a technique for distinguishing weakly active from strongly active constraints. We show that this information can be used to modify the sequential quadratic programming algorithm so that it exhibits superlinear convergence to the solution under assumptions weaker than those made in previous analyses.
Kou, Gaoshan; Feng, Yonge
2015-09-01
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
A simplified dual neural network for quadratic programming with its KWTA application.
Liu, Shubao; Wang, Jun
2006-11-01
The design, analysis, and application of a new recurrent neural network for quadratic programming, called simplified dual neural network, are discussed. The analysis mainly concentrates on the convergence property and the computational complexity of the neural network. The simplified dual neural network is shown to be globally convergent to the exact optimal solution. The complexity of the neural network architecture is reduced with the number of neurons equal to the number of inequality constraints. Its application to k-winners-take-all (KWTA) operation is discussed to demonstrate how to solve problems with this neural network.
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)
Jimaa, Shihab A.; Jadah, Mohamed E.
2005-10-01
This paper investigates the performance of using various non-quadratic adaptive algorithms in the adaptation of a non-linear receiver, coupled with a second-order phase tracking subsystem, for asynchronous DS-CDMA communication system impaired by double-spread multipath channel and Gaussian mixture impulsive noise. These algorithms are the lower order (where the power of the cost function is lower than 2), the least-mean mixed norm (where a mixed-norm function is introduced, which combines the LMS and the LMF functions), and the least mean square-fourth switching (where this algorithm switches between LMS and LMF depending on the value of the error). The non-linear receiver comprises feed-forward filter (FFF), feedback filter (FBF), and an equalizer/second order phase locked loop (PLL). The investigations study the effect of using the proposed algorithms on the performance of the non-linear receiver in terms of the mean-square error (MSE) and bit-error-rate (BER). Computer simulation results indicate that the least-mean mixed proposed receiver's algorithm gives the fastest convergence rate and similar BER performance, in comparison with the NLMS adaptive receiver. Furthermore, extensive computer simulation tests have been carried out to determine the optimum values of the step-size, the power of the cost function, and the adaptation parameter of the proposed algorithms. Results show that the optimum values of the step-size for the lower-order, least-mean square fourth, least-mean mixed norm, and the NLMS algorithms are 5x10 -4, 10 -6, 5x10 -4, and 0.01, respectively. The optimum value of the power of the lower-order algorithm is 1.9 and the optimum value of the adaptation parameter of the least-mean mixed algorithm is 0.9.
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.
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.
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.
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.
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
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.
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…
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
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
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
Dynamic Programming Algorithm vs. Genetic Algorithm: Which is Faster?
NASA Astrophysics Data System (ADS)
Petković, Dušan
The article compares two different approaches for the optimization problem of large join queries (LJQs). Almost all commercial database systems use a form of the dynamic programming algorithm to solve the ordering of join operations for large join queries, i.e. joins with more than dozen join operations. The property of the dynamic programming algorithm is that the execution time increases significantly in the case, where the number of join operations in a query is large. Genetic algorithms (GAs), as a data mining technique, have been shown as a promising technique in solving the ordering of join operations in LJQs. Using the existing implementation of GA, we compare the dynamic programming algorithm implemented in commercial database systems with the corresponding GA module. Our results show that the use of a genetic algorithm is a better solution for optimization of large join queries, i.e., that such a technique outperforms the implementations of the dynamic programming algorithm in conventional query optimization components for very large join queries.
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.
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.
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. PMID:27610319
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.
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.
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)
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.
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.
Models, algorithms and programs for phylogeny reconciliation.
Doyon, Jean-Philippe; Ranwez, Vincent; Daubin, Vincent; Berry, Vincent
2011-09-01
Gene sequences contain a gold mine of phylogenetic information. But unfortunately for taxonomists this information does not only tell the story of the species from which it was collected. Genes have their own complex histories which record speciation events, of course, but also many other events. Among them, gene duplications, transfers and losses are especially important to identify. These events are crucial to account for when reconstructing the history of species, and they play a fundamental role in the evolution of genomes, the diversification of organisms and the emergence of new cellular functions. We review reconciliations between gene and species trees, which are rigorous approaches for identifying duplications, transfers and losses that mark the evolution of a gene family. Existing reconciliation models and algorithms are reviewed and difficulties in modeling gene transfers are discussed. We also compare different reconciliation programs along with their advantages and disadvantages.
Models, algorithms and programs for phylogeny reconciliation.
Doyon, Jean-Philippe; Ranwez, Vincent; Daubin, Vincent; Berry, Vincent
2011-09-01
Gene sequences contain a gold mine of phylogenetic information. But unfortunately for taxonomists this information does not only tell the story of the species from which it was collected. Genes have their own complex histories which record speciation events, of course, but also many other events. Among them, gene duplications, transfers and losses are especially important to identify. These events are crucial to account for when reconstructing the history of species, and they play a fundamental role in the evolution of genomes, the diversification of organisms and the emergence of new cellular functions. We review reconciliations between gene and species trees, which are rigorous approaches for identifying duplications, transfers and losses that mark the evolution of a gene family. Existing reconciliation models and algorithms are reviewed and difficulties in modeling gene transfers are discussed. We also compare different reconciliation programs along with their advantages and disadvantages. PMID:21949266
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. PMID:19228555
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.
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.
Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows
Wang, Di; Kleinberg, Robert D.
2009-01-01
Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C2, C3, C4,…. It is known that C2 can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing Ck (k > 2) require solving a linear program. In this paper we prove that C3 can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}n, this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network. PMID:20161596
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.
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.
A dynamic programming algorithm for RNA structure prediction including pseudoknots.
Rivas, E; Eddy, S R
1999-02-01
We describe a dynamic programming algorithm for predicting optimal RNA secondary structure, including pseudoknots. The algorithm has a worst case complexity of O(N6) in time and O(N4) in storage. The description of the algorithm is complex, which led us to adopt a useful graphical representation (Feynman diagrams) borrowed from quantum field theory. We present an implementation of the algorithm that generates the optimal minimum energy structure for a single RNA sequence, using standard RNA folding thermodynamic parameters augmented by a few parameters describing the thermodynamic stability of pseudoknots. We demonstrate the properties of the algorithm by using it to predict structures for several small pseudoknotted and non-pseudoknotted RNAs. Although the time and memory demands of the algorithm are steep, we believe this is the first algorithm to be able to fold optimal (minimum energy) pseudoknotted RNAs with the accepted RNA thermodynamic model.
NASA Astrophysics Data System (ADS)
Withers, Christopher S.; Nadarajah, Saralees
2012-06-01
We show that there are exactly four quadratic polynomials, Q(x) = x 2 + ax + b, such that
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.
Ellis, John; Fairbairn, Malcolm; Sueiro, Maria E-mail: malcolm.fairbairn@kcl.ac.uk
2014-02-01
Inflationary models based on a single scalar field φ with a quadratic potential V = ½m{sup 2}φ{sup 2} are disfavoured by the recent Planck constraints on the scalar index, n{sub s}, and the tensor-to-scalar ratio for cosmological density perturbations, r{sub T}. In this paper we study how such a quadratic inflationary model can be rescued by postulating additional fields with quadratic potentials, such as might occur in sneutrino models, which might serve as either curvatons or supplementary inflatons. Introducing a second scalar field reduces but does not remove the pressure on quadratic inflation, but we find a sample of three-field models that are highly compatible with the Planck data on n{sub s} and r{sub T}. We exhibit a specific three-sneutrino example that is also compatible with the data on neutrino mass difference and mixing angles.
Kim, E-K; Ha, S-G; Lee, J; Park, Y B; Jung, K-Y
2015-01-26
Efficient unconditionally stable FDTD method is developed for the electromagnetic analysis of dispersive media. Toward this purpose, a quadratic complex rational function (QCRF) dispersion model is applied to the alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method. The 3-D update equations of QCRF-ADI-FDTD are derived using Maxwell's curl equations and the constitutive relation. The periodic boundary condition of QCRF-ADI-FDTD is discussed in detail. A 3-D numerical example shows that the time-step size can be increased by the proposed QCRF-ADI-FDTD beyond the Courant-Friedrich-Levy (CFL) number, without numerical instability. It is observed that, for refined computational cells, the computational time of QCRF-ADI-FDTD is reduced to 28.08 % of QCRF-FDTD, while the L_{2} relative error norm of a field distribution is 6.92 %.
Dynamic programming algorithm for detecting dim infrared moving targets
NASA Astrophysics Data System (ADS)
He, Lisha; Mao, Liangjing; Xie, Lijun
2009-10-01
Infrared (IR) target detection is a key part of airborne infrared weapon system, especially the detection of poor dim moving IR target embedded in complex context. This paper presents an improved Dynamic Programming (DP) algorithm in allusion to low Signal to Noise Ratio (SNR) infrared dim moving targets under cluttered context. The algorithm brings the dim target to prominence by accumulating the energy of pixels in the image sequence, after suppressing the background noise with a mathematical morphology preprocessor. As considering the continuity and stabilization of target's energy and forward direction, this algorithm has well solved the energy scattering problem that exists in the original DP algorithm. An effective energy segmentation threshold is given by a Contrast-Limited Adaptive Histogram Equalization (CLAHE) filter with a regional peak extraction algorithm. Simulation results show that the improved DP tracking algorithm performs well in detecting poor dim targets.
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).
Research on trust-region algorithms for nonlinear programming
Dennis, J.E.; Tapia, R.A.
1991-11-01
This report discusses research on the following topics: interior- point methods for linear programming; trust-region SQP newton's method for general nonlinear programming problems; trust-region SQP newton's method for large sparse nonlinear programming problems with applications to oil reservoir management; a unified approach to global convergence of trust-region methods for nonsmooth optimization; and SQP augmented lagrangian BRGS algorithm for constrained optimization. (LSP).
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)
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]…
A practical algorithm for static analysis of parallel programs
McDowell, C.E. )
1989-06-01
One approach to analyzing the behavior of a concurrent program requires determining the reachable program states. A program state consists of a set of task states, the values of shared variables used for synchronization, and local variables that derive the values directly from synchronization operations. However, the number of reachable states rises exponentially with the number of tasks and becomes intractable for many concurrent programs. A variation of this approach merges a set of related states into a single virtual state. Using this approach, the analysis of concurrent programs becomes feasible as the number of virtual states is often orders of magnitude less than the number of reachable states. This paper presents a method for determining the virtual states that describe the reachable program states, and the reduction in the number of states is analyzed. The algorithms given have been implemented in a state program analyzer for multitasking Fortran, and the results obtained are discussed.
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.
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.
A dynamic programming algorithm for finding alternative RNA secondary structures.
Williams, A L; Tinoco, I
1986-01-10
Dynamic programming algorithms that predict RNA secondary structure by minimizing the free energy have had one important limitation. They were able to predict only one optimal structure. Given the uncertainties of the thermodynamic data and the effects of proteins and other environmental factors on structure, the optimal structure predicted by these methods may not have biological significance. We present a dynamic programming algorithm that can determine optimal and suboptimal secondary structures for an RNA. The power and utility of the method is demonstrated in the folding of the intervening sequence of the rRNA of Tetrahymena. By first identifying the major secondary structures corresponding to the lowest free energy minima, a secondary structure of possible biological significance is derived.
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. PMID:27384395
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.
NASA Astrophysics Data System (ADS)
Colin, M.; Di Menza, L.; Saut, J. C.
2016-03-01
In this paper, we investigate the properties of solitonic structures arising in quadratic media. First, we recall the derivation of systems governing the interaction process for waves propagating in such media and we check the local and global well-posedness of the corresponding Cauchy problem. Then, we look for stationary states in the context of normal or anomalous dispersion regimes, that lead us to either elliptic or non-elliptic systems and we address the problem of orbital stability. Finally, some numerical experiments are carried out in order to compute localized states for several regimes and to study dynamic stability as well as long-time asymptotics.
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.
Learning to control the program evolution process with cultural algorithms
Zannoni; Reynolds
1997-01-01
Traditional software engineering dictates the use of modular and structured programming and top-down stepwise refinement techniques that reduce the amount of variability arising in the development process by establishing standard procedures to be followed while writing software. This focusing leads to reduced variability in the resulting products, due to the use of standardized constructs. Genetic programming (GP) performs heuristic search in the space of programs. Programs produced through the GP paradigm emerge as the result of simulated evolution and are built through a bottom-up process, incrementally augmenting their functionality until a satisfactory level of performance is reached. Can we automatically extract knowledge from the GP programming process that can be useful to focus the search and reduce product variability, thus leading to a more effective use of the available resources? An answer to this question is investigated with the aid of cultural algorithms. A new system, cultural algorithms with genetic programming (CAGP), is presented. The system has two levels. The first is the pool of genetic programs (population level), and the second is a knowledge repository (belief set) that is built during the GP run and is used to guide the search process. The microevolution within the population brings about potentially meaningful characteristics of the programs for the achievement of the given task, such as properties exhibited by the best performers in the population. CAGP extracts these features and represents them as the set of the current beliefs. Beliefs correspond to constraints that all the genetic operators and programs must follow. Interaction between the two levels occurs in one direction through the extraction process and, in the other, through the modulation of an individual's program parameters according to which, and how many, of the constraints it follows. CAGP is applied to solve an instance of the symbolic regression problem, in which a
Quadratic spatial soliton interactions
NASA Astrophysics Data System (ADS)
Jankovic, Ladislav
Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30
Richard, M.J.
1987-01-01
An efficient methodology for using commercial flowsheeting programs with advanced mathematical programming algorithms was developed for the optimization of operating plants. The methodology was demonstrated and validated using ChemShare Corporation's DESIGN/2000 simulation of the Freeport Chemical Company's plant for sulfuric acid manufacture and three nonlinear programming techniques: successive linear programming, successive quadratic programming, and the generalized reduced-gradient method. The application of this methodology begins with the development of a feasible base-case simulation. Partial derivatives of the economic model and constraint equations are computed using fully converged simulations. This information is used to formulate an optimization problem that can be solved with the NLP algorithms giving improved values of the economic model. A line search is constructed through the point found from the nonlinear programming algorithm to find the best feasible point to repeat the procedure. The procedure is repeated using the ChemShare simulation program and the NLP code until convergence criteria are met. This method was applied to three flowsheeting problems; a plant-scale-contact sulfuric acid process model, a packed-bed-reactor design model, and an adiabatic-flash problem.
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.
Quadratic soliton self-reflection at a quadratically nonlinear interface
NASA Astrophysics Data System (ADS)
Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai
2003-11-01
The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.
Recognition of Graphs with Convex Quadratic Stability Number
NASA Astrophysics Data System (ADS)
Pacheco, Maria F.; Cardoso, Domingos M.
2009-09-01
A stable set of a graph is a set of mutually non-adjacent vertices. The determination of a maximum size stable set, which is called maximum stable set, and the determination of its size, which is called stability number, are central combinatorial optimization problems. However, given a nonnegative integer k, to determine if a graph G has a stable set of size k is NP-complete. In this paper we deal with graphs for which the stability number can be determined by solving a convex quadratic programming problem. Such graphs were introduced in [13] and are called graphs with convex-QP stability number. A few algorithmic techniques for the recognition of this type of graphs in particular families are presented.
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…
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.
Efficient Nonlinear Programming Algorithms for Chemical Process Control and Operations
NASA Astrophysics Data System (ADS)
Biegler, Lorenz T.
Optimization is applied in numerous areas of chemical engineering including the development of process models from experimental data, design of process flowsheets and equipment, planning and scheduling of chemical process operations, and the analysis of chemical processes under uncertainty and adverse conditions. These off-line tasks require the solution of nonlinear programs (NLPs) with detailed, large-scale process models. Recently, these tasks have been complemented by time-critical, on-line optimization problems with differential-algebraic equation (DAE) process models that describe process behavior over a wide range of operating conditions, and must be solved sufficiently quickly. This paper describes recent advances in this area especially with dynamic models. We outline large-scale NLP formulations and algorithms as well as NLP sensitivity for on-line applications, and illustrate these advances on a commercial-scale low density polyethylene (LDPE) process.
Effective potential and quadratic divergences
Einhorn, M.B. ); Jones, D.R.T. )
1992-12-01
We use the effective potential to give a simple derivation of Veltman's formula for the quadratic divergence in the Higgs self-energy. We also comment on the effect of going beyond the one-loop approximation.
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.
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.
Convex quadratic optimization on artificial neural networks
Adler, I.; Verma, S.
1994-12-31
We present continuous-valued Hopfield recurrent neural networks on which we map convex quadratic optimization problems. We consider two different convex quadratic programs, each of which is mapped to a different neural network. Activation functions are shown to play a key role in the mapping under each model. The class of activation functions which can be used in this mapping is characterized in terms of the properties needed. It is shown that the first derivatives of penalty as well as barrier functions belong to this class. The trajectories of dynamics under the first model are shown to be closely related to affine-scaling trajectories of interior-point methods. On the other hand, the trajectories of dynamics under the second model correspond to projected steepest descent pathways.
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.
NASA Astrophysics Data System (ADS)
Chernyaev, Yu. A.
2016-03-01
A numerical algorithm for minimizing a convex function on a smooth surface is proposed. The algorithm is based on reducing the original problem to a sequence of convex programming problems. Necessary extremum conditions are examined, and the convergence of the algorithm is analyzed.
Toward a molecular programming language for algorithmic self-assembly
NASA Astrophysics Data System (ADS)
Patitz, Matthew John
Self-assembly is the process whereby relatively simple components autonomously combine to form more complex objects. Nature exhibits self-assembly to form everything from microscopic crystals to living cells to galaxies. With a desire to both form increasingly sophisticated products and to understand the basic components of living systems, scientists have developed and studied artificial self-assembling systems. One such framework is the Tile Assembly Model introduced by Erik Winfree in 1998. In this model, simple two-dimensional square 'tiles' are designed so that they self-assemble into desired shapes. The work in this thesis consists of a series of results which build toward the future goal of designing an abstracted, high-level programming language for designing the molecular components of self-assembling systems which can perform powerful computations and form into intricate structures. The first two sets of results demonstrate self-assembling systems which perform infinite series of computations that characterize computably enumerable and decidable languages, and exhibit tools for algorithmically generating the necessary sets of tiles. In the next chapter, methods for generating tile sets which self-assemble into complicated shapes, namely a class of discrete self-similar fractal structures, are presented. Next, a software package for graphically designing tile sets, simulating their self-assembly, and debugging designed systems is discussed. Finally, a high-level programming language which abstracts much of the complexity and tedium of designing such systems, while preventing many of the common errors, is presented. The summation of this body of work presents a broad coverage of the spectrum of desired outputs from artificial self-assembling systems and a progression in the sophistication of tools used to design them. By creating a broader and deeper set of modular tools for designing self-assembling systems, we hope to increase the complexity which is
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…
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.
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…
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.
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.
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.
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.
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.
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…
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.
The NRMP matching algorithm revisited: theory versus practice. National Resident Matching Program.
Peranson, E; Randlett, R R
1995-06-01
The authors examine the algorithm used by the National Resident Matching Program (NRMP) in its centralized matching of applicants to U.S. residency programs ("the Match"). Their goal is to evaluate the current NRMP matching algorithm to determine whether it still fulfills its intended purpose adequately and whether changes could be made that would improve the Match. They describe the basic NRMP algorithm and many of the variations of the matching process ("match variations") incorporated over the last 20 years to meet participants' requirements. An overview of the current state of the theory of preference matching is presented, including descriptions of the characteristics of stable matches in general, program-optimal and applicant-optimal matchings, and strategies for formulating preference lists. The characteristics of the current NRMP algorithm are then compared with the theoretical findings. Research conducted long after the original NRMP algorithm was devised has shown that an algorithm that produces stable matches is the best approach for matching applicants to positions. In the absence of requirements to satisfy match variations, the NRMP's deferred-acceptance algorithm produces a program-optimal stable match. When match variations, such as those handled by the NRMP, must be introduced, it is possible that no stable matching exists, and the resulting matching produced by the NRMP algorithm may not be program-optimal. The question of program-optimal versus applicant-optimal matchings is discussed. Theoretical and empirical evidence currently available suggest that differences between these two kinds of matchings are likely to be small. However, further tests and research are needed to assess the real differences in the results produced by different stable matching algorithms that produce program-optimal or applicant-optimal stable matches.(ABSTRACT TRUNCATED AT 250 WORDS)
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...
Quantum bouncer with quadratic dissipation
NASA Astrophysics Data System (ADS)
González, G.
2008-02-01
The energy loss due to a quadratic velocity dependent force on a quantum particle bouncing on a perfectly reflecting surface is obtained for a full cycle of motion. We approach this problem by means of a new effective phenomenological Hamiltonian which corresponds to the actual energy of the system and obtained the correction to the eigenvalues of the energy in first order quantum perturbation theory for the case of weak dissipation.
Geometrical Solutions of Quadratic Equations.
ERIC Educational Resources Information Center
Grewal, A. S.; Godloza, L.
1999-01-01
Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)
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.
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.
An algorithm and a fortran program (chemequil-2) for calculation of complex equilibria.
Tripathi, V S
1986-12-01
A computer program, CHEMEQUIL-2 (CHEMical EQUILibrium), based on interfacing an iterative algorithm with the Newton-Raphson method, for calculating equilibrium compositions in aqueous mixtures of metals and ligands, is described. The program is also capable of simulating acid-base titrations. It has been compared with MINIQUAD, COMPLEX and MINEQL with respect to execution time and memory requirements. As a result of algorithm development and program design, CHEMEQUIL-2 offers considerable savings in both execution time (by 1-2 orders of magnitude) and memory requirements, especially for large problems, compared to these programs. The computational efficiency of CHEMEQUIL-2 makes it well suited for use in hydrogeochemieal transport models.
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.
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.
A Riccati approach for constrained linear quadratic optimal control
NASA Astrophysics Data System (ADS)
Sideris, Athanasios; Rodriguez, Luis A.
2011-02-01
An active-set method is proposed for solving linear quadratic optimal control problems subject to general linear inequality path constraints including mixed state-control and state-only constraints. A Riccati-based approach is developed for efficiently solving the equality constrained optimal control subproblems generated during the procedure. The solution of each subproblem requires computations that scale linearly with the horizon length. The algorithm is illustrated with numerical examples.
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.
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.
Primordial bubbles from quadratic gravity
NASA Astrophysics Data System (ADS)
Occhionero, Franco; Amendola, Luca
1994-10-01
A toy model of inflation with a first order phase transition built on a nonminimal generalization of quadratic gravity effectively implements a two field inflation and copiously spurs bubbles before the end of the slow roll. In particular, the phase transition may be brought to completion quickly enough to leave an observable signature at the large scales. We identify analytically and numerically the parameter space region capable of fitting the observed galaxy correlation function, while passing the microwave background constraints. Thus, astronomical observations can yield information upon the parameters of fundamental physics.
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.
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.
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.
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.
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.
Quadratic invariants for discrete clusters of weakly interacting waves
NASA Astrophysics Data System (ADS)
Harper, Katie L.; Bustamante, Miguel D.; Nazarenko, Sergey V.
2013-06-01
We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix {A} with entries 1, -1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J ≡ N - M* ⩾ N - M, where M* is the number of linearly independent rows in {A}. Thus, the problem of finding all independent quadratic invariants is reduced to a linear algebra problem in the Hamiltonian case. We establish that the properties of the quadratic invariants (e.g., locality) are related to the topological properties of the clusters (e.g., types of linkage). To do so, we formulate an algorithm for decomposing large clusters into smaller ones and show how various invariants are related to certain parts of a cluster, including the basic structures leading to M* < M. We illustrate our findings by presenting examples from the Charney-Hasegawa-Mima wave model, and by showing a classification of small (up to three-triad) clusters.
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.
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.
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.
Programming environment for parallel vision algorithms. Annual report, February 1986-February 1987
Brown, C.
1987-02-01
During the second year of the award period, the Computer Science Department of the University of Rochester continued work in: 1) systems support algorithms, 2) the Butterfly programming environment, and 3) vision applications. This research produced several internal and external reports as well as much exportable code. The University of Rochester also employed DARPA Parallel Architecture Benchmark problems to test different algorithms using four different Butterfly programming environments. These tests produced several interesting results and demonstrated that the Butterfly architecture is a flexible general-purpose architecture that can be effectively programmed by non-experts, using tools developed at BBN and Rochester. The University of Rochester is continuing to study the issues and concerns surrounding the effective implementation of parallel 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.
Convergence properties of a quadratic approach to the inverse-scattering problem
NASA Astrophysics Data System (ADS)
Persico, Raffaele; Soldovieri, Francesco; Pierri, Rocco
2002-12-01
The local-minima question that arises in the framework of a quadratic approach to inverse-scattering problems is investigated. In particular, a sufficient condition for the absence of local minima is given, and some guidelines to ensure the reliability of the algorithm are outlined for the case of data not belonging to the range of the relevant quadratic operator. This is relevant also when an iterated solution procedure based on a quadratic approximation of the electromagnetic scattering at each step is considered.
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
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.
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.
A reexamination of the NRMP matching algorithm. National Resident Matching Program.
Williams, K J
1995-06-01
Most graduating medical students in the United States find their first professional appointments through the National Resident Matching Program (NRMP). This service receives rank-order lists of preferences from students and from hospitals, and then generates final assignments of students to hospitals through the use of a specific computerized matching algorithm. The author uses recent findings from the mathematics and economics literatures to demonstrate three difficulties with the NRMP's matching algorithm and the official descriptions thereof. First, the algorithm favors hospitals over students, a feature known to the NRMP since at least 1976, but, in the author's opinion, not made clear in NRMP literature for students. Second, the author argues that the NRMP's justification that its algorithm mimics orderly, noncentralized admission processes is not correct. Institutions operating under non-centralized procedures must typically make more initial offers than there are positions, in the realization that some fraction of their offers will be declined. This arrangement enlarges the choices available to many applicants, and thereby benefits them, whereas the NRMP's algorithm unrealistically assumes that no institution would ever send out any extra offers. Third, the NRMP's algorithm contains incentives for students to misrepresent their true preferences when constructing their rank-order lists. This feature is a substantial disadvantage of the current algorithm and is incorrectly described in literature distributed to students and in published articles from the NRMP.(ABSTRACT TRUNCATED AT 250 WORDS)
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…
Binary Quadratic Forms: A Historical View
ERIC Educational Resources Information Center
Khosravani, Azar N.; Beintema, Mark B.
2006-01-01
We present an expository account of the development of the theory of binary quadratic forms. Beginning with the formulation and proof of the Two-Square Theorem, we show how the study of forms of the type x[squared] + ny[squared] led to the discovery of the Quadratic Reciprocity Law, and how this theorem, along with the concept of reduction relates…
Faraday rotation due to quadratic gravitation
NASA Astrophysics Data System (ADS)
Chen, Yihan; Liu, Liping; Tian, Wen-Xiu
2011-01-01
The linearized field equations of quadratic gravitation in stationary space-time are written in quasi-Maxwell form. The rotation of the polarization plane for an electromagnetic wave propagating in the gravito-electromagnetic field caused by a rotating gravitational lens is discussed. The influences of the Yukawa potential in quadratic gravitation on the gravitational Faraday rotation are investigated.
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.
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…
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.
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.
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.
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.
A Dynamic Programming Algorithm for Optimal Design of Tidal Power Plants
NASA Astrophysics Data System (ADS)
Nag, B.
2013-03-01
A dynamic programming algorithm is proposed and demonstrated on a test case to determine the optimum operating schedule of a barrage tidal power plant to maximize the energy generation over a tidal cycle. Since consecutive sets of high and low tides can be predicted accurately for any tidal power plant site, this algorithm can be used to calculate the annual energy generation for different technical configurations of the plant. Thus an optimal choice of a tidal power plant design can be made from amongst different design configurations yielding the least cost of energy generation. Since this algorithm determines the optimal time of operation of sluice gate opening and turbine gates opening to maximize energy generation over a tidal cycle, it can also be used to obtain the annual schedule of operation of a tidal power plant and the minute-to-minute energy generation, for dissemination amongst power distribution utilities.
Quantum integrability of quadratic Killing tensors
Duval, C.; Valent, G.
2005-05-01
Quantum integrability of classical integrable systems given by quadratic Killing tensors on curved configuration spaces is investigated. It is proven that, using a 'minimal' quantization scheme, quantum integrability is ensured for a large class of classic examples.
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.)
NASA Astrophysics Data System (ADS)
Niwa, Keiichi; Hayashida, Tomohiro; Sakawa, Masatoshi; Yang, Yishen
2010-10-01
We consider two-level programming problems in which there are one decision maker (the leader) at the upper level and two or more decision makers (the followers) at the lower level and decision variables of the leader and the followers are 0-1 variables. We assume that there is coordination among the followers while between the leader and the group of all the followers, there is no motivation to cooperate each other, and fuzzy goals for objective functions of the leader and the followers are introduced so as to take fuzziness of their judgments into consideration. The leader maximizes the degree of satisfaction (the value of the membership function) and the followers choose in concert in order to maximize a minimum among their degrees of satisfaction. We propose a modified computational method that solves problems related to the computational method based on the genetic algorithm (the existing method) for obtaining the Stackelberg solution. Specifically, the distributed genetic algorithm is introduced with respect to the upper level genetic algorithm, which handles decision variables for the leader in order to shorten the computational time of the existing method. Parallelization of the lower level genetic algorithm is also performed along with parallelization of the upper level genetic algorithm. In order to demonstrate the effectiveness of the proposed computational method, numerical experiments are carried out.
Toh, H
1997-08-01
Two approximations were introduced into the double dynamic programming algorithm, in order to reduce the computational time for structural alignment. One of them was the so-called distance cut-off, which approximately describes the structural environment of each residue by its local environment. In the approximation, a sphere with a given radius is placed at the center of the side chain of each residue. The local environment of a residue is constituted only by the residues with side chain centers that are present within the sphere, which is expressed by a set of center-to-center distances from the side chain of the residue to those of all the other constituent residues. The residues outside the sphere are neglected from the local environment. Another approximation is associated with the distance cut-off, which is referred to here as the delta N cut-off. If two local environments are similar to each other, the numbers of residues constituting the environments are expected to be similar. The delta N cut-off was introduced based on the idea. If the difference between the numbers of the constituent residues of two local environments is greater than a given threshold value, delta N, the evaluation of the similarity between the local environments is skipped. The introduction of the two approximations dramatically reduced the computational time for structural alignment by the double dynamic programming algorithm. However, the approximations also decreased the accuracy of the alignment. To improve the accuracy with the approximations, a program with a two-step alignment algorithm was constructed. At first, an alignment was roughly constructed with the approximations. Then, the epsilon-suboptimal region for the alignment was determined. Finally, the double dynamic programming algorithm with full structural environments was applied to the residue pairs within the epsilon-suboptimal region to produce an improved alignment.
The explicit dependence of quadrat variance on the ratio of clump size to quadrat size.
Ferrandino, Francis J
2005-05-01
ABSTRACT In the past decade, it has become common practice to pool mapped binary epidemic data into quadrats. The resultant "quadrat counts" can then be analyzed by fitting them to a probability distribution (i.e., betabinomial). Often a binary form of Taylor's power law is used to relate the quadrat variance to the quadrat mean. The fact that there is an intrinsic dependence of such analyses on quadrat size and shape is well known. However, a clear-cut exposition of the direct connection between the spatial properties of the two-dimensional pattern of infected plants in terms of the geometry of the quadrat and the results of quadrat-based analyses is lacking. This problem was examined both empirically and analytically. The empirical approach is based on a set of stochastically generated "mock epidemics" using a Neyman-Scott cluster process. The resultant spatial point-patterns of infected plants have a fixed number of disease foci characterized by a known length scale (monodisperse) and saturated to a known disease level. When quadrat samples of these epidemics are fit to a beta-binomial distribution, the resulting measures of aggregation are totally independent of disease incidence and most strongly dependent on the ratio of the length scale of the quadrat to the length scale of spatial aggregation and to a lesser degree on disease saturation within individual foci. For the analytical approach, the mathematical form for the variation in the sum of random variates is coupled to the geometry of a quadrat through an assumed exponential autocorrelation function. The net result is an explicit equation expressing the intraquadrat correlation, quadrat variance, and the index of dispersion in terms of the ratio of the quadrat length scale to the correlative length scale.
Programming environment for parallel-vision algorithms. Annual report, February 1985-February 1986
Brown
1986-08-01
During the first year of the award period, three main lines of work were pursued: systems support algorithms, Butterfly programming environment, and vision applications. Today's multiprocessor computer architectures are not efficiently programmed or even conceptualized with standard computer languages, and their operating systems and debugging tools are also challengingly different. The University of Rochester is doing work in the area of tools for controlling large-grain parallelism, as one finds in a distributed multiprocessor application like the Autonomous Land Vehicle, or in tightly coupled processors like the Hypercube or the Butterfly Parallel Processor.
Kempi, V
1987-04-01
A FORTRAN IV program is presented for deconvolution analysis using the matrix algorithm method. With the deconvolution technique retention functions are calculated from time-activity curve data representing both kidneys and blood background. The program computes for each kidney the minimum and maximum time of the retention function. It also calculates the initial amplitudes, absolute as well as relative, and the mean transit time of the retention functions. The design of the program allows for optional reviews of intermediate outputs at important stages. It also allows for the plotting of conventional time-activity curves of both kidneys corrected for blood background. Finally, the program plots the retention functions and some of their characteristics.
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.
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.
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. PMID:23136918
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.
Quadratic Finite Element Method for 1D Deterministic Transport
Tolar, Jr., D R; Ferguson, J M
2004-01-06
In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ({und r}) and angular ({und {Omega}}) dependences on the angular flux {psi}{und r},{und {Omega}}are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of {psi}{und r},{und {Omega}}. Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable ({mu}) in developing the one-dimensional (1D) spherical geometry S{sub N} equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S{sub N} algorithms.
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.
Liu, Zhijun; Kingery, William L; Huddleston, David H; Hossain, Faisal; Hashim, Noor B; Kieffer, Janna M
2008-06-01
This study performs a comparison of two nutrient algorithms of Hydrological Simulation Program Fortran, PQUAL/IQUAL and AGCHEM. Watershed nutrient models with, PQUAL/IQUAL and AGCHEM, were developed and calibrated separately with observed data in the Wolf River watershed. Compared to AGCHEM modules, the PQUAL/IQUAL algorithm was found to have several disadvantages. Examples are: (i) it is a simple loading estimation algorithm, and cannot represent the soil nutrient processes; and (ii) the interactions of modeled nutrient species in the soil cannot be simulated. The AGCHEM modules are capable of explicitly representing the comprehensive nutrient processes in the soil such as fertilization, atmospheric deposition, manure application, plant uptake process, and the transformation processes. Therefore, AGCHEM modules afford the ability to evaluate the alternative management practice and model the interactions between nutrient species. However, our modeling results indicated that the inclusion of AGCHEM modules do not significantly improve the nutrient modeling performance but rather take much more time in model development. The nutrient algorithms selection for total maximum daily loads development depends on the data availability, required modeling accuracy, and available time for model development.
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,…
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.
Speed improvement of B-snake algorithm using dynamic programming optimization.
Charfi, Maher; Zrida, Jalel
2011-10-01
This paper presents a novel approach to contour approximation carried out by means of the B-snake algorithm and the dynamic programming (DP) optimization technique. Using the proposed strategy for contour point search procedure, computing complexity is reduced to O(N×M(2)), whereas the standard DP method has an O(N×M(4)) complexity, with N being the number of contour sample points and M being the number of candidates in the search space. The storage requirement was also decreased from N×M(3) to N×M memory elements. Some experiments on noise corrupted synthetic image, magnetic resonance, and computer tomography medical images have shown that the proposed approach results are equivalent to those obtained by the standard DP algorithm.
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.
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.
Quadratic forms of projective spaces over rings
NASA Astrophysics Data System (ADS)
Levchuk, V. M.; Starikova, O. A.
2006-06-01
In the passage from fields to rings of coefficients quadratic forms with invertible matrices lose their decisive role. It turns out that if all quadratic forms over a ring are diagonalizable, then in effect this is always a local principal ideal ring R with 2\\in R^*. The problem of the construction of a `normal' diagonal form of a quadratic form over a ring R faces obstacles in the case of indices \\vert R^*:R^{*2}\\vert greater than 1. In the case of index 2 this problem has a solution given in Theorem 2.1 for 1+R^{*2}\\subseteq R^{*2} (an extension of the law of inertia for real quadratic forms) and in Theorem 2.2 for 1+R^2 containing an invertible non-square. Under the same conditions on a ring R with nilpotent maximal ideal the number of classes of projectively congruent quadratic forms of the projective space associated with a free R-module of rank n is explicitly calculated (Proposition 3.2). Up to projectivities, the list of forms is presented for the projective plane over R and also (Theorem 3.3) over the local ring F\\lbrack\\lbrack x,y\\rbrack\\rbrack/\\langle x^{2},xy,y^{2}\\rangle with non-principal maximal ideal, where F=2F is a field with an invertible non-square in 1+F^{2} and \\vert F^{*}:F^{*2}\\vert=2. In the latter case the number of classes of non-diagonalizable quadratic forms of rank 0 depends on one's choice of the field F and is not even always finite; all the other forms make up 21 classes.
Quadratic-Like Dynamics of Cubic Polynomials
NASA Astrophysics Data System (ADS)
Blokh, Alexander; Oversteegen, Lex; Ptacek, Ross; Timorin, Vladlen
2016-02-01
A small perturbation of a quadratic polynomial f with a non-repelling fixed point gives a polynomial g with an attracting fixed point and a Jordan curve Julia set, on which g acts like angle doubling. However, there are cubic polynomials with a non-repelling fixed point, for which no perturbation results into a polynomial with Jordan curve Julia set. Motivated by the study of the closure of the Cubic Principal Hyperbolic Domain, we describe such polynomials in terms of their quadratic-like restrictions.
On orthogonality preserving quadratic stochastic operators
NASA Astrophysics Data System (ADS)
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd
2015-05-01
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.
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.
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
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.
Convex half-quadratic criteria and interacting auxiliary variables for image restoration.
Idier, J
2001-01-01
This paper deals with convex half-quadratic criteria and associated minimization algorithms for the purpose of image restoration. It brings a number of original elements within a unified mathematical presentation based on convex duality. Firstly, the Geman and Yang's and Geman and Reynolds's constructions are revisited, with a view to establishing the convexity properties of the resulting half-quadratic augmented criteria, when the original nonquadratic criterion is already convex. Secondly, a family of convex Gibbsian energies that incorporate interacting auxiliary variables is revealed as a potentially fruitful extension of the Geman and Reynolds's construction.
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.
iPoint: an integer programming based algorithm for inferring protein subnetworks.
Atias, Nir; Sharan, Roded
2013-07-01
Large scale screening experiments have become the workhorse of molecular biology, producing data at an ever increasing scale. The interpretation of such data, particularly in the context of a protein interaction network, has the potential to shed light on the molecular pathways underlying the phenotype or the process in question. A host of approaches have been developed in recent years to tackle this reconstruction challenge. These approaches aim to infer a compact subnetwork that connects the genes revealed by the screen while optimizing local (individual path lengths) or global (likelihood) aspects of the subnetwork. Yosef et al. [Mol. Syst. Biol., 2009, 5, 248] were the first to provide a joint optimization of both criteria, albeit approximate in nature. Here we devise an integer linear programming formulation for the joint optimization problem, allowing us to solve it to optimality in minutes on current networks. We apply our algorithm, iPoint, to various data sets in yeast and human and evaluate its performance against state-of-the-art algorithms. We show that iPoint attains very compact and accurate solutions that outperform previous network inference algorithms with respect to their local and global attributes, their consistency across multiple experiments targeting the same pathway, and their agreement with current biological knowledge.
A 'C' program for inverting gravity profile data using the ``Open-Reject-Fill'' algorithm
NASA Astrophysics Data System (ADS)
Nagendra, R.; Prasad, P. V. S.; Mallela, Venu G. K. M.
1994-06-01
A computer program "GINVERT" in C is presented to invert the gravity anomalies of two-dimensional (2-D) bodies. The inversion scheme based on the Open-Reject-Fill criterion assumes a model space consisting of a contiguous set of rectangular prisms. Each elemental prism in the model space is assigned a density contrast and the inversion algorithm proceeds by filling some prisms while leaving others empty. The elements are added only to the periphery of the growing model. One element is allowed at each pass. Models are filled to grow in any combination of directions, or in all directions. The model continues to proliferate to attain a form which yields a gravity value approximating the observed gravity to the desired accuracy. This 'Expanding seed' method efficiently generates sets of inverse models which are bereft of an interpreter's subjective error. The practical effectiveness of the GINVERT program is demonstrated by the inversion of synthetic and real data examples.
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.
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
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.
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…
Implementation of Multivariate Quadratic Quasigroup for Wireless Sensor Network
NASA Astrophysics Data System (ADS)
Maia, Ricardo José Menezes; Barreto, Paulo Sérgio Licciardi Messeder; de Oliveira, Bruno Trevizan
Wireless sensor networks (WSN) consists of sensor nodes with limited energy, processing, communication and memory. Security in WSN is becoming critical with the emergence of applications that require mechanisms for authenticity, integrity and confidentiality. Due to resource constraints in WSN, matching public key cryptosystems (PKC) for these networks is an open research problem. Recently a new PKC based on quasigroups multivariate quadratic. Experiments performed show that MQQ performed in less time than existing major PKC, so that some articles claim that has MQQ speed of a typical symmetric block cipher. Considering features promising to take a new path in the difficult task of providing wireless sensor networks in public key cryptosystems. This paper implements in nesC a new class of public key algorithm called Multivariate Quadratic Quasigroup. This implementation focuses on modules for encryption and decryption of 160-bit MQQ, the modules have been implemented on platforms TelosB and MICAz. We measured execution time and space occupied in the ROM and RAM of the sensors.
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)
Dennis, J.E.; Tapia, R.A.
1991-11-01
This report discusses research on the following topics: interior- point methods for linear programming; trust-region SQP newton`s method for general nonlinear programming problems; trust-region SQP newton`s method for large sparse nonlinear programming problems with applications to oil reservoir management; a unified approach to global convergence of trust-region methods for nonsmooth optimization; and SQP augmented lagrangian BRGS algorithm for constrained optimization. (LSP).
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)
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.
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.
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. PMID:23848802
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.
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.
Extended Decentralized Linear-Quadratic-Gaussian Control
NASA Technical Reports Server (NTRS)
Carpenter, J. Russell
2000-01-01
A straightforward extension of a solution to the decentralized linear-Quadratic-Gaussian problem is proposed that allows its use for commonly encountered classes of problems that are currently solved with the extended Kalman filter. This extension allows the system to be partitioned in such a way as to exclude the nonlinearities from the essential algebraic relationships that allow the estimation and control to be optimally decentralized.
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.
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.
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. PMID:16902710
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…
Chang, Chih-Hua
2015-03-01
This paper proposes new inversion algorithms for the estimation of Chlorophyll-a concentration (Chla) and the ocean's inherent optical properties (IOPs) from the measurement of remote sensing reflectance (Rrs). With in situ data from the NASA bio-optical marine algorithm data set (NOMAD), inversion algorithms were developed by the novel gene expression programming (GEP) approach, which creates, manipulates and selects the most appropriate tree-structured functions based on evolutionary computing. The limitations and validity of the proposed algorithms are evaluated by simulated Rrs spectra with respect to NOMAD, and a closure test for IOPs obtained at a single reference wavelength. The application of GEP-derived algorithms is validated against in situ, synthetic and satellite match-up data sets compiled by NASA and the International Ocean Color Coordinate Group (IOCCG). The new algorithms are able to provide Chla and IOPs retrievals to those derived by other state-of-the-art regression approaches and obtained with the semi- and quasi-analytical algorithms, respectively. In practice, there are no significant differences between GEP, support vector regression, and multilayer perceptron model in terms of the overall performance. The GEP-derived algorithms are successfully applied in processing the images taken by the Sea Wide Field-of-view Sensor (SeaWiFS), generate Chla and IOPs maps which show better details of developing algal blooms, and give more information on the distribution of water constituents between different water bodies. PMID:25836776
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.
Quadratic spline collocation and parareal deferred correction method for parabolic PDEs
NASA Astrophysics Data System (ADS)
Liu, Jun; Wang, Yan; Li, Rongjian
2016-06-01
In this paper, we consider a linear parabolic PDE, and use optimal quadratic spline collocation (QSC) methods for the space discretization, proceed the parareal technique on the time domain. Meanwhile, deferred correction technique is used to improve the accuracy during the iterations. The error estimation is presented and the stability is analyzed. Numerical experiments, which is carried out on a parallel computer with 40 CPUs, are attached to exhibit the effectiveness of the hybrid algorithm.
Holographic entropy increases in quadratic curvature gravity
NASA Astrophysics Data System (ADS)
Bhattacharjee, Srijit; Sarkar, Sudipta; Wall, Aron C.
2015-09-01
Standard methods for calculating the black hole entropy beyond general relativity are ambiguous when the horizon is nonstationary. We fix these ambiguities in all quadratic curvature gravity theories, by demanding that the entropy be increasing at every time, for linear perturbations to a stationary black hole. Our result matches with the entropy formula found previously in holographic entanglement entropy calculations. We explicitly calculate the entropy increase for Vaidya-like solutions in Ricci-tensor gravity to show that (unlike the Wald entropy) the holographic entropy obeys a second law.
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.
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.
ERIC Educational Resources Information Center
Ozdener, Nesrin
2008-01-01
This study focuses on how students in vocational high schools and universities interpret the algorithms in structural computer programming that concerns time-efficiency. The targeted research group consisted of 242 students from two vocational high schools and two departments of the Faculty of Education in Istanbul. This study used qualitative and…
Efficient algorithms for function approximation with piecewise linear sigmoidal networks.
Hush, D R; Horne, B
1998-01-01
This paper presents a computationally efficient algorithm for function approximation with piecewise linear sigmoidal nodes. A one hidden layer network is constructed one node at a time using the well-known method of fitting the residual. The task of fitting an individual node is accomplished using a new algorithm that searches for the best fit by solving a sequence of quadratic programming problems. This approach offers significant advantages over derivative-based search algorithms (e.g., backpropagation and its extensions). Unique characteristics of this algorithm include: finite step convergence, a simple stopping criterion, solutions that are independent of initial conditions, good scaling properties and a robust numerical implementation. Empirical results are included to illustrate these characteristics.
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.
Contact symmetries of constrained quadratic Lagrangians
NASA Astrophysics Data System (ADS)
Dimakis, N.; Terzis, Petros A.; Christodoulakis, T.
2016-01-01
The conditions for the existence of (polynomial in the velocities) contact symmetries of constrained systems that are described by quadratic Lagrangians is presented. These Lagrangians mainly appear in mini-superspace reductions of gravitational plus matter actions. In the literature, one usually adopts a gauge condition (mostly for the lapse N) prior to searching for symmetries. This, however, is an unnecessary restriction which may lead to a loss of symmetries and consequently to the respective integrals of motion. A generalization of the usual procedure rests in the identification of the lapse function N as an equivalent degree of freedom and the according extension of the infinitesimal generator. As a result, conformal Killing tensors (with appropriate conformal factors) can define integrals of motion (instead of just Killing tensors used in the regular gauge fixed case). Additionally, rheonomic integrals of motion - whose existence is unique in this type of singular systems - of various orders in the momenta can be constructed. An example of a relativistic particle in a pp-wave space-time and under the influence of a quadratic potential is illustrated.
Mathews, David H.; Disney, Matthew D.; Childs, Jessica L.; Schroeder, Susan J.; Zuker, Michael; Turner, Douglas H.
2004-01-01
A dynamic programming algorithm for prediction of RNA secondary structure has been revised to accommodate folding constraints determined by chemical modification and to include free energy increments for coaxial stacking of helices when they are either adjacent or separated by a single mismatch. Furthermore, free energy parameters are revised to account for recent experimental results for terminal mismatches and hairpin, bulge, internal, and multibranch loops. To demonstrate the applicability of this method, in vivo modification was performed on 5S rRNA in both Escherichia coli and Candida albicans with 1-cyclohexyl-3-(2-morpholinoethyl) carbodiimide metho-p-toluene sulfonate, dimethyl sulfate, and kethoxal. The percentage of known base pairs in the predicted structure increased from 26.3% to 86.8% for the E. coli sequence by using modification constraints. For C. albicans, the accuracy remained 87.5% both with and without modification data. On average, for these sequences and a set of 14 sequences with known secondary structure and chemical modification data taken from the literature, accuracy improves from 67% to 76%. This enhancement primarily reflects improvement for three sequences that are predicted with <40% accuracy on the basis of energetics alone. For these sequences, inclusion of chemical modification constraints improves the average accuracy from 28% to 78%. For the 11 sequences with <6% pseudoknotted base pairs, structures predicted with constraints from chemical modification contain on average 84% of known canonical base pairs. PMID:15123812
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.
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. PMID:24807455
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.
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.
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.
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.
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. PMID:27179616
NASA Technical Reports Server (NTRS)
Powell, Richard W.
1998-01-01
This paper describes the development and evaluation of a numerical roll reversal predictor-corrector guidance algorithm for the atmospheric flight portion of the Mars Surveyor Program 2001 Orbiter and Lander missions. The Lander mission utilizes direct entry and has a demanding requirement to deploy its parachute within 10 km of the target deployment point. The Orbiter mission utilizes aerocapture to achieve a precise captured orbit with a single atmospheric pass. Detailed descriptions of these predictor-corrector algorithms are given. Also, results of three and six degree-of-freedom Monte Carlo simulations which include navigation, aerodynamics, mass properties and atmospheric density uncertainties are presented.
A parallel algorithm for the eigenvalues and eigenvectors for a general complex matrix
NASA Technical Reports Server (NTRS)
Shroff, Gautam
1989-01-01
A new parallel Jacobi-like algorithm is developed for computing the eigenvalues of a general complex matrix. Most parallel methods for this parallel typically display only linear convergence. Sequential norm-reducing algorithms also exit and they display quadratic convergence in most cases. The new algorithm is a parallel form of the norm-reducing algorithm due to Eberlein. It is proven that the asymptotic convergence rate of this algorithm is quadratic. Numerical experiments are presented which demonstrate the quadratic convergence of the algorithm and certain situations where the convergence is slow are also identified. The algorithm promises to be very competitive on a variety of parallel architectures.
Quadratic dynamical decoupling with nonuniform error suppression
Quiroz, Gregory; Lidar, Daniel A.
2011-10-15
We analyze numerically the performance of the near-optimal quadratic dynamical decoupling (QDD) single-qubit decoherence errors suppression method [J. West et al., Phys. Rev. Lett. 104, 130501 (2010)]. The QDD sequence is formed by nesting two optimal Uhrig dynamical decoupling sequences for two orthogonal axes, comprising N{sub 1} and N{sub 2} pulses, respectively. Varying these numbers, we study the decoherence suppression properties of QDD directly by isolating the errors associated with each system basis operator present in the system-bath interaction Hamiltonian. Each individual error scales with the lowest order of the Dyson series, therefore immediately yielding the order of decoherence suppression. We show that the error suppression properties of QDD are dependent upon the parities of N{sub 1} and N{sub 2}, and near-optimal performance is achieved for general single-qubit interactions when N{sub 1}=N{sub 2}.
Quadratic quantum cosmology with Schutz' perfect fluid
NASA Astrophysics Data System (ADS)
Vakili, Babak
2010-01-01
We study the classical and quantum models of a Friedmann-Robertson-Walker (FRW) cosmology, coupled to a perfect fluid, in the context of the f(R) gravity. Using Schutz' representation for the perfect fluid, we show that, under a particular gauge choice, it may lead to the identification of a time parameter for the corresponding dynamical system. Moreover, this formalism gives rise to a Schrödinger-Wheeler-DeWitt (SWD) equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wavefunction of the universe. In the case of f(R) = R2 (pure quadratic model), for some particular choices of the perfect fluid source, exact solutions to the SWD equation can be obtained and the corresponding results are compared to the usual f(R) = R model.
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.
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.
Dynamics and linear quadratic optimal control of flexible multibody systems
NASA Astrophysics Data System (ADS)
Tung, Chin-Wei
1994-12-01
An efficient algorithm for the modeling, dynamic analysis, and optimal control of flexible multibody systems (FMBS) is presented. The cantilevered Bernoulli-Euler beam model and the assumed mode method are used to represent flexibility of elastic bodies in 3D vibration problems. Centrifugal stiffening effects are introduced to correctly represent the dynamic response. The governing equations of motion are based on Kane's equations, adopting a recursive formulation and strategic positioning of the generalized coordinates. The linear quadratic optimization scheme is employed to formulate the vibration control problem. The solutions to the Riccati equation and the use of Kalman gain as optimal control feedbacks to the control of flexibility are also introduced. Based on the optimal control theory and the property of the built-in redundancy for flexible multibody systems, the performance index measure in the optimization control of such systems can be classified into two manifolds: (1) using the extra degrees of freedom resulting from redundancy as control inputs and choosing an integral-type performance index which results in a global optimization scheme and (2) using the joint forces and torques as control inputs and allowing the system output state to keep close track to a reference state while the performance index is kept minimum. Several numerical examples are presented to demonstrate the effectiveness of the methodologies developed.
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
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)
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.
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.
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.)
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…
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…
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.
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.
Quadratic elongation: A quantitative measure of distortion in coordination polyhedra
Robinson, Kelly F.; Gibbs, G.V.; Ribbe, P.H.
1971-01-01
Quadratic elongation and the variance of bond angles are linearly correlated for distorted octahedral and tetrahedral coordination complexes, both of which show variations in bond length and bond angle. The quadratic elonga tion is dimensionless, giving a quantitative measure of polyhedral distortion which is independent of the effective size of the polyhedron.
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…
An adaptive ant colony system algorithm for continuous-space optimization problems.
Li, Yan-jun; Wu, Tie-jun
2003-01-01
Ant colony algorithms comprise a novel category of evolutionary computation methods for optimization problems, especially for sequencing-type combinatorial optimization problems. An adaptive ant colony algorithm is proposed in this paper to tackle continuous-space optimization problems, using a new objective-function-based heuristic pheromone assignment approach for pheromone update to filtrate solution candidates. Global optimal solutions can be reached more rapidly by self-adjusting the path searching behaviors of the ants according to objective values. The performance of the proposed algorithm is compared with a basic ant colony algorithm and a Square Quadratic Programming approach in solving two benchmark problems with multiple extremes. The results indicated that the efficiency and reliability of the proposed algorithm were greatly improved. PMID:12656341
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…
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.
A superlinear interior points algorithm for engineering design optimization
NASA Technical Reports Server (NTRS)
Herskovits, J.; Asquier, J.
1990-01-01
We present a quasi-Newton interior points algorithm for nonlinear constrained optimization. It is based on a general approach consisting of the iterative solution in the primal and dual spaces of the equalities in Karush-Kuhn-Tucker optimality conditions. This is done in such a way to have primal and dual feasibility at each iteration, which ensures satisfaction of those optimality conditions at the limit points. This approach is very strong and efficient, since at each iteration it only requires the solution of two linear systems with the same matrix, instead of quadratic programming subproblems. It is also particularly appropriate for engineering design optimization inasmuch at each iteration a feasible design is obtained. The present algorithm uses a quasi-Newton approximation of the second derivative of the Lagrangian function in order to have superlinear asymptotic convergence. We discuss theoretical aspects of the algorithm and its computer implementation.
A 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.
Adiabatic Quantum Programming: Minor Embedding With Hard Faults
Klymko, Christine F; Sullivan, Blair D; Humble, Travis S
2013-01-01
Adiabatic quantum programming defines the time-dependent mapping of a quantum algorithm into the hardware or logical fabric. An essential programming step is the embedding of problem-specific information into the logical fabric to define the quantum computational transformation. We present algorithms for embedding arbitrary instances of the adiabatic quantum optimization algorithm into a square lattice of specialized unit cells. Our methods are shown to be extensible in fabric growth, linear in time, and quadratic in logical footprint. In addition, we provide methods for accommodating hard faults in the logical fabric without invoking approximations to the original problem. These hard fault-tolerant embedding algorithms are expected to prove useful for benchmarking the adiabatic quantum optimization algorithm on existing quantum logical hardware. We illustrate this versatility through numerical studies of embeddabilty versus hard fault rates in square lattices of complete bipartite unit cells.
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
NASA Astrophysics Data System (ADS)
Chen, Shinn-Horng; Chou, Jyh-Horng; Zheng, Liang-An; Lin, Sheng-Kai
2010-08-01
This paper presents a design method for designing the robust-stable and quadratic-finite-horizon-optimal controllers of uncertain active suspension systems. The method integrates a robust stabilisability condition, the orthogonal functions approach (OFA) and the hybrid Taguchi-genetic algorithm (HTGA). Using the integrative computational method, a robust-stable and quadratic-finite-horizon-optimal controller with low-trajectory sensitivity can be obtained such that (i) the active suspension system with elemental parametric uncertainties is stabilised and (ii) a quadratic-finite-horizon-integral performance index including a quadratic trajectory sensitivity term for the nominal active suspension system is minimised. The robust stabilisability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the OFA, an algebraic algorithm only involving the algebraic computation is derived for solving the nominal active suspension feedback dynamic equations. By using the OFA and the LMI-based robust stabilisability condition, the dynamic optimisation problem for the robust-stable and quadratic-finite-horizon-optimal controller design of the linear uncertain active suspension system is transformed into a static-constrained-optimisation problem represented by the algebraic equations with constraint of LMI-based robust stabilisability condition; thus greatly simplifies the design problem. Then, for the static-constrained-optimisation problem, the HTGA is employed to find the robust-stable and quadratic-finite-horizon-optimal controllers of the linear uncertain active suspension systems. A design example is given to demonstrate the applicability of the proposed integrative computational approach.
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).
Optimal channels for channelized quadratic estimators.
Kupinski, Meredith K; Clarkson, Eric
2016-06-01
We present a new method for computing optimized channels for estimation tasks that is feasible for high-dimensional image data. Maximum-likelihood (ML) parameter estimates are challenging to compute from high-dimensional likelihoods. The dimensionality reduction from M measurements to L channels is a critical advantage of channelized quadratic estimators (CQEs), since estimating likelihood moments from channelized data requires smaller sample sizes and inverting a smaller covariance matrix is easier. The channelized likelihood is then used to form ML estimates of the parameter(s). In this work we choose an imaging example in which the second-order statistics of the image data depend upon the parameter of interest: the correlation length. Correlation lengths are used to approximate background textures in many imaging applications, and in these cases an estimate of the correlation length is useful for pre-whitening. In a simulation study we compare the estimation performance, as measured by the root-mean-squared error (RMSE), of correlation length estimates from CQE and power spectral density (PSD) distribution fitting. To abide by the assumptions of the PSD method we simulate an ergodic, isotropic, stationary, and zero-mean random process. These assumptions are not part of the CQE formalism. The CQE method assumes a Gaussian channelized likelihood that can be a valid for non-Gaussian image data, since the channel outputs are formed from weighted sums of the image elements. We have shown that, for three or more channels, the RMSE of CQE estimates of correlation length is lower than conventional PSD estimates. We also show that computing CQE by using a standard nonlinear optimization method produces channels that yield RMSE within 2% of the analytic optimum. CQE estimates of anisotropic correlation length estimation are reported to demonstrate this technique on a two-parameter estimation problem. PMID:27409452
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 [
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. PMID:15362130
NASA Astrophysics Data System (ADS)
Machnes, S.; Sander, U.; Glaser, S. J.; de Fouquières, P.; Gruslys, A.; Schirmer, S.; Schulte-Herbrüggen, T.
2011-08-01
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.
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.
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.
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.
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)
Fast-rolling shutter compensation based on piecewise quadratic approximation of a camera trajectory
NASA Astrophysics Data System (ADS)
Lee, Yun Gu; Kai, Guo
2014-09-01
Rolling shutter effect commonly exists in a video camera or a mobile phone equipped with a complementary metal-oxide semiconductor sensor, caused by a row-by-row exposure mechanism. As video resolution in both spatial and temporal domains increases dramatically, removing rolling shutter effect fast and effectively becomes a challenging problem, especially for devices with limited hardware resources. We propose a fast method to compensate rolling shutter effect, which uses a piecewise quadratic function to approximate a camera trajectory. The duration of a quadratic function in each segment is equal to one frame (or half-frame), and each quadratic function is described by an initial velocity and a constant acceleration. The velocity and acceleration of each segment are estimated using only a few global (or semiglobal) motion vectors, which can be simply predicted from fast motion estimation algorithms. Then geometric image distortion at each scanline is inferred from the predicted camera trajectory for compensation. Experimental results on mobile phones with full-HD video demonstrate that our method can not only be implemented in real time, but also achieve satisfactory visual quality.
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.
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%.
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.
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
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.
On a 'Mysterious' Case of a Quadratic Hamiltonian
NASA Astrophysics Data System (ADS)
Sakovich, Sergei
2006-07-01
We show that one of the five cases of a quadratic Hamiltonian, which were recently selected by Sokolov and Wolf who used the Kovalevskaya-Lyapunov test, fails to pass the Painlevé test for integrability.
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.
A Polynomial-Time Algorithm for Optimizing over N-Fold 4-Block Decomposable Integer Programs
NASA Astrophysics Data System (ADS)
Hemmecke, Raymond; Köppe, Matthias; Weismantel, Robert
In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time solvable for any linear objective. Moreover, we present a polynomial-time computable optimality certificate for the case of fixed blocks, variable N and any convex separable objective function. We conclude with two sample applications, stochastic integer programs with second-order dominance constraints and stochastic integer multi-commodity flows, which (for fixed blocks) can be solved in polynomial time in the number of scenarios and commodities and in the binary encoding length of the input data. In the proof of our main theorem we combine several non-trivial constructions from the theory of Graver bases. We are confident that our approach paves the way for further extensions.
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.
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.
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…
A transient, quadratic nodal method for triangular-Z geometry
DeLorey, T.F.
1993-06-01
Many systematically-derived nodal methods have been developed for Cartesian geometry due to the extensive interest in Light Water Reactors. These methods typically model the transverse-integrated flux as either an analytic or low order polynomial function of position within the node. Recently, quadratic nodal methods have been developed for R-Z and hexagonal geometry. A static and transient quadratic nodal method is developed for triangular-Z geometry. This development is particularly challenging because the quadratic expansion in each node must be performed between the node faces and the triangular points. As a consequence, in the 2-D plane, the flux and current at the points of the triangles must be treated. Quadratic nodal equations are solved using a non-linear iteration scheme, which utilizes the corrected, mesh-centered finite difference equations, and forces these equations to match the quadratic equations by computing discontinuity factors during the solution. Transient nodal equations are solved using the improved quasi-static method, which has been shown to be a very efficient solution method for transient problems. Several static problems are used to compare the quadratic nodal method to the Coarse Mesh Finite Difference (CMFD) method. The quadratic method is shown to give more accurate node-averaged fluxes. However, it appears that the method has difficulty predicting node leakages near reactor boundaries and severe material interfaces. The consequence is that the eigenvalue may be poorly predicted for certain reactor configurations. The transient methods are tested using a simple analytic test problem, a heterogeneous heavy water reactor benchmark problem, and three thermal hydraulic test problems. Results indicate that the transient methods have been implemented correctly.
Evaluation of a Particle Swarm Algorithm For Biomechanical Optimization
Schutte, Jaco F.; Koh, Byung; Reinbolt, Jeffrey A.; Haftka, Raphael T.; George, Alan D.; Fregly, Benjamin J.
2006-01-01
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. PMID:16060353
NASA Technical Reports Server (NTRS)
Milman, Mark H.
1987-01-01
The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary systems. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.
Study on MAX-MIN Ant System with Random Selection in Quadratic Assignment Problem
NASA Astrophysics Data System (ADS)
Iimura, Ichiro; Yoshida, Kenji; Ishibashi, Ken; Nakayama, Shigeru
Ant Colony Optimization (ACO), which is a type of swarm intelligence inspired by ants' foraging behavior, has been studied extensively and its effectiveness has been shown by many researchers. The previous studies have reported that MAX-MIN Ant System (MMAS) is one of effective ACO algorithms. The MMAS maintains the balance of intensification and diversification concerning pheromone by limiting the quantity of pheromone to the range of minimum and maximum values. In this paper, we propose MAX-MIN Ant System with Random Selection (MMASRS) for improving the search performance even further. The MMASRS is a new ACO algorithm that is MMAS into which random selection was newly introduced. The random selection is one of the edgechoosing methods by agents (ants). In our experimental evaluation using ten quadratic assignment problems, we have proved that the proposed MMASRS with the random selection is superior to the conventional MMAS without the random selection in the viewpoint of the search performance.
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.
NASA Astrophysics Data System (ADS)
Patanè, Domenico; Ferrari, Ferruccio
1999-06-01
A few automated data acquisition and processing systems operate on mainframes, some are run on UNIX-based workstations and others on personal computer, equipped with either DOS or UNIX-derived operating systems. Several large and complex software packages for automatic and interactive analysis of seismic data have been developed in recent years mainly for UNIX-based systems, and some of these programs use a variety of artificial intelligence techniques. Here, the first operational version of a new software package, named PC-Seism, for analyzing seismic data from a local network is presented. This package, composed of three separate modules, provides an example of a new generation of visual object-oriented programs for interactive and automatic seismic data processing run on a personal computer. In particular, we discuss the automatic procedures implemented in the ASDP (Automatic Seismic Data Processing) module. A multi-algorithm approach to the on-line detection and location of local earthquakes is adopted in ASDP, and its operative mode is similar to that used in more complex systems, where the algorithms run on different processors and parallel computations are generally performed. Since highly complex computation routines may still be prohibitive for current PC when the number of analyzing traces becomes large, we have opted for simplicity and have planned three main routines (working in cascade mode) and a multi-station analysis (MSA) procedure in ASDP, to recognize phase picking, declare and locate earthquakes. Basically, signal detection on a single-component trace is obtained by a short-term average to long-term average ratio (STA/LTA) taken along a characteristic function (CF) envelope generated from the seismogram. To confirm and identify earthquake phase arrivals and to discard noise disturbances, two other sections of analysis are applied on short signal windows after the declared triggers. A spectral analysis is applied as detector of earthquake phase
NASA Astrophysics Data System (ADS)
Baker, B. I.; Friberg, P. A.
2014-12-01
Modern seismic networks typically deploy three component (3C) sensors, but still fail to utilize all of the information available in the seismograms when performing automated phase picking for real-time event location. In most cases a variation on a short term over long term average threshold detector is used for picking and then an association program is used to assign phase types to the picks. However, the 3C waveforms from an earthquake contain an abundance of information related to the P and S phases in both their polarization and energy partitioning. An approach that has been overlooked and has demonstrated encouraging results is the Component Energy Comparison Method (CECM) by Nagano et al. as published in Geophysics 1989. CECM is well suited to being used in real-time because the calculation is not computationally intensive. Furthermore, the CECM method has fewer tuning variables (3) than traditional pickers in Earthworm such as the Rex Allen algorithm (N=18) or even the Anthony Lomax Filter Picker module (N=5). In addition to computing the CECM detector we study the detector sensitivity by rotating the signal into principle components as well as estimating the P phase onset from a curvature function describing the CECM as opposed to the CECM itself. We present our results implementing this algorithm in a real-time module for Earthworm and show the improved phase picks as compared to the traditional single component pickers using Earthworm.
NASA Technical Reports Server (NTRS)
Watson, J. S.; Mistretta, G. D.; Bonavito, N. L.
1975-01-01
A quadrature algorithm is presented which employs analytical expressions for the variations of satellite orbital elements caused by air drag. The Hamiltonian is formally preserved and the Jacobi constants of the motion are advanced with time through the variational equations. The atmospheric density profile is written as a fitted exponential function of the eccentric anomaly, which adheres to tabulated data at all altitudes and simultaneously reduces the variational equations to definite integrals with closed form evaluations, whose limits are in terms of the eccentric anomaly. Results are given for two intense air drag satellites and indicate that the satellite ephemerides produced by this method in conjunction with the Vinti program are of very high accuracy.
On Volterra quadratic stochastic operators with continual state space
Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar
2015-05-15
Let (X,F) be a measurable space, and S(X,F) be the set of all probability measures on (X,F) where X is a state space and F is σ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (Vλ)(A) = ∫{sub X}∫{sub X}P(x,y,A)dλ(x)dλ(y), where P(x, y, A) is regarded as a function of two variables x and y with fixed A ∈ F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim{sub n→∞} V{sup n }(λ) is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X = [0,1] with Borel σ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.
Support Vector Machine algorithm for regression and classification
2001-08-01
The software is an implementation of the Support Vector Machine (SVM) algorithm that was invented and developed by Vladimir Vapnik and his co-workers at AT&T Bell Laboratories. The specific implementation reported here is an Active Set method for solving a quadratic optimization problem that forms the major part of any SVM program. The implementation is tuned to specific constraints generated in the SVM learning. Thus, it is more efficient than general-purpose quadratic optimization programs. Amore » decomposition method has been implemented in the software that enables processing large data sets. The size of the learning data is virtually unlimited by the capacity of the computer physical memory. The software is flexible and extensible. Two upper bounds are implemented to regulate the SVM learning for classification, which allow users to adjust the false positive and false negative rates. The software can be used either as a standalone, general-purpose SVM regression or classification program, or be embedded into a larger software system.« less
Support Vector Machine algorithm for regression and classification
Yu, Chenggang; Zavaljevski, Nela
2001-08-01
The software is an implementation of the Support Vector Machine (SVM) algorithm that was invented and developed by Vladimir Vapnik and his co-workers at AT&T Bell Laboratories. The specific implementation reported here is an Active Set method for solving a quadratic optimization problem that forms the major part of any SVM program. The implementation is tuned to specific constraints generated in the SVM learning. Thus, it is more efficient than general-purpose quadratic optimization programs. A decomposition method has been implemented in the software that enables processing large data sets. The size of the learning data is virtually unlimited by the capacity of the computer physical memory. The software is flexible and extensible. Two upper bounds are implemented to regulate the SVM learning for classification, which allow users to adjust the false positive and false negative rates. The software can be used either as a standalone, general-purpose SVM regression or classification program, or be embedded into a larger software system.
Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation
NASA Astrophysics Data System (ADS)
Fernández, Francisco M.
2016-06-01
We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit.
Quadratic α‧-corrections to heterotic double field theory
NASA Astrophysics Data System (ADS)
Lee, Kanghoon
2015-10-01
We investigate α‧-corrections of heterotic double field theory up to quadratic order in the language of supersymmetric O (D, D + dim G) gauged double field theory. After introducing double-vielbein formalism with a parametrization which reproduces heterotic supergravity, we show that supersymmetry for heterotic double field theory up to leading order α‧-correction is obtained from supersymmetric gauged double field theory. We discuss the necessary modifications of the symmetries defined in supersymmetric gauged double field theory. Further, we construct supersymmetric completion at quadratic order in α‧.
Algorithms and Algorithmic Languages.
ERIC Educational Resources Information Center
Veselov, V. M.; Koprov, V. M.
This paper is intended as an introduction to a number of problems connected with the description of algorithms and algorithmic languages, particularly the syntaxes and semantics of algorithmic languages. The terms "letter, word, alphabet" are defined and described. The concept of the algorithm is defined and the relation between the algorithm and…
NASA Astrophysics Data System (ADS)
Komura, Yukihiro; Okabe, Yutaka
2016-03-01
We present new versions of sample CUDA programs for the GPU computing of the Swendsen-Wang multi-cluster spin flip algorithm. In this update, we add the method of GPU-based cluster-labeling algorithm without the use of conventional iteration (Komura, 2015) to those programs. For high-precision calculations, we also add a random-number generator in the cuRAND library. Moreover, we fix several bugs and remove the extra usage of shared memory in the kernel functions.
Design of a multiple kernel learning algorithm for LS-SVM by convex programming.
Jian, Ling; Xia, Zhonghang; Liang, Xijun; Gao, Chuanhou
2011-06-01
As a kernel based method, the performance of least squares support vector machine (LS-SVM) depends on the selection of the kernel as well as the regularization parameter (Duan, Keerthi, & Poo, 2003). Cross-validation is efficient in selecting a single kernel and the regularization parameter; however, it suffers from heavy computational cost and is not flexible to deal with multiple kernels. In this paper, we address the issue of multiple kernel learning for LS-SVM by formulating it as semidefinite programming (SDP). Furthermore, we show that the regularization parameter can be optimized in a unified framework with the kernel, which leads to an automatic process for model selection. Extensive experimental validations are performed and analyzed.
NASA Astrophysics Data System (ADS)
Sumin, M. I.
2015-06-01
A parametric nonlinear programming problem in a metric space with an operator equality constraint in a Hilbert space is studied assuming that its lower semicontinuous value function at a chosen individual parameter value has certain subdifferentiability properties in the sense of nonlinear (nonsmooth) analysis. Such subdifferentiability can be understood as the existence of a proximal subgradient or a Fréchet subdifferential. In other words, an individual problem has a corresponding generalized Kuhn-Tucker vector. Under this assumption, a stable sequential Kuhn-Tucker theorem in nondifferential iterative form is proved and discussed in terms of minimizing sequences on the basis of the dual regularization method. This theorem provides necessary and sufficient conditions for the stable construction of a minimizing approximate solution in the sense of Warga in the considered problem, whose initial data can be approximately specified. A substantial difference of the proved theorem from its classical same-named analogue is that the former takes into account the possible instability of the problem in the case of perturbed initial data and, as a consequence, allows for the inherited instability of classical optimality conditions. This theorem can be treated as a regularized generalization of the classical Uzawa algorithm to nonlinear programming problems. Finally, the theorem is applied to the "simplest" nonlinear optimal control problem, namely, to a time-optimal control problem.
Applications of a quadratic extended interior penalty function for structural optimization
NASA Technical Reports Server (NTRS)
Haftka, R. T.; Starnes, J. H., Jr.
1975-01-01
A quadratic extended interior penalty function formulation especially well suited for second-order unconstrained optimization procedures is presented. Analytical derivatives of constraints and an approximate analysis technique are used. Minimum-mass design results are presented which indicate that the combination of these procedures can help make mathematical programming a useful optimization tool for large-order structural design problems with a large number of design variables and multiple constraints. Examples include statically loaded high- and low-aspect-ratio wings simultaneously subjected to stress, displacement, minimum gage and, in some cases, maximum strain constraints.
Users manual for flight control design programs
NASA Technical Reports Server (NTRS)
Nalbandian, J. Y.
1975-01-01
Computer programs for the design of analog and digital flight control systems are documented. The program DIGADAPT uses linear-quadratic-gaussian synthesis algorithms in the design of command response controllers and state estimators, and it applies covariance propagation analysis to the selection of sampling intervals for digital systems. Program SCHED executes correlation and regression analyses for the development of gain and trim schedules to be used in open-loop explicit-adaptive control laws. A linear-time-varying simulation of aircraft motions is provided by the program TVHIS, which includes guidance and control logic, as well as models for control actuator dynamics. The programs are coded in FORTRAN and are compiled and executed on both IBM and CDC computers.
Tuning a fuzzy controller using quadratic response surfaces
NASA Technical Reports Server (NTRS)
Schott, Brian; Whalen, Thomas
1992-01-01
Response surface methodology, an alternative method to traditional tuning of a fuzzy controller, is described. An example based on a simulated inverted pendulum 'plant' shows that with (only) 15 trial runs, the controller can be calibrated using a quadratic form to approximate the response surface.
A Unified Approach to Teaching Quadratic and Cubic Equations.
ERIC Educational Resources Information Center
Ward, A. J. B.
2003-01-01
Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)
Canonical realization of Bondi-Metzner-Sachs symmetry: Quadratic Casimir
NASA Astrophysics Data System (ADS)
Gomis, Joaquim; Longhi, Giorgio
2016-01-01
We study the canonical realization of Bondi-Metzner-Sacks symmetry for a massive scalar field introduced by Longhi and Materassi [J. Math. Phys. 40, 480 (1999)]. We construct an invariant scalar product for the generalized momenta. As a consequence we introduce a quadratic Casimir with the supertranslations.
Finding the Best Quadratic Approximation of a Function
ERIC Educational Resources Information Center
Yang, Yajun; Gordon, Sheldon P.
2011-01-01
This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…
Visualising the Complex Roots of Quadratic Equations with Real Coefficients
ERIC Educational Resources Information Center
Bardell, Nicholas S.
2012-01-01
The roots of the general quadratic equation y = ax[superscript 2] + bx + c (real a, b, c) are known to occur in the following sets: (i) real and distinct; (ii) real and coincident; and (iii) a complex conjugate pair. Case (iii), which provides the focus for this investigation, can only occur when the values of the real coefficients a, b, and c are…
Analysis of Quadratic Diophantine Equations with Fibonacci Number Solutions
ERIC Educational Resources Information Center
Leyendekkers, J. V.; Shannon, A. G.
2004-01-01
An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.
Quadratic Expressions by Means of "Summing All the Matchsticks"
ERIC Educational Resources Information Center
Gierdien, M. Faaiz
2012-01-01
This note presents demonstrations of quadratic expressions that come about when particular problems are posed with respect to matchsticks that form regular triangles, squares, pentagons and so on. Usually when such "matchstick" problems are used as ways to foster algebraic thinking, the expressions for the number of matchstick quantities are…
Confidence set interference with a prior quadratic bound. [in geophysics
NASA Technical Reports Server (NTRS)
Backus, George E.
1989-01-01
Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.
Quadratic blind linear unmixing: A graphical user interface for tissue characterization.
Gutierrez-Navarro, O; Campos-Delgado, D U; Arce-Santana, E R; Jo, Javier A
2016-02-01
Spectral unmixing is the process of breaking down data from a sample into its basic components and their abundances. Previous work has been focused on blind unmixing of multi-spectral fluorescence lifetime imaging microscopy (m-FLIM) datasets under a linear mixture model and quadratic approximations. This method provides a fast linear decomposition and can work without a limitation in the maximum number of components or end-members. Hence this work presents an interactive software which implements our blind end-member and abundance extraction (BEAE) and quadratic blind linear unmixing (QBLU) algorithms in Matlab. The options and capabilities of our proposed software are described in detail. When the number of components is known, our software can estimate the constitutive end-members and their abundances. When no prior knowledge is available, the software can provide a completely blind solution to estimate the number of components, the end-members and their abundances. The characterization of three case studies validates the performance of the new software: ex-vivo human coronary arteries, human breast cancer cell samples, and in-vivo hamster oral mucosa. The software is freely available in a hosted webpage by one of the developing institutions, and allows the user a quick, easy-to-use and efficient tool for multi/hyper-spectral data decomposition.
Quadratic Blind Linear Unmixing: A Graphical User Interface for Tissue Characterization
Gutierrez-Navarro, O.; Campos-Delgado, D.U.; Arce-Santana, E. R.; Jo, Javier A.
2016-01-01
Spectral unmixing is the process of breaking down data from a sample into its basic components and their abundances. Previous work has been focused on blind unmixing of multi-spectral fluorescence lifetime imaging microscopy (m-FLIM) datasets under a linear mixture model and quadratic approximations. This method provides a fast linear decomposition and can work without a limitation in the maximum number of components or end-members. Hence this work presents an interactive software which implements our blind end-member and abundance extraction (BEAE) and quadratic blind linear unmixing (QBLU) algorithms in Matlab. The options and capabilities of our proposed software are described in detail. When the number of components is known, our software can estimate the constitutive end-members and their abundances. When no prior knowledge is available, the software can provide a completely blind solution to estimate the number of components, the end-members and their abundances. The characterization of three case studies validates the performance of the new software: ex-vivo human coronary arteries, human breast cancer cell samples, and in-vivo hamster oral mucosa. The software is freely available in a hosted webpage by one of the developing institutions, and allows the user a quick, easy-to-use and efficient tool for multi/hyper-spectral data decomposition. PMID:26589467
A user oriented microcomputer facility for designing linear quadratic Gaussian feedback compensators
NASA Technical Reports Server (NTRS)
Houpt, P. K.; Wahid, J.; Johnson, T. L.; Ward, S. A.
1978-01-01
A laboratory design facility for digital microprocessor implementation of linear-quadratic-Gaussian feedback compensators is described. Outputs from user interactive programs for solving infinite time horizon LQ regulator and Kalman filter problems were conditioned for implementation on the laboratory microcomputer system. The software consisted of two parts: an offline high-level program for solving the LQ Ricatti equations and generating associated feedback and filter gains and a cross compiler/macro assembler which generates object code for the target microprocessor system. A PDP 11/70 with a UNIX operating system was used for all high level program and data management, and the target microprocessor system is an Intel MDS (8080-based processor). Application to the control of a two dimensional inverted pendulum is presented and issues in expanding the design/prototyping system to other target machine architectures are discussed.
A path following algorithm for the graph matching problem.
Zaslavskiy, Mikhail; Bach, Francis; Vert, Jean-Philippe
2009-12-01
We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We, therefore, construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore, perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four data sets: simulated graphs, QAPLib, retina vessel images, and handwritten Chinese characters. In all cases, the results are competitive with the state of the art.
Anderson, Charles W; Young, Peter Michael; Buehner, Michael R; Knight, James N; Bush, Keith A; Hittle, Douglas C
2007-07-01
The applicability of machine learning techniques for feedback control systems is limited by a lack of stability guarantees. Robust control theory offers a framework for analyzing the stability of feedback control loops, but for the integral quadratic constraint (IQC) framework used here, all components are required to be represented as linear, time-invariant systems plus uncertainties with, for IQCs used here, bounded gain. In this paper, the stability of a control loop including a recurrent neural network (NN) is analyzed by replacing the nonlinear and time-varying components of the NN with IQCs on their gain. As a result, a range of the NN's weights is found within which stability is guaranteed. An algorithm is demonstrated for training the recurrent NN using reinforcement learning and guaranteeing stability while learning.
Gravitomagnetic effects in quadratic gravity with a scalar field
NASA Astrophysics Data System (ADS)
Finch, Andrew; Said, Jackson Levi
2016-10-01
The two gravitomagnetic effects which influence bodies orbiting around a gravitational source are the geodetic effect and the Lense-Thirring effect. The former describes the precession angle of the axis of a spinning gyroscope while in orbit around a nonrotating gravitational source whereas the latter provides a correction for this angle in the case of a spinning source. In this paper we derive the relevant equations in quadratic gravity and relate them to their equivalents in general relativity. Starting with an investigation into Kepler's third law in quadratic gravity with a scalar field, the effects of an axisymmetric and rotating gravitational source on an orbiting body in a circular, equatorial orbit are introduced.
Design of Linear Quadratic Regulators and Kalman Filters
NASA Technical Reports Server (NTRS)
Lehtinen, B.; Geyser, L.
1986-01-01
AESOP solves problems associated with design of controls and state estimators for linear time-invariant systems. Systems considered are modeled in state-variable form by set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are linear quadratic regulator (LQR) design problem and steady-state Kalman filter design problem. AESOP is interactive. User solves design problems and analyzes solutions in single interactive session. Both numerical and graphical information available to user during the session.
Nonlocal quadratic Poisson algebras, monodromy map, and Bogoyavlensky lattices
NASA Astrophysics Data System (ADS)
Suris, Yuri B.
1997-08-01
A new Lax representation for the Bogoyavlensky lattice is found and its r-matrix interpretation is elaborated. The r-matrix structure turns out to be related to a highly nonlocal quadratic Poisson structure on a direct sum of associative algebras. The theory of such nonlocal structures is developed and the Poisson property of the monodromy map is worked out in the most general situation. Some problems concerning the duality of Lax representations are raised.
Quantum integrals of motion for variable quadratic Hamiltonians
Cordero-Soto, Ricardo; Suazo, Erwin; Suslov, Sergei K.
2010-09-15
We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.
Discrete quadratic solitons with competing second-harmonic components
Setzpfandt, Frank; Pertsch, Thomas; Sukhorukov, Andrey A.
2011-11-15
We describe families of discrete solitons in quadratic waveguide arrays supported by competing cascaded nonlinear interactions between one fundamental and two second-harmonic modes. We characterize the existence, stability, and excitation dynamics of these solitons and show that their features may resemble those of solitons in saturable media. Our results also demonstrate that a power threshold may appear for soliton formation, leading to a suppression of beam self-focusing which explains recent experimental observations.
Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality
NASA Technical Reports Server (NTRS)
Acikmese, Ahmet Behcet; Corless, Martin
2004-01-01
We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.
Measurement of quadratic electrogyration effect in castor oil
NASA Astrophysics Data System (ADS)
Izdebski, Marek; Ledzion, Rafał; Górski, Piotr
2015-07-01
This work presents a detailed analysis of electrogyration measurement in liquids with the usage of an optical polarimetric technique. Theoretical analysis of the optical response to an applied electric field is illustrated by experimental data for castor oil which exhibits natural optical activity, quadratic electro-optic effect and quadratic electrogyration effect. Moreover, the experimental data show that interaction of the oil with a pair of flat electrodes induces a significant dichroism and natural linear birefringence. The combination of these effects occurring at the same time complicates the procedure of measurements. It has been found that a single measurement is insufficient to separate the contribution of the electrogyration effect, but it is possible on the basis of several measurements performed with various orientations of the polarizer and the analyser. The obtained average values of the quadratic electrogyration coefficient β13 in castor oil at room temperature are from - 0.92 ×10-22 to - 1.44 ×10-22m2V-2 depending on the origin of the oil. Although this study is focused on measurements in castor oil, the presented analysis is much more general.
Revisiting the naturalness problem: Who is afraid of quadratic divergences?
NASA Astrophysics Data System (ADS)
Aoki, Hajime; Iso, Satoshi
2012-07-01
It is widely believed that quadratic divergences severely restrict natural constructions of particle physics models beyond the standard model (SM). Supersymmetry provides a beautiful solution, but the recent LHC experiments have excluded large parameter regions of supersymmetric extensions of the SM. It will now be important to reconsider whether we have been misinterpreting the quadratic divergences in field theories. In this paper, we revisit the problem from the viewpoint of the Wilsonian renormalization group and argue that quadratic divergences—which can always be absorbed into a position of the critical surface—should be simply subtracted in model constructions. Such a picture gives another justification to the argument [W. A. Bardeen, Report No. FERMILAB-CONF-95-391-T] that the scale invariance of the SM, except for the soft-breaking terms, is an alternative solution to the naturalness problem. It also largely broadens possibilities of model constructions beyond the SM since we just need to take care of logarithmic divergences, which cause mixings of various physical scales and runnings of couplings.
On the convergence of inexact Uzawa algorithms
Welfert, B.D.
1994-12-31
The author considers the solution of symmetric indefinite systems which can be cast in matrix block form, where diagonal blocks A and C are symmetric positive definite and semi-definite, respectively. Systems of this type arise frequently in quadratic minimization problems, as well as mixed finite element discretizations of fluid flow equation. The author uses the Uzawa algorithm to precondition the matrix equations.
Interactive application of quadratic expansion of chi-square statistic to nonlinear curve fitting
NASA Technical Reports Server (NTRS)
Badavi, F. F.; Everhart, Joel L.
1987-01-01
This report contains a detailed theoretical description of an all-purpose, interactive curve-fitting routine that is based on P. R. Bevington's description of the quadratic expansion of the Chi-Square statistic. The method is implemented in the associated interactive, graphics-based computer program. Taylor's expansion of Chi-Square is first introduced, and justifications for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations is derived, then solved by matrix algebra. A brief description of the code is presented along with a limited number of changes that are required to customize the program of a particular task. To evaluate the performance of the method and the goodness of nonlinear curve fitting, two typical engineering problems are examined and the graphical and tabular output of each is discussed. A complete listing of the entire package is included as an appendix.
NASA Astrophysics Data System (ADS)
Gladwin, D.; Stewart, P.; Stewart, J.
2011-02-01
This article addresses the problem of maintaining a stable rectified DC output from the three-phase AC generator in a series-hybrid vehicle powertrain. The series-hybrid prime power source generally comprises an internal combustion (IC) engine driving a three-phase permanent magnet generator whose output is rectified to DC. A recent development has been to control the engine/generator combination by an electronically actuated throttle. This system can be represented as a nonlinear system with significant time delay. Previously, voltage control of the generator output has been achieved by model predictive methods such as the Smith Predictor. These methods rely on the incorporation of an accurate system model and time delay into the control algorithm, with a consequent increase in computational complexity in the real-time controller, and as a necessity relies to some extent on the accuracy of the models. Two complementary performance objectives exist for the control system. Firstly, to maintain the IC engine at its optimal operating point, and secondly, to supply a stable DC supply to the traction drive inverters. Achievement of these goals minimises the transient energy storage requirements at the DC link, with a consequent reduction in both weight and cost. These objectives imply constant velocity operation of the IC engine under external load disturbances and changes in both operating conditions and vehicle speed set-points. In order to achieve these objectives, and reduce the complexity of implementation, in this article a controller is designed by the use of Genetic Programming methods in the Simulink modelling environment, with the aim of obtaining a relatively simple controller for the time-delay system which does not rely on the implementation of real time system models or time delay approximations in the controller. A methodology is presented to utilise the miriad of existing control blocks in the Simulink libraries to automatically evolve optimal control
Hutula, D.N.; Wiancko, B.E.
1980-03-01
ACCEPT is a three-dimensional finite element computer program for analysis of large-deformation elastic-plastic-creep response of Zircaloy tubes subjected to temperature, surface pressures, and axial force. A twenty-mode, tri-quadratic, isoparametric element is used along with a Zircaloy materials model. A linear time-incremental procedure with residual force correction is used to solve for the time-dependent response. The program features an algorithm which automatically chooses the time step sizes to control the accuracy and numerical stability of the solution. A contact-separation capability allows modeling of interaction of reactor fuel rod cladding with fuel pellets or external supports.
NASA Astrophysics Data System (ADS)
Coudarcher, Rémi; Duculty, Florent; Serot, Jocelyn; Jurie, Frédéric; Derutin, Jean-Pierre; Dhome, Michel
2005-12-01
SKiPPER is a SKeleton-based Parallel Programming EnviRonment being developed since 1996 and running at LASMEA Laboratory, the Blaise-Pascal University, France. The main goal of the project was to demonstrate the applicability of skeleton-based parallel programming techniques to the fast prototyping of reactive vision applications. This paper deals with the special features embedded in the latest version of the project: algorithmic skeleton nesting capabilities and a fully dynamic operating model. Throughout the case study of a complete and realistic image processing application, in which we have pointed out the requirement for skeleton nesting, we are presenting the operating model of this feature. The work described here is one of the few reported experiments showing the application of skeleton nesting facilities for the parallelisation of a realistic application, especially in the area of image processing. The image processing application we have chosen is a 3D face-tracking algorithm from appearance.
A computational algorithm for spacecraft control and momentum management
NASA Technical Reports Server (NTRS)
Dzielski, John; Bergmann, Edward; Paradiso, Joseph
1990-01-01
Developments in the area of nonlinear control theory have shown how coordinate changes in the state and input spaces of a dynamical system can be used to transform certain nonlinear differential equations into equivalent linear equations. These techniques are applied to the control of a spacecraft equipped with momentum exchange devices. An optimal control problem is formulated that incorporates a nonlinear spacecraft model. An algorithm is developed for solving the optimization problem using feedback linearization to transform to an equivalent problem involving a linear dynamical constraint and a functional approximation technique to solve for the linear dynamics in terms of the control. The original problem is transformed into an unconstrained nonlinear quadratic program that yields an approximate solution to the original problem. Two examples are presented to illustrate the results.
Algorithm For Optimal Control Of Large Structures
NASA Technical Reports Server (NTRS)
Salama, Moktar A.; Garba, John A..; Utku, Senol
1989-01-01
Cost of computation appears competitive with other methods. Problem to compute optimal control of forced response of structure with n degrees of freedom identified in terms of smaller number, r, of vibrational modes. Article begins with Hamilton-Jacobi formulation of mechanics and use of quadratic cost functional. Complexity reduced by alternative approach in which quadratic cost functional expressed in terms of control variables only. Leads to iterative solution of second-order time-integral matrix Volterra equation of second kind containing optimal control vector. Cost of algorithm, measured in terms of number of computations required, is of order of, or less than, cost of prior algoritms applied to similar problems.
Large Scale Non-Linear Programming for PDE Constrained Optimization
VAN BLOEMEN WAANDERS, BART G.; BARTLETT, ROSCOE A.; LONG, KEVIN R.; BOGGS, PAUL T.; SALINGER, ANDREW G.
2002-10-01
Three years of large-scale PDE-constrained optimization research and development are summarized in this report. We have developed an optimization framework for 3 levels of SAND optimization and developed a powerful PDE prototyping tool. The optimization algorithms have been interfaced and tested on CVD problems using a chemically reacting fluid flow simulator resulting in an order of magnitude reduction in compute time over a black box method. Sandia's simulation environment is reviewed by characterizing each discipline and identifying a possible target level of optimization. Because SAND algorithms are difficult to test on actual production codes, a symbolic simulator (Sundance) was developed and interfaced with a reduced-space sequential quadratic programming framework (rSQP++) to provide a PDE prototyping environment. The power of Sundance/rSQP++ is demonstrated by applying optimization to a series of different PDE-based problems. In addition, we show the merits of SAND methods by comparing seven levels of optimization for a source-inversion problem using Sundance and rSQP++. Algorithmic results are discussed for hierarchical control methods. The design of an interior point quadratic programming solver is presented.
Compact stellar models obeying quadratic equation of state
NASA Astrophysics Data System (ADS)
Bhar, Piyali; Singh, Ksh. Newton; Pant, Neeraj
2016-10-01
In present paper we obtain a new model of compact star by considering quadratic equation of state for the matter distribution and assuming a physically reasonable choice for metric coefficient g_{rr}. The solution is singularity free and well behaved inside the stellar interior. Several features are described analytically as well as graphically. From our analysis we have shown that our model is compatible with the observational data of the compact stars. We have discussed a detail analysis of neutron star PSR J1614-2230 via different graphs after determining all the constant parameters from boundary conditions.
Rigorous performance bounds for quadratic and nested dynamical decoupling
Xia, Yuhou; Uhrig, Goetz S.; Lidar, Daniel A.
2011-12-15
We present rigorous performance bounds for the quadratic dynamical decoupling pulse sequence which protects a qubit from general decoherence, and for its nested generalization to an arbitrary number of qubits. Our bounds apply under the assumptions of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians such as those realized by baths of nuclear spins in quantum dots. We prove that if the total sequence time is fixed then the trace-norm distance between the unperturbed and protected system states can be made arbitrarily small by increasing the number of applied pulses.
Reaction Wheel Control Design Using Linear Quadratic Controller
NASA Astrophysics Data System (ADS)
Nubli Muhamad, Nur; Susanto, Erwin; Syihabuddin, Budi; Prasetya Dwi Wibawa, Ig.
2016-01-01
This paper studies the design of active attitude control system of a nanosatellite in a single axis. In this paper, we consider dc motor based reaction wheel as an actuator, because of its pointing accuracy. However, the power consumption of the dc motor is often relatively large and needed to be optimized. Linear quadratic controller is supposed to have an ability to minimize power consumption and able to enhance the system performance. To show the advantage of this method, simulation result of attitude response, state trajectory, and trajectory of DC motor voltage are presented.
Frontogenesis driven by horizontally quadratic distributions of density
NASA Technical Reports Server (NTRS)
Jacqmin, David
1991-01-01
Attention is given to the quadratic density distribution in a channel, which has been established by Simpson and Linden to be the simplest case of the horizontally nonlinear distribution of fluid density required for the production of frontogenesis. The porous-media and Boussinesq flow models are examined, and their evolution equations are reduced to one-dimensional systems. While both the porous-media and the inviscid/nondiffusive Boussinesq systems exhibit classic frontogenesis behavior, the viscous Boussinesq system exhibits a more complex behavior: boundary-layer effects force frontogenesis away from the lower boundary, and at late times the steepest density gradients are close to mid-channel.
Quantum mechanical study of a generic quadratically coupled optomechanical system
NASA Astrophysics Data System (ADS)
Shi, H.; Bhattacharya, M.
2013-04-01
Typical optomechanical systems involving optical cavities and mechanical oscillators rely on a coupling that varies linearly with the oscillator displacement. However, recently a coupling varying instead as the square of the mechanical displacement has been realized, presenting new possibilities for nondemolition measurements and mechanical squeezing. In this article we present a quantum mechanical study of a generic quadratic-coupling optomechanical Hamiltonian. First, neglecting dissipation, we provide analytical results for the dressed states, spectrum, phonon statistics and entanglement. Subsequently, accounting for dissipation, we supply a numerical treatment using a master equation approach. We expect our results to be of use to optomechanical spectroscopy, state transfer, wave-function engineering, and entanglement generation.
On a quadratic transformation due to Kummer and its generalizations
NASA Astrophysics Data System (ADS)
Shekhawat, Nidhi; Rathie, Arjun K.; Prakash, Om
2016-05-01
The aim of this paper is to obtain explicit expressions of (1-x ) -a2F1[a ,b 2 b +j ; -2/x 1 -x ] for j = 0, ±1,…, ±9. For j = 0, we have a well-known quadratic transformations formula of Kummer. The results are obtained by using the known hypergeometric identities available in the literature. Several known results obtained earlier by Kim, et al. follow special cases of our main findings. The results derived in this paper are simple, interesting and potentially useful in the applicable sciences.
Quadratic integrand double-hybrid made spin-component-scaled
NASA Astrophysics Data System (ADS)
Brémond, Éric; Savarese, Marika; Sancho-García, Juan C.; Pérez-Jiménez, Ángel J.; Adamo, Carlo
2016-03-01
We propose two analytical expressions aiming to rationalize the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) schemes for double-hybrid exchange-correlation density-functionals. Their performances are extensively tested within the framework of the nonempirical quadratic integrand double-hybrid (QIDH) model on energetic properties included into the very large GMTKN30 benchmark database, and on structural properties of semirigid medium-sized organic compounds. The SOS variant is revealed as a less computationally demanding alternative to reach the accuracy of the original QIDH model without losing any theoretical background.
Complex complete quadratic combination method for damped system with repeated eigenvalues
NASA Astrophysics Data System (ADS)
Yu, Ruifang; Zhou, Xiyuan; Abduwaris, Abduwahit
2016-09-01
A new response-spectrum mode superposition method, entirely in real value form, is developed to analyze the maximum structural response under earthquake ground motion for generally damped linear systems with repeated eigenvalues and defective eigenvectors. This algorithm has clear physical concepts and is similar to the complex complete quadratic combination (CCQC) method previously established. Since it can consider the effect of repeated eigenvalues, it is called the CCQC-R method, in which the correlation coefficients of high-order modal responses are enclosed in addition to the correlation coefficients in the normal CCQC method. As a result, the formulas for calculating the correlation coefficients of high-order modal responses are deduced in this study, including displacement, velocity and velocity-displacement correlation coefficients. Furthermore, the relationship between high-order displacement and velocity covariance is derived to make the CCQC-R algorithm only relevant to the high-order displacement response spectrum. Finally, a practical step-by-step integration procedure for calculating high-order displacement response spectrum is obtained by changing the earthquake ground motion input, which is evaluated by comparing it to the theory solution under the sine-wave input. The method derived here is suitable for generally linear systems with classical or non-classical damping.
ORACLS: A system for linear-quadratic-Gaussian control law design
NASA Technical Reports Server (NTRS)
Armstrong, E. S.
1978-01-01
A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.
Generic Optimization Program User Manual Version 3.0.0
Wetter, Michael
2009-05-11
GenOpt is an optimization program for the minimization of a cost function that is evaluated by an external simulation program. It has been developed for optimization problems where the cost function is computationally expensive and its derivatives are not available or may not even exist. GenOpt can be coupled to any simulation program that reads its input from text files and writes its output to text files. The independent variables can be continuous variables (possibly with lower and upper bounds), discrete variables, or both, continuous and discrete variables. Constraints on dependent variables can be implemented using penalty or barrier functions. GenOpt uses parallel computing to evaluate the simulations. GenOpt has a library with local and global multi-dimensional and one-dimensional optimization algorithms, and algorithms for doing parametric runs. An algorithm interface allows adding new minimization algorithms without knowing the details of the program structure. GenOpt is written in Java so that it is platform independent. The platform independence and the general interface make GenOpt applicable to a wide range of optimization problems. GenOpt has not been designed for linear programming problems, quadratic programming problems, and problems where the gradient of the cost function is available. For such problems, as well as for other problems, special tailored software exists that is more efficient.
Singular linear-quadratic control problem for systems with linear delay
Sesekin, A. N.
2013-12-18
A singular linear-quadratic optimization problem on the trajectories of non-autonomous linear differential equations with linear delay is considered. The peculiarity of this problem is the fact that this problem has no solution in the class of integrable controls. To ensure the existence of solutions is required to expand the class of controls including controls with impulse components. Dynamical systems with linear delay are used to describe the motion of pantograph from the current collector with electric traction, biology, etc. It should be noted that for practical problems fact singularity criterion of quality is quite commonly occurring, and therefore the study of these problems is surely important. For the problem under discussion optimal programming control contained impulse components at the initial and final moments of time is constructed under certain assumptions on the functional and the right side of the control system.
Electroweak vacuum stability and finite quadratic radiative corrections
NASA Astrophysics Data System (ADS)
Masina, Isabella; Nardini, Germano; Quiros, Mariano
2015-08-01
If the Standard Model (SM) is an effective theory, as currently believed, it is valid up to some energy scale Λ to which the Higgs vacuum expectation value is sensitive throughout radiative quadratic terms. The latter ones destabilize the electroweak vacuum and generate the SM hierarchy problem. For a given perturbative ultraviolet (UV) completion, the SM cutoff can be computed in terms of fundamental parameters. If the UV mass spectrum involves several scales, the cutoff is not unique and each SM sector has its own UV cutoff Λi. We have performed this calculation assuming the minimal supersymmetric standard model (MSSM) is the SM UV completion. As a result, from the SM point of view, the quadratic corrections to the Higgs mass are equivalent to finite threshold contributions. For the measured values of the top quark and Higgs masses, and depending on the values of the different cutoffs Λi, these contributions can cancel even at renormalization scales as low as multi-TeV, unlike the case of a single cutoff where the cancellation only occurs at Planckian energies, a result originally obtained by Veltman. From the MSSM point of view, the requirement of stability of the electroweak minimum under radiative corrections is incorporated into the matching conditions and provides an extra constraint on the focus point solution to the little hierarchy problem in the MSSM. These matching conditions can be employed for precise calculations of the Higgs sector in scenarios with heavy supersymmetric fields.
Wave propagation in elastic medium with heterogeneous quadratic nonlinearity
Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin
2011-06-23
This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter {beta} when the nonlinearity distribution in the layer is a stochastic process.
Confidence set inference with a prior quadratic bound
NASA Technical Reports Server (NTRS)
Backus, George E.
1989-01-01
In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z=(z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y (sup 0) = (y (sub 1) (sup 0), ..., y (sub D (sup 0)), using full or partial knowledge of the statistical distribution of the random errors in y (sup 0). The data space Y containing y(sup 0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x, Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. Confidence set inference is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface.
Quadratic Reciprocity and the Group Orders of Particle States
DAI,YANG; BORISOV,ALEXEY B.; LONGWORTH,JAMES W.; BOYER,KEITH; RHODES,CHARLES K.
2001-06-01
The construction of inverse states in a finite field F{sub P{sub P{alpha}}} enables the organization of the mass scale by associating particle states with residue class designations. With the assumption of perfect flatness ({Omega}total = 1.0), this approach leads to the derivation of a cosmic seesaw congruence which unifies the concepts of space and mass. The law of quadratic reciprocity profoundly constrains the subgroup structure of the multiplicative group of units F{sub P{sub {alpha}}}* defined by the field. Four specific outcomes of this organization are (1) a reduction in the computational complexity of the mass state distribution by a factor of {approximately}10{sup 30}, (2) the extension of the genetic divisor concept to the classification of subgroup orders, (3) the derivation of a simple numerical test for any prospective mass number based on the order of the integer, and (4) the identification of direct biological analogies to taxonomy and regulatory networks characteristic of cellular metabolism, tumor suppression, immunology, and evolution. It is generally concluded that the organizing principle legislated by the alliance of quadratic reciprocity with the cosmic seesaw creates a universal optimized structure that functions in the regulation of a broad range of complex phenomena.
Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing
NASA Technical Reports Server (NTRS)
Choi, Benjamin B.
2002-01-01
Linear-Quadratic-Gaussian (LQG) control is a modern state-space technique for designing optimal dynamic regulators. It enables us to trade off regulation performance and control effort, and to take into account process and measurement noise. The Structural Mechanics and Dynamics Branch at the NASA Glenn Research Center has developed an LQG control for a fault-tolerant magnetic bearing suspension rig to optimize system performance and to reduce the sensor and processing noise. The LQG regulator consists of an optimal state-feedback gain and a Kalman state estimator. The first design step is to seek a state-feedback law that minimizes the cost function of regulation performance, which is measured by a quadratic performance criterion with user-specified weighting matrices, and to define the tradeoff between regulation performance and control effort. The next design step is to derive a state estimator using a Kalman filter because the optimal state feedback cannot be implemented without full state measurement. Since the Kalman filter is an optimal estimator when dealing with Gaussian white noise, it minimizes the asymptotic covariance of the estimation error.
Linear quadratic stochastic control of atomic hydrogen masers.
Koppang, P; Leland, R
1999-01-01
Data are given showing the results of using the linear quadratic Gaussian (LQG) technique to steer remote hydrogen masers to Coordinated Universal Time (UTC) as given by the United States Naval Observatory (USNO) via two-way satellite time transfer and the Global Positioning System (GPS). Data also are shown from the results of steering a hydrogen maser to the real-time USNO mean. A general overview of the theory behind the LQG technique also is given. The LQG control is a technique that uses Kalman filtering to estimate time and frequency errors used as input into a control calculation. A discrete frequency steer is calculated by minimizing a quadratic cost function that is dependent on both the time and frequency errors and the control effort. Different penalties, chosen by the designer, are assessed by the controller as the time and frequency errors and control effort vary from zero. With this feature, controllers can be designed to force the time and frequency differences between two standards to zero, either more or less aggressively depending on the application.
QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.
Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit
2014-01-01
We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed. PMID:25301974
An Instability Index Theory for Quadratic Pencils and Applications
NASA Astrophysics Data System (ADS)
Bronski, Jared; Johnson, Mathew A.; Kapitula, Todd
2014-04-01
Primarily motivated by the stability analysis of nonlinear waves in second-order in time Hamiltonian systems, in this paper we develop an instability index theory for quadratic operator pencils acting on a Hilbert space. In an extension of the known theory for linear pencils, explicit connections are made between the number of eigenvalues of a given quadratic operator pencil with positive real parts to spectral information about the individual operators comprising the coefficients of the spectral parameter in the pencil. As an application, we apply the general theory developed here to yield spectral and nonlinear stability/instability results for abstract second-order in time wave equations. More specifically, we consider the problem of the existence and stability of spatially periodic waves for the "good" Boussinesq equation. In the analysis our instability index theory provides an explicit, and somewhat surprising, connection between the stability of a given periodic traveling wave solution of the "good" Boussinesq equation and the stability of the same periodic profile, but with different wavespeed, in the nonlinear dynamics of a related generalized Korteweg-de Vries equation.
Half-quadratic-based iterative minimization for robust sparse representation.
He, Ran; Zheng, Wei-Shi; Tan, Tieniu; Sun, Zhenan
2014-02-01
Robust sparse representation has shown significant potential in solving challenging problems in computer vision such as biometrics and visual surveillance. Although several robust sparse models have been proposed and promising results have been obtained, they are either for error correction or for error detection, and learning a general framework that systematically unifies these two aspects and explores their relation is still an open problem. In this paper, we develop a half-quadratic (HQ) framework to solve the robust sparse representation problem. By defining different kinds of half-quadratic functions, the proposed HQ framework is applicable to performing both error correction and error detection. More specifically, by using the additive form of HQ, we propose an ℓ1-regularized error correction method by iteratively recovering corrupted data from errors incurred by noises and outliers; by using the multiplicative form of HQ, we propose an ℓ1-regularized error detection method by learning from uncorrupted data iteratively. We also show that the ℓ1-regularization solved by soft-thresholding function has a dual relationship to Huber M-estimator, which theoretically guarantees the performance of robust sparse representation in terms of M-estimation. Experiments on robust face recognition under severe occlusion and corruption validate our framework and findings.
Mass Conservation and Positivity Preservation with Ensemble-type Kalman Filter Algorithms
NASA Astrophysics Data System (ADS)
Janjic, Tijana; McLaughlin, Dennis B.; Cohn, Stephen E.; Verlaan, Martin
2014-05-01
Maintaining conservative physical laws numerically has long been recognized as being important in the development of numerical weather prediction (NWP) models. In the broader context of data assimilation, concerted efforts to maintain conservation laws numerically and to understand the significance of doing so have begun only recently. In order to enforce physically based conservation laws of total mass and positivity in the ensemble Kalman filter, we incorporate constraints to ensure that the filter ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. We show that the analysis steps of ensemble transform Kalman filter (ETKF) algorithm and ensemble Kalman filter algorithm (EnKF) can conserve the mass integral, but do not preserve positivity. Further, if localization is applied or if negative values are simply set to zero, then the total mass is not conserved either. In order to ensure mass conservation, a projection matrix that corrects for localization effects is constructed. In order to maintain both mass conservation and positivity preservation through the analysis step, we construct a data assimilation algorithm based on quadratic programming and ensemble Kalman filtering. Mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate constraints. Some simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. The results show clear improvements in both analyses and forecasts, particularly in the presence of localized features. Behavior of the algorithm is also tested in presence of model error.
Mass Conservation and Positivity Preservation with Ensemble-type Kalman Filter Algorithms
NASA Technical Reports Server (NTRS)
Janjic, Tijana; McLaughlin, Dennis B.; Cohn, Stephen E.; Verlaan, Martin
2013-01-01
Maintaining conservative physical laws numerically has long been recognized as being important in the development of numerical weather prediction (NWP) models. In the broader context of data assimilation, concerted efforts to maintain conservation laws numerically and to understand the significance of doing so have begun only recently. In order to enforce physically based conservation laws of total mass and positivity in the ensemble Kalman filter, we incorporate constraints to ensure that the filter ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. We show that the analysis steps of ensemble transform Kalman filter (ETKF) algorithm and ensemble Kalman filter algorithm (EnKF) can conserve the mass integral, but do not preserve positivity. Further, if localization is applied or if negative values are simply set to zero, then the total mass is not conserved either. In order to ensure mass conservation, a projection matrix that corrects for localization effects is constructed. In order to maintain both mass conservation and positivity preservation through the analysis step, we construct a data assimilation algorithms based on quadratic programming and ensemble Kalman filtering. Mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate constraints. Some simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. The results show clear improvements in both analyses and forecasts, particularly in the presence of localized features. Behavior of the algorithm is also tested in presence of model error.
Cao, Buwen; Luo, Jiawei; Liang, Cheng; Wang, Shulin; Song, Dan
2015-10-01
The identification of protein complexes in protein-protein interaction (PPI) networks has greatly advanced our understanding of biological organisms. Existing computational methods to detect protein complexes are usually based on specific network topological properties of PPI networks. However, due to the inherent complexity of the network structures, the identification of protein complexes may not be fully addressed by using single network topological property. In this study, we propose a novel MultiObjective Evolutionary Programming Genetic Algorithm (MOEPGA) which integrates multiple network topological features to detect biologically meaningful protein complexes. Our approach first systematically analyzes the multiobjective problem in terms of identifying protein complexes from PPI networks, and then constructs the objective function of the iterative algorithm based on three common topological properties of protein complexes from the benchmark dataset, finally we describe our algorithm, which mainly consists of three steps, population initialization, subgraph mutation and subgraph selection operation. To show the utility of our method, we compared MOEPGA with several state-of-the-art algorithms on two yeast PPI datasets. The experiment results demonstrate that the proposed method can not only find more protein complexes but also achieve higher accuracy in terms of fscore. Moreover, our approach can cover a certain number of proteins in the input PPI network in terms of the normalized clustering score. Taken together, our method can serve as a powerful framework to detect protein complexes in yeast PPI networks, thereby facilitating the identification of the underlying biological functions.
El-Qulity, Said Ali; Mohamed, Ali Wagdy
2016-01-01
This paper proposes a nonlinear integer goal programming model (NIGPM) for solving the general problem of admission capacity planning in a country as a whole. The work aims to satisfy most of the required key objectives of a country related to the enrollment problem for higher education. The system general outlines are developed along with the solution methodology for application to the time horizon in a given plan. The up-to-date data for Saudi Arabia is used as a case study and a novel evolutionary algorithm based on modified differential evolution (DE) algorithm is used to solve the complexity of the NIGPM generated for different goal priorities. The experimental results presented in this paper show their effectiveness in solving the admission capacity for higher education in terms of final solution quality and robustness. PMID:26819583
SPARSE: quadratic time simultaneous alignment and folding of RNAs without sequence-based heuristics
Will, Sebastian; Otto, Christina; Miladi, Milad; Möhl, Mathias; Backofen, Rolf
2015-01-01
Motivation: RNA-Seq experiments have revealed a multitude of novel ncRNAs. The gold standard for their analysis based on simultaneous alignment and folding suffers from extreme time complexity of O(n6). Subsequently, numerous faster ‘Sankoff-style’ approaches have been suggested. Commonly, the performance of such methods relies on sequence-based heuristics that restrict the search space to optimal or near-optimal sequence alignments; however, the accuracy of sequence-based methods breaks down for RNAs with sequence identities below 60%. Alignment approaches like LocARNA that do not require sequence-based heuristics, have been limited to high complexity (≥ quartic time). Results: Breaking this barrier, we introduce the novel Sankoff-style algorithm ‘sparsified prediction and alignment of RNAs based on their structure ensembles (SPARSE)’, which runs in quadratic time without sequence-based heuristics. To achieve this low complexity, on par with sequence alignment algorithms, SPARSE features strong sparsification based on structural properties of the RNA ensembles. Following PMcomp, SPARSE gains further speed-up from lightweight energy computation. Although all existing lightweight Sankoff-style methods restrict Sankoff’s original model by disallowing loop deletions and insertions, SPARSE transfers the Sankoff algorithm to the lightweight energy model completely for the first time. Compared with LocARNA, SPARSE achieves similar alignment and better folding quality in significantly less time (speedup: 3.7). At similar run-time, it aligns low sequence identity instances substantially more accurate than RAF, which uses sequence-based heuristics. Availability and implementation: SPARSE is freely available at http://www.bioinf.uni-freiburg.de/Software/SPARSE. Contact: backofen@informatik.uni-freiburg.de Supplementary information: Supplementary data are available at Bioinformatics online. PMID:25838465
Primal-dual interior point methods over quadratic, semidefinite and p-cones
Adler, I.
1994-12-31
It has been observed that some interior point algorithms for linear programming can be extended, in a sense step by step, to optimization problems over more general domains, such as the cone of positive semidefinite matrices and the so-called {open_quotes}ice cream{close_quotes} cone. Most of the algorithms that have been extended, however are mostly primal or dual algorithms. It turns out that analogous extensions of primal-dual methods are more challenging. We discuss such extensions and complexity issues related to such generalizations.
PIFCGT: A PIF autopilot design program for general aviation aircraft
NASA Technical Reports Server (NTRS)
Broussard, J. R.
1983-01-01
This report documents the PIFCGT computer program. In FORTRAN, PIFCGT is a computer design aid for determing Proportional-Integral-Filter (PIF) control laws for aircraft autopilots implemented with a Command Generator Tracker (CGT). The program uses Linear-Quadratic-Regulator synthesis algorithms to determine feedback gains, and includes software to solve the feedforward matrix equation which is useful in determining the command generator tracker feedforward gains. The program accepts aerodynamic stability derivatives and computes the corresponding aerodynamic linear model. The nine autopilot modes that can be designed include four maneuver modes (ROLL SEL, PITCH SEL, HDG SEL, ALT SEL), four final approach models (APR GS, APR LOCI, APR LOCR, APR LOCP), and a BETA HOLD mode. The program has been compiled and executed on a CDC computer.
Repopulation Kinetics and the Linear-Quadratic Model
NASA Astrophysics Data System (ADS)
O'Rourke, S. F. C.; McAneney, H.; Starrett, C.; O'Sullivan, J. M.
2009-08-01
The standard Linear-Quadratic (LQ) survival model for radiotherapy is used to investigate different schedules of radiation treatment planning for advanced head and neck cancer. We explore how these treament protocols may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al. [1], which was concerned with the case of exponential repopulation between treatments. Treatment schedules investigated include standarized and accelerated fractionation. Calculations based on the present work show, that even with growth laws scaled to ensure that the repopulation kinetics for advanced head and neck cancer are comparable, considerable variation in the survival fraction to orders of magnitude emerged. Calculations show that application of the Gompertz model results in a significantly poorer prognosis for tumour eradication. Gaps in treatment also highlight the differences in the LQ model with the effect of repopulation kinetics included.
Renormalisation of correlations in a barrier billiard: Quadratic irrational trajectories
NASA Astrophysics Data System (ADS)
Adamson, L. N. C.; Osbaldestin, A. H.
2014-03-01
We present an analysis of autocorrelation functions in symmetric barrier billiards using a renormalisation approach for quadratic irrational trajectories. Depending on the nature of the barrier, this leads to either self-similar or chaotic behaviour. In the self-similar case we give an analysis of the half barrier and present a detailed calculation of the locations, asymptotic heights and signs of the main peaks in the autocorrelation function. Then we consider arbitrary barriers, illustrating that typically these give rise to chaotic correlations of the autocorrelation function which we further represent by showing the invariant sets associated with these correlations. Our main ingredient here is a functional recurrence which has been previously derived and used in work on the Harper equation, strange non-chaotic attractors and a quasi-periodically forced two-level system.
Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions.
Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza
2016-08-12
We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D-1. The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s-wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4π-periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary. PMID:27563986
Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions
NASA Astrophysics Data System (ADS)
Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza
2016-08-01
We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D -1 . The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s -wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4 π -periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary.
Schwarz and multilevel methods for quadratic spline collocation
Christara, C.C.; Smith, B.
1994-12-31
Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.
Wind turbine power tracking using an improved multimodel quadratic approach.
Khezami, Nadhira; Benhadj Braiek, Naceur; Guillaud, Xavier
2010-07-01
In this paper, an improved multimodel optimal quadratic control structure for variable speed, pitch regulated wind turbines (operating at high wind speeds) is proposed in order to integrate high levels of wind power to actively provide a primary reserve for frequency control. On the basis of the nonlinear model of the studied plant, and taking into account the wind speed fluctuations, and the electrical power variation, a multimodel linear description is derived for the wind turbine, and is used for the synthesis of an optimal control law involving a state feedback, an integral action and an output reference model. This new control structure allows a rapid transition of the wind turbine generated power between different desired set values. This electrical power tracking is ensured with a high-performance behavior for all other state variables: turbine and generator rotational speeds and mechanical shaft torque; and smooth and adequate evolution of the control variables.
Cosmology for quadratic gravity in generalized Weyl geometry
NASA Astrophysics Data System (ADS)
Beltrán Jiménez, Jose; Heisenberg, Lavinia; Koivisto, Tomi S.
2016-04-01
A class of vector-tensor theories arises naturally in the framework of quadratic gravity in spacetimes with linear vector distortion. Requiring the absence of ghosts for the vector field imposes an interesting condition on the allowed connections with vector distortion: the resulting one-parameter family of connections generalises the usual Weyl geometry with polar torsion. The cosmology of this class of theories is studied, focusing on isotropic solutions wherein the vector field is dominated by the temporal component. De Sitter attractors are found and inhomogeneous perturbations around such backgrounds are analysed. In particular, further constraints on the models are imposed by excluding pathologies in the scalar, vector and tensor fluctuations. Various exact background solutions are presented, describing a constant and an evolving dark energy, a bounce and a self-tuning de Sitter phase. However, the latter two scenarios are not viable under a closer scrutiny.
Bdzil, J.B.; Jackson, T.L.; Stewart, D.S.
1999-02-02
In the design of explosive systems the generic problem that one must consider is the propagation of a well-developed detonation wave sweeping through an explosive charge with a complex shape. At a given instant of time the lead detonation shock is a surface that occupies a region of the explosive and has a dimension that is characteristic of the explosive device, typically on the scale of meters. The detonation shock is powered by a detonation reaction zone, sitting immediately behind the shock, which is on the scale of 1 millimeter or less. Thus, the ratio of the reaction zone thickness to the device dimension is of the order of 1/1,000 or less. This scale disparity can lead to great difficulties in computing three-dimensional detonation dynamics. An attack on the dilemma for the computation of detonation systems has lead to the invention of sub-scale models for a propagating detonation front that they refer to herein as program burn models. The program burn model seeks not to resolve the fine scale of the reaction zone in the sense of a DNS simulation. The goal of a program burn simulation is to resolve the hydrodynamics in the inert product gases on a grid much coarser than that required to resolve a physical reaction zone. The authors first show that traditional program burn algorithms for detonation hydrocodes used for explosive design are inconsistent and yield incorrect shock dynamic behavior. To overcome these inconsistencies, they are developing a new class of program burn models based on detonation shock dynamic (DSD) theory. It is hoped that this new class will yield a consistent and robust algorithm which reflects the correct shock dynamic behavior.
Confidence set inference with a prior quadratic bound
NASA Technical Reports Server (NTRS)
Backus, George E.
1988-01-01
In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z = (z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y(0)=(y sub 1(0),...,y sub D(0)) knowledge of the statistical distribution of the random errors in y(0). The data space Y containing y(0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x (e.g., energy or dissipation rate), Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. CSI is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface. Neither the heat flow nor the energy bound is strong enough to permit estimation of B(r) at single points on the CMB, but the heat flow bound permits estimation of uniform averages of B(r) over discs on the CMB, and both bounds permit weighted disc-averages with continous weighting kernels. Both bounds also permit estimation of low-degree Gauss coefficients at the CMB. The heat flow bound resolves them up to degree 8 if the crustal field at satellite altitudes must be treated as a systematic error, but can resolve to degree 11 under the most favorable statistical treatment of the crust. These two limits produce circles of confusion on the CMB with diameters of 25 deg and 19 deg respectively.
Spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity
Golubkov, A A; Makarov, Vladimir A
2011-11-30
We present a brief review of the results of fifty years of development efforts in spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity. The recent original results obtained by the authors show the fundamental possibility of determining, from experimental data, the coordinate dependences of complex quadratic susceptibility tensor components of a onedimensionally inhomogeneous (along the z axis) medium with an arbitrary frequency dispersion, if the linear dielectric properties of the medium also vary along the z axis and are described by a diagonal tensor of the linear dielectric constant. It is assumed that the medium in question has the form of a plane-parallel plate, whose surfaces are perpendicular to the direction of the inhomogeneity. Using the example of several components of the tensors X{sup (2)}(z, {omega}{sub 1} {+-} {omega}{sub 2}; {omega}{sub 1}, {+-} {omega}{sub 2}), we describe two methods for finding their spatial profiles, which differ in the interaction geometry of plane monochromatic fundamental waves with frequencies {omega}{sub 1} and {omega}{sub 2}. The both methods are based on assessing the intensity of the waves propagating from the plate at the sum or difference frequency and require measurements over a range of angles of incidence of the fundamental waves. Such measurements include two series of additional estimates of the intensities of the waves generated under special conditions by using the test and additional reference plates, which eliminates the need for complicated phase measurements of the complex amplitudes of the waves at the sum (difference) frequency.
Sensitivity Analysis of Parameters in Linear-Quadratic Radiobiologic Modeling
Fowler, Jack F.
2009-04-01
Purpose: Radiobiologic modeling is increasingly used to estimate the effects of altered treatment plans, especially for dose escalation. The present article shows how much the linear-quadratic (LQ) (calculated biologically equivalent dose [BED] varies when individual parameters of the LQ formula are varied by {+-}20% and by 1%. Methods: Equivalent total doses (EQD2 = normalized total doses (NTD) in 2-Gy fractions for tumor control, acute mucosal reactions, and late complications were calculated using the linear- quadratic formula with overall time: BED = nd (1 + d/ [{alpha}/{beta}]) - log{sub e}2 (T - Tk) / {alpha}Tp, where BED is BED = total dose x relative effectiveness (RE = nd (1 + d/ [{alpha}/{beta}]). Each of the five biologic parameters in turn was altered by {+-}10%, and the altered EQD2s tabulated; the difference was finally divided by 20. EQD2 or NTD is obtained by dividing BED by the RE for 2-Gy fractions, using the appropriate {alpha}/{beta} ratio. Results: Variations in tumor and acute mucosal EQD ranged from 0.1% to 0.45% per 1% change in each parameter for conventional schedules, the largest variation being caused by overall time. Variations in 'late' EQD were 0.4% to 0.6% per 1% change in the only biologic parameter, the {alpha}/{beta} ratio. For stereotactic body radiotherapy schedules, variations were larger, up to 0.6 to 0.9 for tumor and 1.6% to 1.9% for late, per 1% change in parameter. Conclusions: Robustness occurs similar to that of equivalent uniform dose (EUD), for the same reasons. Total dose, dose per fraction, and dose-rate cause their major effects, as well known.
Lee, S.P.; Smathers, J.B.; Withers, H.R.
1995-09-30
Radiotherapy plans based on physical dose distributions do not necessarily entirely reflect the biological effects under various fractionation schemes. Over the past decade, the linear-quadratic (LQ) model has emerged as a convenient tool to quantify biological effects for radiotherapy. In this work, we set out to construct a mechanism to display biologically oriented dose distribution based on the LQ model. A computer program that converts a physical dose distribution calculated by a commercially available treatment planning system to a biologically effective dose (BED) distribution has been developed and verified against theoretical calculations. This software accepts a user`s input of biological parameters for each structure of interest (linear and quadratic dose-response and repopulation kinetic parameters), as well as treatment scheme factors (number of fractions, fractional dose, and treatment time). It then presents a two-dimensional BED display in conjunction with anatomical structures. Furthermore, to facilitate clinicians` intuitive comparison with conventional fractionation regimen, a conversion of BED to normalized isoeffective dose (NID) is also allowed. We have demonstrated the feasibility of constructing a biologically oriented dose distribution for clinical practice of radiotherapy. The discordance between physical dose distributions and the biological counterparts based on the given treatment schemes was quantified. The computerized display of BED at nonprescription points greatly enhanced the versatility of this tool. Although the routine use of this implementation in clinical radiotherapy should be cautiously done, depending largely on the accuracy of the published biological parameters, it may, nevertheless, help the clinicians derive an optimal treatment plan with a particular fractionation scheme or use it as a quantitative tool for outcome analysis in clinical research. 45 refs., 3 figs., 5 tabs.
ERIC Educational Resources Information Center
Doukakis, Spyros; Giannakos, Michail N.; Koilias, Christos; Vlamos, Panayiotis
2013-01-01
This paper presents results of a questionnaire focused on investigating students' confidence and behavioral intention in the area of programming, particularly that of structures, problem solving, and programming commands (Conditional--Loop). Responses from 116 1st year students regarding informatics were used. The results indicate that the…
NASA Technical Reports Server (NTRS)
Armstrong, E. S.
1975-01-01
A digital computer program (ORACLS) for implementing the optimal regulator theory approach to the design of controllers for linear time-invariant systems is described. The user-oriented program employs the latest numerical techniques and is applicable to both the digital and continuous control problems.
Performance Trend of Different Algorithms for Structural Design Optimization
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Coroneos, Rula M.; Guptill, James D.; Hopkins, Dale A.
1996-01-01
Nonlinear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Center, a project was initiated to assess performance of different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with the sequential unconstrained minimizations technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.
Comparative Evaluation of Different Optimization Algorithms for Structural Design Applications
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Coroneos, Rula M.; Guptill, James D.; Hopkins, Dale A.
1996-01-01
Non-linear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Centre, a project was initiated to assess the performance of eight different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using the eight different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems, however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with Sequential Unconstrained Minimizations Technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.
Ita, B. I.
2014-11-12
By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained.
Neighboring optimal guidance theory and computer program
NASA Technical Reports Server (NTRS)
Powers, W. F.
1974-01-01
Developments of the linear quadratic optimal control problem are discussed. The theory is applicable to the development of neighboring optimal feedback guidance gains, and is useful as a tool for synthesizing feedback control laws. A computer program which requires only the pertinent matrices of the linear quadratic problem is described.
Multiple target detection in video using quadratic multi-frame correlation filtering
Kerekes, Ryan A; Kumar, B. V. K. Vijaya
2008-01-01
Most integrated target detection and tracking systems employ state-space models to keep track of an explicit number o findividual targets. Recently, a non-state-space framework was developed for enhancing target detection in video by applying probabilistic motion models to the soft information in correlation outputs before thresholding. This framework has been referred to as multi-frame correlation ltering (MFCF), and because it avoids the use of state-space models and the formation of explicit tracks, the framework is well-suited for handling scenes with unknown numbers of targets at unknown positions. In this paper, we propose to use quadratic correlation lters(QCFs)in the MFCF framework for robust target detection. We test our detection algorithm on real and synthe sized single-target and multi-target video sequences. Simulation results show that MFCF can signi cantly reduce (to zero in the best case) the false alarm rates of QCFs at detection rates above 95%in the presence of large amounts of uncorrelated noise. We also show that MFCF is more adept at rejecting those false peaks due to uncorrelated noise rather than those due to clutter and compression noise; consequently, we show that lters used in the framework should be made to favor clutter rejection over noise tolerance.
Spacecraft Formation Flying Maneuvers Using Linear Quadratic Regulation With No Radial Axis Inputs
NASA Technical Reports Server (NTRS)
Starin, Scott R.; Yedavalli, R. K.; Sparks, Andrew G.; Bauer, Frank H. (Technical Monitor)
2001-01-01
Regarding multiple spacecraft formation flying, the observation has been made that control thrust need only be applied coplanar to the local horizon to achieve complete controllability of a two-satellite (leader-follower) formation. A formulation of orbital dynamics using the state of one satellite relative to another is used. Without the need for thrust along the radial (zenith-nadir) axis of the relative reference frame, propulsion system simplifications and weight reduction may be accomplished. This work focuses on the validation of this control system on its own merits, and in comparison to a related system which does provide thrust along the radial axis of the relative frame. Maneuver simulations are performed using commercial ODE solvers to propagate the Keplerian dynamics of a controlled satellite relative to an uncontrolled leader. These short maneuver simulations demonstrate the capacity of the controller to perform changes from one formation geometry to another. Control algorithm performance is evaluated based on measures such as the fuel required to complete a maneuver and the maximum acceleration required by the controller. Based on this evaluation, the exclusion of the radial axis of control still allows enough control authority to use Linear Quadratic Regulator (LQR) techniques to design a gain matrix of adequate performance over finite maneuvers. Additional simulations are conducted including perturbations and using no radial control inputs. A major conclusion presented is that control inputs along the three axes have significantly different relationships to the governing orbital dynamics that may be exploited using LQR.
Parallel projected variable metric algorithms for unconstrained optimization
NASA Technical Reports Server (NTRS)
Freeman, T. L.
1989-01-01
The parallel variable metric optimization algorithms of Straeter (1973) and van Laarhoven (1985) are reviewed, and the possible drawbacks of the algorithms are noted. By including Davidon (1975) projections in the variable metric updating, researchers can generalize Straeter's algorithm to a family of parallel projected variable metric algorithms which do not suffer the above drawbacks and which retain quadratic termination. Finally researchers consider the numerical performance of one member of the family on several standard example problems and illustrate how the choice of the displacement vectors affects the performance of the algorithm.
Albuquerque, Fabio; Beier, Paul
2015-01-01
Here we report that prioritizing sites in order of rarity-weighted richness (RWR) is a simple, reliable way to identify sites that represent all species in the fewest number of sites (minimum set problem) or to identify sites that represent the largest number of species within a given number of sites (maximum coverage problem). We compared the number of species represented in sites prioritized by RWR to numbers of species represented in sites prioritized by the Zonation software package for 11 datasets in which the size of individual planning units (sites) ranged from <1 ha to 2,500 km2. On average, RWR solutions were more efficient than Zonation solutions. Integer programming remains the only guaranteed way find an optimal solution, and heuristic algorithms remain superior for conservation prioritizations that consider compactness and multiple near-optimal solutions in addition to species representation. But because RWR can be implemented easily and quickly in R or a spreadsheet, it is an attractive alternative to integer programming or heuristic algorithms in some conservation prioritization contexts. PMID:25780930
Mousavi, Seyed Mahmoud; Husseinzadeh, Danial; Alikhani, Sadegh
2014-04-01
Efficient models are required to predict the optimum values of ozone concentration in different levels of its precursors' concentrations and temperatures. A novel model based on the application of a genetic programming (GP) optimization is presented in this article. Ozone precursors' concentrations and run time average temperature have been chosen as model's parameters. Generalization performances of two different homemade models based on genetic programming and genetic algorithm (GA), which can be used for calculating theoretical ozone concentration, are compared with conventional semi-empirical model performance. Experimental data of Mashhad city ambient air have been employed to investigate the prediction ability of properly trained GP, GA, and conventional semi-empirical models. It is clearly demonstrated that the in-house algorithm which is used for the model based on GP, provides better generalization performance over the model optimized with GA and the conventional semi-empirical ones. The proposed model is found accurate enough and can be used for urban air ozone concentration prediction.
Nikolaev, V.I.; Yatsko, S.N.
1995-12-01
A mathematical model and a package of programs are presented for simulating the atmospheric turbulent diffusion of contaminating impurities from land based and other sources. Test calculations and investigations of the effect of various factors are carried out.
Conservation of Mass and Preservation of Positivity with Ensemble-Type Kalman Filter Algorithms
NASA Technical Reports Server (NTRS)
Janjic, Tijana; Mclaughlin, Dennis; Cohn, Stephen E.; Verlaan, Martin
2014-01-01
This paper considers the incorporation of constraints to enforce physically based conservation laws in the ensemble Kalman filter. In particular, constraints are used to ensure that the ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. In certain situations filtering algorithms such as the ensemble Kalman filter (EnKF) and ensemble transform Kalman filter (ETKF) yield updated ensembles that conserve mass but are negative, even though the actual states must be nonnegative. In such situations if negative values are set to zero, or a log transform is introduced, the total mass will not be conserved. In this study, mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate non-negativity constraints. Simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. In two examples, an update that includes a non-negativity constraint is able to properly describe the transport of a sharp feature (e.g., a triangle or cone). A number of implementation questions still need to be addressed, particularly the need to develop a computationally efficient quadratic programming update for large ensemble.
ERIC Educational Resources Information Center
Ellis, Amy B.; Grinstead, Paul
2008-01-01
This article presents secondary students' generalizations about the connections between algebraic and graphical representations of quadratic functions, focusing specifically on the roles of the parameters a, b, and c in the general form of a quadratic function, y = ax[superscript 2] + bx + c. Students' generalizations about these connections led…
ERIC Educational Resources Information Center
Man, Yiu-Kwong
2012-01-01
In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear…
Pseudo-continuous-time quadratic regulators with pole placement in a specific region
NASA Technical Reports Server (NTRS)
Shieh, L. S.; Zhang, J. L.; Ganesan, S.
1990-01-01
The paper comments on the pseudo-continuous-time quadratic regulator developed in an earlier paper. It also presents a new digital redesign technique, based on matching all the states at all the sampling instants, for finding the pseudo-continuous-time quadratic regulator.
Geometrical Solutions of Some Quadratic Equations with Non-Real Roots
ERIC Educational Resources Information Center
Pathak, H. K.; Grewal, A. S.
2002-01-01
This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…
ERIC Educational Resources Information Center
Strickland, Tricia K.; Maccini, Paula
2013-01-01
The current study focuses on the effects of incorporating multiple visual representations on students' conceptual understanding of quadratic expressions embedded within area word problems and students' procedural fluency of transforming quadratic expressions in standard form to factored-form and vice versa. The intervention included the…
The cyclicity of period annulus of a quadratic reversible Lotka-Volterra system
NASA Astrophysics Data System (ADS)
Li, Chengzhi; Llibre, Jaume
2009-12-01
We prove that by perturbing the periodic annulus of the quadratic polynomial reversible Lotka-Volterra differential system \\dot x=y+\\case{3}{2}(x^2-y^2) , \\dot y=-x(1-y) , inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles.
NASA Astrophysics Data System (ADS)
Komura, Yukihiro; Okabe, Yutaka
2014-03-01
We present sample CUDA programs for the GPU computing of the Swendsen-Wang multi-cluster spin flip algorithm. We deal with the classical spin models; the Ising model, the q-state Potts model, and the classical XY model. As for the lattice, both the 2D (square) lattice and the 3D (simple cubic) lattice are treated. We already reported the idea of the GPU implementation for 2D models (Komura and Okabe, 2012). We here explain the details of sample programs, and discuss the performance of the present GPU implementation for the 3D Ising and XY models. We also show the calculated results of the moment ratio for these models, and discuss phase transitions. Catalogue identifier: AERM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERM_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5632 No. of bytes in distributed program, including test data, etc.: 14688 Distribution format: tar.gz Programming language: C, CUDA. Computer: System with an NVIDIA CUDA enabled GPU. Operating system: System with an NVIDIA CUDA enabled GPU. Classification: 23. External routines: NVIDIA CUDA Toolkit 3.0 or newer Nature of problem: Monte Carlo simulation of classical spin systems. Ising, q-state Potts model, and the classical XY model are treated for both two-dimensional and three-dimensional lattices. Solution method: GPU-based Swendsen-Wang multi-cluster spin flip Monte Carlo method. The CUDA implementation for the cluster-labeling is based on the work by Hawick et al. [1] and that by Kalentev et al. [2]. Restrictions: The system size is limited depending on the memory of a GPU. Running time: For the parameters used in the sample programs, it takes about a minute for each program. Of course, it depends on the system size, the number of Monte Carlo steps, etc. References: [1] K
Digital program for solving the linear stochastic optimal control and estimation problem
NASA Technical Reports Server (NTRS)
Geyser, L. C.; Lehtinen, B.
1975-01-01
A computer program is described which solves the linear stochastic optimal control and estimation (LSOCE) problem by using a time-domain formulation. The LSOCE problem is defined as that of designing controls for a linear time-invariant system which is disturbed by white noise in such a way as to minimize a performance index which is quadratic in state and control variables. The LSOCE problem and solution are outlined; brief descriptions are given of the solution algorithms, and complete descriptions of each subroutine, including usage information and digital listings, are provided. A test case is included, as well as information on the IBM 7090-7094 DCS time and storage requirements.
NASA Astrophysics Data System (ADS)
Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho
2016-03-01
In this paper, we analyse the convergence and stability properties of generalised policy iteration (GPI) applied to discrete-time linear quadratic regulation problems. GPI is one kind of the generalised adaptive dynamic programming methods used for solving optimal control problems, and is composed of policy evaluation and policy improvement steps. To analyse the convergence and stability of GPI, the dynamic programming (DP) operator is defined. Then, GPI and its equivalent formulas are presented based on the notation of DP operator. The convergence of the approximate value function to the exact one in policy evaluation is proven based on the equivalent formulas. Furthermore, the positive semi-definiteness, stability, and the monotone convergence (PI-mode and VI-mode convergence) of GPI are presented under certain conditions on the initial value function. The online least square method is also presented for the implementation of GPI. Finally, some numerical simulations are carried out to verify the effectiveness of GPI as well as to further investigate the convergence and stability properties.
Quadratic Fermi node in a 3D strongly correlated semimetal.
Kondo, Takeshi; Nakayama, M; Chen, R; Ishikawa, J J; Moon, E-G; Yamamoto, T; Ota, Y; Malaeb, W; Kanai, H; Nakashima, Y; Ishida, Y; Yoshida, R; Yamamoto, H; Matsunami, M; Kimura, S; Inami, N; Ono, K; Kumigashira, H; Nakatsuji, S; Balents, L; Shin, S
2015-12-07
Strong spin-orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin-orbit and strong electron-electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.
Quadratic Optimization in the Problems of Active Control of Sound
NASA Technical Reports Server (NTRS)
Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).
Monitoring bioeroding sponges: using rubble, Quadrat, or intercept surveys?
Schönberg, C H L
2015-04-01
Relating to recent environmental changes, bioerosion rates of calcium carbonate materials appear to be increasing worldwide, often driven by sponges that cause bioerosion and are recognized bioindicators for coral reef health. Various field methods were compared to encourage more vigorous research on bioeroding sponges and their inclusion in major monitoring projects. The rubble technique developed by Holmes et al. (2000) had drawbacks often due to small specimen sizes: it was time-costly, generated large variation, and created a biased impression about dominant species. Quadrat surveys were most rapid but overestimated cover of small specimens. Line intercepts are recommended as easiest, least spatially biased, and most accurate, especially when comparing results from different observers. Intercepts required fewer samples and provided the best statistical efficiency, evidenced by better significances and test power. Bioeroding sponge abundances and biodiversities are influenced by water depth, sediment quality, and most importantly by availability of suitable attached substrate. Any related data should thus be standardized to amount of suitable substrate to allow comparison between different environments, concentrating on dominant, easily recognized species to avoid bias due to experience of observers.
Inverse problem of quadratic time-dependent Hamiltonians
NASA Astrophysics Data System (ADS)
Guo, Guang-Jie; Meng, Yan; Chang, Hong; Duan, Hui-Zeng; Di, Bing
2015-08-01
Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wave-packet obeying the quadratic time-dependent Hamiltonian (QTDH). However, in general, most of the practical cases are not exactly solvable, for we need general solutions of the Riccatti equations which are not generally known. We therefore bypass directly solving for the temporal evolution wave function, and study its inverse problem. We start with a particular evolution of the wave-packet, and get the required Hamiltonian by using the inverse method. The inverse approach opens up a new way to find new exact solutions to the QTDH. Some typical examples are studied in detail. For a specific time-dependent periodic harmonic oscillator, the Berry phase is obtained exactly. Project supported by the National Natural Science Foundation of China (Grant No. 11347171), the Natural Science Foundation of Hebei Province of China (Grant No. A2012108003), and the Key Project of Educational Commission of Hebei Province of China (Grant No. ZD2014052).
Junction conditions in quadratic gravity: thin shells and double layers
NASA Astrophysics Data System (ADS)
Reina, Borja; Senovilla, José M. M.; Vera, Raül
2016-05-01
The junction conditions for the most general gravitational theory with a Lagrangian containing terms quadratic in the curvature are derived. We include the cases with a possible concentration of matter on the joining hypersurface—termed as thin shells, domain walls or braneworlds in the literature—as well as the proper matching conditions where only finite jumps of the energy-momentum tensor are allowed. In the latter case we prove that the matching conditions are more demanding than in general relativity. In the former case, we show that generically the shells/domain walls are of a new kind because they possess, in addition to the standard energy-momentum tensor, a double layer energy-momentum contribution which actually induces an external energy flux vector and an external scalar pressure/tension on the shell. We prove that all these contributions are necessary to make the entire energy-momentum tensor divergence-free, and we present the field equations satisfied by these energy-momentum quantities. The consequences of all these results are briefly analyzed.
Quadratic isothermal amplification for the detection of microRNA.
Duan, Ruixue; Zuo, Xiaolei; Wang, Shutao; Quan, Xiyun; Chen, Dongliang; Chen, Zhifei; Jiang, Lei; Fan, Chunhai; Xia, Fan
2014-03-01
This protocol describes an isothermal amplification approach for ultrasensitive detection of specific microRNAs (miRNAs). It achieves this level of sensitivity through quadratic amplification of the target oligonucleotide by using a Bst DNA polymerase-induced strand-displacement reaction and a lambda exonuclease-aided recycling reaction. First, the target miRNA binds to a specifically designed molecular beacon, causing it to become a fluorescence emitter. A primer then binds to the activated beacon, and Bst polymerase initiates the synthesis of a double-stranded DNA segment templated on the molecular beacon. This causes the concomitant release of the target miRNA from the beacon--the first round of 'recycling'. Second, the duplex beacon thus produced is a suitable substrate for a nicking enzyme present in solution. After the duplex beacon is nicked, the lambda exonuclease digests the beacon and releases the DNA single strand just synthesized, which is complementary to the molecular beacon, inducing the second round of recycling. The miRNA detection limit of this protocol is 10 fmol at 37 °C and 1 amol at 4 °C. This approach also affords high selectivity when applied to miRNA extracted from MCF-7 and PC3 cell lines and even from breast cancer tissue samples. Upon isolation of miRNA, the detection process can be completed in ∼2 h.
Quadratic stabilisability of multi-agent systems under switching topologies
NASA Astrophysics Data System (ADS)
Guan, Yongqiang; Ji, Zhijian; Zhang, Lin; Wang, Long
2014-12-01
This paper addresses the stabilisability of multi-agent systems (MASs) under switching topologies. Necessary and/or sufficient conditions are presented in terms of graph topology. These conditions explicitly reveal how the intrinsic dynamics of the agents, the communication topology and the external control input affect stabilisability jointly. With the appropriate selection of some agents to which the external inputs are applied and the suitable design of neighbour-interaction rules via a switching topology, an MAS is proved to be stabilisable even if so is not for each of uncertain subsystem. In addition, a method is proposed to constructively design a switching rule for MASs with norm-bounded time-varying uncertainties. The switching rules designed via this method do not rely on uncertainties, and the switched MAS is quadratically stabilisable via decentralised external self-feedback for all uncertainties. With respect to applications of the stabilisability results, the formation control and the cooperative tracking control are addressed. Numerical simulations are presented to demonstrate the effectiveness of the proposed results.
Quadratic Fermi node in a 3D strongly correlated semimetal
Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E. -G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; et al
2015-12-07
We report that strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour ismore » predicted, for which we observe some evidence. Lastly, our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.« less
Linear versus quadratic portfolio optimization model with transaction cost
NASA Astrophysics Data System (ADS)
Razak, Norhidayah Bt Ab; Kamil, Karmila Hanim; Elias, Siti Masitah
2014-06-01
Optimization model is introduced to become one of the decision making tools in investment. Hence, it is always a big challenge for investors to select the best model that could fulfill their goal in investment with respect to risk and return. In this paper we aims to discuss and compare the portfolio allocation and performance generated by quadratic and linear portfolio optimization models namely of Markowitz and Maximin model respectively. The application of these models has been proven to be significant and popular among others. However transaction cost has been debated as one of the important aspects that should be considered for portfolio reallocation as portfolio return could be significantly reduced when transaction cost is taken into consideration. Therefore, recognizing the importance to consider transaction cost value when calculating portfolio' return, we formulate this paper by using data from Shariah compliant securities listed in Bursa Malaysia. It is expected that, results from this paper will effectively justify the advantage of one model to another and shed some lights in quest to find the best decision making tools in investment for individual investors.
GR angular momentum in the quadratic spinor Lagrangian formulation
NASA Astrophysics Data System (ADS)
Li, Siao-Jing
2016-08-01
We inquire into the question of whether the quadratic spinor Lagrangian (QSL) formulation can describe the angular momentum for a general-relativistic system. The QSL Hamiltonian has previously been shown to be able to yield an energy-momentum quasilocalization which brings a proof of the positive gravitational energy when the spinor satisfies the conformal Witten equation. After inspection, we find that, under the constraint that the spinor on the asymptotic boundary is a constant, the QSL Hamiltonian is successful in giving an angular momentum quasilocalization. We also make certain the spinor in the Hamiltonian plays the role of a gauge field, a warrant of our permission to impose constraints on the spinor. Then, by some adjustment of the QSL Hamiltonian, we gain a covariant center-of-mass moment quasilocalization only under the condition that the displacement on the asymptotic boundary is a Killing boost vector. We expect the spinor expression will bring a proof of some connection between the gravitational energy and angular momentum.
Quadratic Fermi node in a 3D strongly correlated semimetal
Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E. -G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; Ishida, Y.; Yoshida, R.; Yamamoto, H.; Matsunami, M.; Kimura, S.; Inami, N.; Ono, K.; Kumigashira, H.; Nakatsuji, S.; Balents, L.; Shin, S.
2015-12-07
We report that strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr_{2}Ir_{2}O_{7}, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Lastly, our discovery implies that Pr_{2}Ir_{2}O_{7} is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.
Quadratic Fermi node in a 3D strongly correlated semimetal
Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E.-G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; Ishida, Y.; Yoshida, R.; Yamamoto, H.; Matsunami, M.; Kimura, S.; Inami, N.; Ono, K.; Kumigashira, H.; Nakatsuji, S.; Balents, L.; Shin, S.
2015-01-01
Strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states. PMID:26640114
NASA Astrophysics Data System (ADS)
Umansky, Moti; Weihs, Daphne
2012-08-01
In many physical and biophysical studies, single-particle tracking is utilized to reveal interactions, diffusion coefficients, active modes of driving motion, dynamic local structure, micromechanics, and microrheology. The basic analysis applied to those data is to determine the time-dependent mean-square displacement (MSD) of particle trajectories and perform time- and ensemble-averaging of similar motions. The motion of particles typically exhibits time-dependent power-law scaling, and only trajectories with qualitatively and quantitatively comparable MSD should be ensembled. Ensemble averaging trajectories that arise from different mechanisms, e.g., actively driven and diffusive, is incorrect and can result inaccurate correlations between structure, mechanics, and activity. We have developed an algorithm to automatically and accurately determine power-law scaling of experimentally measured single-particle MSD. Trajectories can then categorized and grouped according to user defined cutoffs of time, amplitudes, scaling exponent values, or combinations. Power-law fits are then provided for each trajectory alongside categorized groups of trajectories, histograms of power laws, and the ensemble-averaged MSD of each group. The codes are designed to be easily incorporated into existing user codes. We expect that this algorithm and program will be invaluable to anyone performing single-particle tracking, be it in physical or biophysical systems. Catalogue identifier: AEMD_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMD_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 25 892 No. of bytes in distributed program, including test data, etc.: 5 572 780 Distribution format: tar.gz Programming language: MATLAB (MathWorks Inc.) version 7.11 (2010b) or higher, program
Fast Quantum Algorithms for Numerical Integrals and Stochastic Processes
NASA Technical Reports Server (NTRS)
Abrams, D.; Williams, C.
1999-01-01
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known classical deterministic algotithms and a quadratic speed increase incomparison to classical Monte Carlo methods.
Munguia, Lluis-Miquel; Oxberry, Geoffrey; Rajan, Deepak
2016-05-01
Stochastic mixed-integer programs (SMIPs) deal with optimization under uncertainty at many levels of the decision-making process. When solved as extensive formulation mixed- integer programs, problem instances can exceed available memory on a single workstation. In order to overcome this limitation, we present PIPS-SBB: a distributed-memory parallel stochastic MIP solver that takes advantage of parallelism at multiple levels of the optimization process. We also show promising results on the SIPLIB benchmark by combining methods known for accelerating Branch and Bound (B&B) methods with new ideas that leverage the structure of SMIPs. Finally, we expect the performance of PIPS-SBB to improve furthermore » as more functionality is added in the future.« less
NASA Technical Reports Server (NTRS)
Jurenko, Robert J.; Bush, T. Jason; Ottander, John A.
2014-01-01
A method for transitioning linear time invariant (LTI) models in time varying simulation is proposed that utilizes both quadratically constrained least squares (LSQI) and Direct Shape Mapping (DSM) algorithms to determine physical displacements. This approach is applicable to the simulation of the elastic behavior of launch vehicles and other structures that utilize multiple LTI finite element model (FEM) derived mode sets that are propagated throughout time. The time invariant nature of the elastic data for discrete segments of the launch vehicle trajectory presents a problem of how to properly transition between models while preserving motion across the transition. In addition, energy may vary between flex models when using a truncated mode set. The LSQI-DSM algorithm can accommodate significant changes in energy between FEM models and carries elastic motion across FEM model transitions. Compared with previous approaches, the LSQI-DSM algorithm shows improvements ranging from a significant reduction to a complete removal of transients across FEM model transitions as well as maintaining elastic motion from the prior state.
NASA Astrophysics Data System (ADS)
Clement, M. D.; Navratil, G. A.; Hanson, J. M.; Bialek, J.; Piglowski, D. A.; Penaflor, B. G.
2015-11-01
A Graphics Processing Unit (GPU) based control system has been installed on the DIII-D tokamak for Resistive Wall Mode (RWM) control similar to one implemented at the HBT-EP tokamak. DIII-D can excite RWMs, which are strong, locked or nearly locked kink modes whose rotation frequencies do not evolve quickly and are slow compared to their growth rates. Simulations have predicted that modern control techniques like Linear Quadratic Gaussian (LQG) control will perform better than classical control techniques when using control coils external to the vacuum vessel. An LQG control algorithm based on the VALEN model for the RWM has been developed and tested on this system. Early tests have shown the algorithm is able to track and suppress with external control coils the plasma response of an n=1 perturbation driven by internal control coils. An overview of the control hardware, VALEN model, control algorithm and initial results will be presented. Supported by the US DOE under DE-FG02-04ER54761 and DE-FC02-04ER54698.
NASA Astrophysics Data System (ADS)
Uilhoorn, F. E.
2016-10-01
In this article, the stochastic modelling approach proposed by Box and Jenkins is treated as a mixed-integer nonlinear programming (MINLP) problem solved with a mesh adaptive direct search and a real-coded genetic class of algorithms. The aim is to estimate the real-valued parameters and non-negative integer, correlated structure of stationary autoregressive moving average (ARMA) processes. The maximum likelihood function of the stationary ARMA process is embedded in Akaike's information criterion and the Bayesian information criterion, whereas the estimation procedure is based on Kalman filter recursions. The constraints imposed on the objective function enforce stability and invertibility. The best ARMA model is regarded as the global minimum of the non-convex MINLP problem. The robustness and computational performance of the MINLP solvers are compared with brute-force enumeration. Numerical experiments are done for existing time series and one new data set.
New type of Weyl semimetal with quadratic double Weyl fermions
Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya; Lee, Chi-Cheng; Chang, Guoqing; Chang, Tay-Rong; Wang, BaoKai; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Sanchez, Daniel; Zheng, Hao; Jeng, Horng-Tay; Bansil, Arun; Neupert, Titus; Lin, Hsin; Hasan, M. Zahid
2016-01-01
Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin–orbit coupling and that, after the inclusion of spin–orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs. PMID:26787914
New type of Weyl semimetal with quadratic double Weyl fermions.
Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya; Lee, Chi-Cheng; Chang, Guoqing; Chang, Tay-Rong; Wang, BaoKai; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Sanchez, Daniel; Zheng, Hao; Jeng, Horng-Tay; Bansil, Arun; Neupert, Titus; Lin, Hsin; Hasan, M Zahid
2016-02-01
Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin-orbit coupling and that, after the inclusion of spin-orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs. PMID:26787914
New type of Weyl semimetal with quadratic double Weyl fermions.
Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya; Lee, Chi-Cheng; Chang, Guoqing; Chang, Tay-Rong; Wang, BaoKai; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Sanchez, Daniel; Zheng, Hao; Jeng, Horng-Tay; Bansil, Arun; Neupert, Titus; Lin, Hsin; Hasan, M Zahid
2016-02-01
Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin-orbit coupling and that, after the inclusion of spin-orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs.
Gravity waves from non-minimal quadratic inflation
Pallis, Constantinos; Shafi, Qaisar
2015-03-12
We discuss non-minimal quadratic inflation in supersymmetric (SUSY) and non-SUSY models which entails a linear coupling of the inflaton to gravity. Imposing a lower bound on the parameter c{sub R}, involved in the coupling between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton while the corresponding effective theory respects the perturbative unitarity up to the Planck scale. Working in the non-SUSY context we also consider radiative corrections to the inflationary potential due to a possible coupling of the inflaton to bosons or fermions. We find ranges of the parameters, depending mildly on the renormalization scale, with adjustable values of the spectral index n{sub s}, tensor-to-scalar ratio r≃(2−4)⋅10{sup −3}, and an inflaton mass close to 3⋅10{sup 13} GeV. In the SUSY framework we employ two gauge singlet chiral superfields, a logarithmic Kähler potential including all the allowed terms up to fourth order in powers of the various fields, and determine uniquely the superpotential by applying a continuous R and a global U(1) symmetry. When the Kähler manifold exhibits a no-scale-type symmetry, the model predicts n{sub s}≃0.963 and r≃0.004. Beyond no-scale SUGRA, n{sub s} and r depend crucially on the coefficient involved in the fourth order term, which mixes the inflaton with the accompanying non-inflaton field in the Kähler potential, and the prefactor encountered in it. Increasing slightly the latter above (−3), an efficient enhancement of the resulting r can be achieved putting it in the observable range. The inflaton mass in the last case is confined in the range (5−9)⋅10{sup 13} GeV.
NASA Technical Reports Server (NTRS)
Wang, Lui; Bayer, Steven E.
1991-01-01
Genetic algorithms are mathematical, highly parallel, adaptive search procedures (i.e., problem solving methods) based loosely on the processes of natural genetics and Darwinian survival of the fittest. Basic genetic algorithms concepts are introduced, genetic algorithm applications are introduced, and results are presented from a project to develop a software tool that will enable the widespread use of genetic algorithm technology.
Algorithm for Constructing Contour Plots
NASA Technical Reports Server (NTRS)
Johnson, W.; Silva, F.
1984-01-01
General computer algorithm developed for construction of contour plots. algorithm accepts as input data values at set of points irregularly distributed over plane. Algorithm based on interpolation scheme: points in plane connected by straight-line segments to form set of triangles. Program written in FORTRAN IV.
On Dijkstra's Algorithm for Deadlock Detection
NASA Astrophysics Data System (ADS)
Li, Youming; Greca, Ardian; Harris, James
We study a classical problem in operating systems concerning deadlock detection for systems with reusable resources. The elegant Dijkstra's algorithm utilizes simple data structures, but it has the cost of quadratic dependence on the number of the processes. Our goal is to reduce the cost in an optimal way without losing the simplicity of the data structures. More specifically, we present a graph-free and almost optimal algorithm with the cost of linear dependence on the number of the processes, when the number of resources is fixed and when the units of requests for resources are bounded by constants.
A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm
NASA Technical Reports Server (NTRS)
Ortiz, Francisco
2004-01-01
COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions
Changes in Obesity Odds Ratio among Iranian Adults, since 2000: Quadratic Inference Functions Method
Etemad, Koorosh; Seifi, Behjat; Mohammad, Kazem; Biglarian, Akbar; Koohpayehzadeh, Jalil
2016-01-01
Background. Monitoring changes in obesity prevalence by risk factors is relevant to public health programs that focus on reducing or preventing obesity. The purpose of this paper was to study trends in obesity odds ratios (ORs) for individuals aged 20 years and older in Iran by using a new statistical methodology. Methods. Data collected by the National Surveys in Iran, from 2000 through 2011. Since responses of the member of each cluster are correlated, the quadratic inference functions (QIF) method was used to model the relationship between the odds of obesity and risk factors. Results. During the study period, the prevalence rate of obesity increased from 12% to 22%. By using QIF method and a model selection criterion for performing stepwise regression analysis, we found that while obesity prevalence generally increased in both sexes, all ages, all employment, residence, and smoking levels, it seems to have changes in obesity ORs since 2000. Conclusions. Because obesity is one of the main risk factors for many diseases, awareness of the differences by factors allows development of targets for prevention and early intervention. PMID:27803729
The Existence of Periodic Orbits and Invariant Tori for Some 3-Dimensional Quadratic Systems
Jiang, Yanan; Han, Maoan; Xiao, Dongmei
2014-01-01
We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ3. PMID:24982980
The existence of periodic orbits and invariant tori for some 3-dimensional quadratic systems.
Jiang, Yanan; Han, Maoan; Xiao, Dongmei
2014-01-01
We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ(3).
Stability of the equilibrium positions of an engine with nonlinear quadratic springs
NASA Astrophysics Data System (ADS)
Stănescu, Nicolae-Doru; Popa, Dinel
2014-06-01
Our paper realizes a study of the equilibrium positions for an engine supported by four identical nonlinear springs of quadratic characteristic. The systems with quadratic characteristic are generally avoided because they lead to mathematical complications. Our goal is to realize such a study for an engine supported on quadratic springs. For the model purposed, we established the equations of motion and we discussed the possibilities for the equilibrium positions. Because of the quadratic characteristic of the springs and of the approximations made for the small rotations, the equations obtained for the equilibrium lead us to a paradox, which consists in the existence of an open neighborhood in which there exists an infinity of positions of indifferent equilibrium, or a curve where the equilibrium positions are situated. Moreover, the study of the stability shows that the stability is assured for the position at which the springs are not compressed. Finally, a numerical example is presented and completely solved.
The existence of periodic orbits and invariant tori for some 3-dimensional quadratic systems.
Jiang, Yanan; Han, Maoan; Xiao, Dongmei
2014-01-01
We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ(3). PMID:24982980
Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality
NASA Technical Reports Server (NTRS)
Acikmese, Ahmet Behcet; Martin, Corless
2004-01-01
We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.
On ideal structure in quadratic DDS in R{sup 2}
Kutnjak, Milan
2008-11-13
We consider the dynamics in a special case of two-dimensional quadratic homogeneous discrete dynamical systems. It is well known (c.f. [1, 2]) that homogeneous quadratic maps are in one to one correspondence with two-dimensional commutative (nonassociative) algebras. Algebraic concepts (such as the structure of algebra and existence of special elements like idempotents and nilpotents) help us to study the dynamics of the corresponding discrete homogeneous quadratic maps. It is well-known that such systems can exhibit chaotic behavior [3], In this article we consider the influence of the existence of an algebra ideal on the dynamics of the corresponding discrete homogeneous quadratic system. We also present some examples in the plane.
Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid
ERIC Educational Resources Information Center
Brilleslyper, Michael A.
2004-01-01
Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.
Algorithm Calculates Cumulative Poisson Distribution
NASA Technical Reports Server (NTRS)
Bowerman, Paul N.; Nolty, Robert C.; Scheuer, Ernest M.
1992-01-01
Algorithm calculates accurate values of cumulative Poisson distribution under conditions where other algorithms fail because numbers are so small (underflow) or so large (overflow) that computer cannot process them. Factors inserted temporarily to prevent underflow and overflow. Implemented in CUMPOIS computer program described in "Cumulative Poisson Distribution Program" (NPO-17714).
Optimal Control Using Pontryagin's Maximum Principle in a Linear Quadratic Differential Game
NASA Astrophysics Data System (ADS)
Khakestari, Marzieh; Ibragimov, Gafurjan; Suleiman, Mohamed
This paper deals with a class of two person zero-sum linear quadratic differential games, where the control functions for both players subject to integral constraints. Also the necessary conditions of the Maximum Principle are studied. Main objective in this work is to obtain optimal control by using method of Pontryagin's Maximum Principle. This method for a time-varying linear quadratic differential game is described. Finally, we discuss about an example.
Models of quadratic quantum algebras and their relation to classical superintegrable systems
Kalnins, E. G.; Miller, W.; Post, S.
2009-05-15
We show how to construct realizations (models) of quadratic algebras for 2D second order superintegrable systems in terms of differential or difference operators in one variable. We demonstrate how various models of the quantum algebras arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras related to superintegrable systems in n dimensions and are intimately related to multivariable orthogonal polynomials.
ERIC Educational Resources Information Center
Community College Journal, 1996
1996-01-01
Includes a collection of eight short articles describing model community college programs. Discusses a literacy program, a mobile computer classroom, a support program for at-risk students, a timber-harvesting program, a multimedia presentation on successful women graduates, a career center, a collaboration with NASA, and an Israeli engineering…
NASA Astrophysics Data System (ADS)
Hsu, Chih-Ming
2014-12-01
Portfolio optimisation is an important issue in the field of investment/financial decision-making and has received considerable attention from both researchers and practitioners. However, besides portfolio optimisation, a complete investment procedure should also include the selection of profitable investment targets and determine the optimal timing for buying/selling the investment targets. In this study, an integrated procedure using data envelopment analysis (DEA), artificial bee colony (ABC) and genetic programming (GP) is proposed to resolve a portfolio optimisation problem. The proposed procedure is evaluated through a case study on investing in stocks in the semiconductor sub-section of the Taiwan stock market for 4 years. The potential average 6-month return on investment of 9.31% from 1 November 2007 to 31 October 2011 indicates that the proposed procedure can be considered a feasible and effective tool for making outstanding investment plans, and thus making profits in the Taiwan stock market. Moreover, it is a strategy that can help investors to make profits even when the overall stock market suffers a loss.
Dantzig, G.B.
1992-10-01
Analogous to gunners firing trial shots to bracket a target in order to adjust direction and distance, we demonstate that it is sometimes faster not to apply an algorithm directly, but to roughly approximately solve several perturbations of the problem and then combine these rough approximations to get an exact solution. To find a feasible solution to an m-equation linear program with a convexity constraint, the von Neumann Algorithm generates a sequence of approximate solutions which converge very slowly to the right hand side b[sup 0]. However, it can be redirected so that in the first few iterations it is guaranteed to move rapidly towards the neighborhood of one of m + 1 perturbed right hand sides [cflx b][sup i], then redirected in turn to the next [cflx b][sup i]. Once within the neighborhood of each [cflx b][sup i], a weighted sum of the approximate solutions. [bar x][sup i] yields the exact solution of the unperturbed problem where the weights are found by solving a system of m + 1 equations in m + 1 unknowns. It is assumed an r > 0 is given for which the problem is feasible for all right hand sides b whose distance [parallel]b - b[sup 0][parallel][sub 2] [le] r. The feasible solution is found in less than 4(m+ 1)[sup 3]/r[sup 2] iterations. The work per iteration is [delta]mn + 2m + n + 9 multiplications plus [delta]mn + m + n + 9 additions or comparisons where [delta] is the density of nonzero coeffients in the matrix.
Dantzig, G.B.
1992-10-01
Analogous to gunners firing trial shots to bracket a target in order to adjust direction and distance, we demonstate that it is sometimes faster not to apply an algorithm directly, but to roughly approximately solve several perturbations of the problem and then combine these rough approximations to get an exact solution. To find a feasible solution to an m-equation linear program with a convexity constraint, the von Neumann Algorithm generates a sequence of approximate solutions which converge very slowly to the right hand side b{sup 0}. However, it can be redirected so that in the first few iterations it is guaranteed to move rapidly towards the neighborhood of one of m + 1 perturbed right hand sides {cflx b}{sup i}, then redirected in turn to the next {cflx b}{sup i}. Once within the neighborhood of each {cflx b}{sup i}, a weighted sum of the approximate solutions. {bar x}{sup i} yields the exact solution of the unperturbed problem where the weights are found by solving a system of m + 1 equations in m + 1 unknowns. It is assumed an r > 0 is given for which the problem is feasible for all right hand sides b whose distance {parallel}b - b{sup 0}{parallel}{sub 2} {le} r. The feasible solution is found in less than 4(m+ 1){sup 3}/r{sup 2} iterations. The work per iteration is {delta}mn + 2m + n + 9 multiplications plus {delta}mn + m + n + 9 additions or comparisons where {delta} is the density of nonzero coeffients in the matrix.
A parallel variable metric optimization algorithm
NASA Technical Reports Server (NTRS)
Straeter, T. A.
1973-01-01
An algorithm, designed to exploit the parallel computing or vector streaming (pipeline) capabilities of computers is presented. When p is the degree of parallelism, then one cycle of the parallel variable metric algorithm is defined as follows: first, the function and its gradient are computed in parallel at p different values of the independent variable; then the metric is modified by p rank-one corrections; and finally, a single univariant minimization is carried out in the Newton-like direction. Several properties of this algorithm are established. The convergence of the iterates to the solution is proved for a quadratic functional on a real separable Hilbert space. For a finite-dimensional space the convergence is in one cycle when p equals the dimension of the space. Results of numerical experiments indicate that the new algorithm will exploit parallel or pipeline computing capabilities to effect faster convergence than serial techniques.
NASA Astrophysics Data System (ADS)
Antoni, Jerome; Liang, Yu; Leclère, Quentin
2015-08-01
In inverse acoustics, the reconstruction of (distant) sound fields from microphone array measurements is fundamentally limited by the size of the array and by the microphone density. One approach to simulate large arrays and/or high microphone density is to scan the object of interest by sequentially moving a small prototype array. This typically requires a sufficient number of high-quality fixed references in order to preserve the phase relationships between consecutive snapshots or that measurements are made in the near-field in order to allow the successive reconstruction of local "patches" of the source by deliberately neglecting waves not radiating through the array (patch holography). In the present work, a solution is introduced to reconstruct the quadratic properties (e.g. source power, quadratic flux, sound intensity) of the radiating object from non-synchronous (sequential) measurements when references are insufficient in quantity or in quality. Remarkably, it also operates without any reference at all in certain conditions. It relies on the assumptions that the sound field is (i) stationary and (ii) spatially correlated and boils down to the factorization of a structured covariance matrix. This is undertaken within a Bayesian probabilistic approach where the source field is encoded by unobservable latent variables which are iteratively reconstructed by using the Expected-Maximization (EM) algorithm. The method is shown to return virtually similar results as if all data were captured simultaneously-or sequentially with sufficient high-quality references. As a consequence, it bears an advantage in terms of cost and simplicity. In addition, it is ultimately able to synthesize statistically equivalent realizations of the source field, which may turn out useful for numerical simulation of sound propagation. A solution is also provided within the Bayesian framework for automatically setting the regularization parameter to its optimal value.
An algorithm for constrained one-step inversion of spectral CT data.
Foygel Barber, Rina; Sidky, Emil Y; Gilat Schmidt, Taly; Pan, Xiaochuan
2016-05-21
We develop a primal-dual algorithm that allows for one-step inversion of spectral CT transmission photon counts data to a basis map decomposition. The algorithm allows for image constraints to be enforced on the basis maps during the inversion. The derivation of the algorithm makes use of a local upper bounding quadratic approximation to generate descent steps for non-convex spectral CT data discrepancy terms, combined with a new convex-concave optimization algorithm. Convergence of the algorithm is demonstrated on simulated spectral CT data. Simulations with noise and anthropomorphic phantoms show examples of how to employ the constrained one-step algorithm for spectral CT data.
NASA Astrophysics Data System (ADS)
Recchioni, Maria Cristina
2001-12-01
This paper investigates the application of the method introduced by L. Pasquini (1989) for simultaneously approaching the zeros of polynomial solutions to a class of second-order linear homogeneous ordinary differential equations with polynomial coefficients to a particular case in which these polynomial solutions have zeros symmetrically arranged with respect to the origin. The method is based on a family of nonlinear equations which is associated with a given class of differential equations. The roots of the nonlinear equations are related to the roots of the polynomial solutions of differential equations considered. Newton's method is applied to find the roots of these nonlinear equations. In (Pasquini, 1994) the nonsingularity of the roots of these nonlinear equations is studied. In this paper, following the lines in (Pasquini, 1994), the nonsingularity of the roots of these nonlinear equations is studied. More favourable results than the ones in (Pasquini, 1994) are proven in the particular case of polynomial solutions with symmetrical zeros. The method is applied to approximate the roots of Hermite-Sobolev type polynomials and Freud polynomials. A lower bound for the smallest positive root of Hermite-Sobolev type polynomials is given via the nonlinear equation. The quadratic convergence of the method is proven. A comparison with a classical method that uses the Jacobi matrices is carried out. We show that the algorithm derived by the proposed method is sometimes preferable to the classical QR type algorithms for computing the eigenvalues of the Jacobi matrices even if these matrices are real and symmetric.
Three penalized EM-type algorithms for PET image reconstruction.
Teng, Yueyang; Zhang, Tie
2012-06-01
Based on Bayes theory, Green introduced the maximum a posteriori (MAP) algorithm to obtain a smoothing reconstruction for positron emission tomography. This algorithm is flexible and convenient for most of the penalties, but it is hard to guarantee convergence. For a common goal, Fessler penalized a weighted least squares (WLS) estimator by a quadratic penalty and then solved it with the successive over-relaxation (SOR) algorithm, however, the algorithm was time-consuming and difficultly parallelized. Anderson proposed another WLS estimator for faster convergence, on which there were few regularization methods studied. For three regularized estimators above, we develop three new expectation maximization (EM) type algorithms to solve them. Unlike MAP and SOR, the proposed algorithms yield update rules by minimizing the auxiliary functions constructed on the previous iterations, which ensure the cost functions monotonically decreasing. Experimental results demonstrated the robustness and effectiveness of the proposed algorithms.
Local multiplicative Schwarz algorithms for convection-diffusion equations
NASA Technical Reports Server (NTRS)
Cai, Xiao-Chuan; Sarkis, Marcus
1995-01-01
We develop a new class of overlapping Schwarz type algorithms for solving scalar convection-diffusion equations discretized by finite element or finite difference methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. The ordering of the subdomain preconditioners is determined by considering the direction of the flow. We prove that the algorithms are optimal in the sense that the convergence rates are independent of the mesh size, as well as the number of subdomains. We show by numerical examples that the new algorithms are less sensitive to the direction of the flow than either the classical multiplicative Schwarz algorithms, and converge faster than the additive Schwarz algorithms. Thus, the new algorithms are more suitable for fluid flow applications than the classical additive or multiplicative Schwarz algorithms.
A Numerical Algorithm for Finding Solution of Cross-Coupled Algebraic Riccati Equations
NASA Astrophysics Data System (ADS)
Mukaidani, Hiroaki; Yamamoto, Seiji; Yamamoto, Toru
In this letter, a computational approach for solving cross-coupled algebraic Riccati equations (CAREs) is investigated. The main purpose of this letter is to propose a new algorithm that combines Newton's method with a gradient-based iterative (GI) algorithm for solving CAREs. In particular, it is noteworthy that both a quadratic convergence under an appropriate initial condition and reduction in dimensions for matrix computation are both achieved. A numerical example is provided to demonstrate the efficiency of this proposed algorithm.
A fast Stokes inversion technique based on quadratic regression
NASA Astrophysics Data System (ADS)
Teng, Fei; Deng, Yuan-Yong
2016-05-01
Stokes inversion calculation is a key process in resolving polarization information on radiation from the Sun and obtaining the associated vector magnetic fields. Even in the cases of simple local thermodynamic equilibrium (LTE) and where the Milne-Eddington approximation is valid, the inversion problem may not be easy to solve. The initial values for the iterations are important in handling the case with multiple minima. In this paper, we develop a fast inversion technique without iterations. The time taken for computation is only 1/100 the time that the iterative algorithm takes. In addition, it can provide available initial values even in cases with lower spectral resolutions. This strategy is useful for a filter-type Stokes spectrograph, such as SDO/HMI and the developed two-dimensional real-time spectrograph (2DS).
NLINEAR - NONLINEAR CURVE FITTING PROGRAM
NASA Technical Reports Server (NTRS)
Everhart, J. L.
1994-01-01
A common method for fitting data is a least-squares fit. In the least-squares method, a user-specified fitting function is utilized in such a way as to minimize the sum of the squares of distances between the data points and the fitting curve. The Nonlinear Curve Fitting Program, NLINEAR, is an interactive curve fitting routine based on a description of the quadratic expansion of the chi-squared statistic. NLINEAR utilizes a nonlinear optimization algorithm that calculates the best statistically weighted values of the parameters of the fitting function and the chi-square that is to be minimized. The inputs to the program are the mathematical form of the fitting function and the initial values of the parameters to be estimated. This approach provides the user with statistical information such as goodness of fit and estimated values of parameters that produce the highest degree of correlation between the experimental data and the mathematical model. In the mathematical formulation of the algorithm, the Taylor expansion of chi-square is first introduced, and justification for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations are derived, which are solved by matrix algebra. To achieve convergence, the algorithm requires meaningful initial estimates for the parameters of the fitting function. NLINEAR is written in Fortran 77 for execution on a CDC Cyber 750 under NOS 2.3. It has a central memory requirement of 5K 60 bit words. Optionally, graphical output of the fitting function can be plotted. Tektronix PLOT-10 routines are required for graphics. NLINEAR was developed in 1987.
Biomedical Mathematics, Unit III: Quadratics. Student Text. Revised Version, 1976.
ERIC Educational Resources Information Center
Biomedical Interdisciplinary Curriculum Project, Berkeley, CA.
This student text presents instructional materials for a unit of mathematics within the Biomedical Interdisciplinary Curriculum Project (BICP), a two-year interdisciplinary precollege curriculum aimed at preparing high school students for entry into college and vocational programs leading to a career in the health field. Lessons concentrate on…
NASA Astrophysics Data System (ADS)
Ariyawansa, K. A.; Tabor, Wayne L.
2009-08-01
A family of algorithms for the approximate solution of the bound-constrained minimization problem is described. These algorithms employ the standard barrier method, with the inner iteration based on trust region methods. Local models are conic functions rather than the usual quadratic functions, and are required to match first and second derivatives of the barrier function at the current iterate. The various members of the family are distinguished by the choice of a vector-valued parameter, which is the zero vector in the degenerate case that quadratic local models are used. Computational results are used to compare the efficiency of various members of the family on a selection of test functions.
AnL1 smoothing spline algorithm with cross validation
NASA Astrophysics Data System (ADS)
Bosworth, Ken W.; Lall, Upmanu
1993-08-01
We propose an algorithm for the computation ofL1 (LAD) smoothing splines in the spacesWM(D), with . We assume one is given data of the formyiD(f(ti) +ɛi, iD1,...,N with {itti}iD1N ⊂D, theɛi are errors withE(ɛi)D0, andf is assumed to be inWM. The LAD smoothing spline, for fixed smoothing parameterλ?;0, is defined as the solution,sλ, of the optimization problem (1/N)∑iD1N yi-g(ti +λJM(g), whereJM(g) is the seminorm consisting of the sum of the squaredL2 norms of theMth partial derivatives ofg. Such an LAD smoothing spline,sλ, would be expected to give robust smoothed estimates off in situations where theɛi are from a distribution with heavy tails. The solution to such a problem is a "thin plate spline" of known form. An algorithm for computingsλ is given which is based on considering a sequence of quadratic programming problems whose structure is guided by the optimality conditions for the above convex minimization problem, and which are solved readily, if a good initial point is available. The "data driven" selection of the smoothing parameter is achieved by minimizing aCV(λ) score of the form .The combined LAD-CV smoothing spline algorithm is a continuation scheme in λ↘0 taken on the above SQPs parametrized inλ, with the optimal smoothing parameter taken to be that value ofλ at which theCV(λ) score first begins to increase. The feasibility of constructing the LAD-CV smoothing spline is illustrated by an application to a problem in environment data interpretation.
Li, Yong; Wang, Xiufeng; Lin, Jing; Shi, Shengyu
2014-01-01
The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM) has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features. PMID:24473281
Daskaloyannis, C. Tanoudis, Y.
2008-05-15
The two-dimensional quantum superintegrable systems with quadratic integrals of motion on a manifold are classified by using the quadratic associative algebra of the integrals of motion. There are six general fundamental classes of quantum superintegrable systems corresponding to the classical ones. Analytic formulas for the involved integrals are calculated in all the cases. All the known quantum superintegrable systems with quadratic integrals are classified as special cases of these six general classes. The coefficients of the quadratic associative algebra of integrals are calculated and they are compared to the coefficients of the corresponding coefficients of the Poisson quadratic algebra of the classical systems. The quantum coefficients are similar to the classical ones multiplied by a quantum coefficient -{h_bar}{sup 2} plus a quantum deformation of order {h_bar}{sup 4} and {h_bar}{sup 6}. The systems inside the classes are transformed using Staeckel transforms in the quantum case as in the classical case. The general form of the Staeckel transform between superintegrable systems is discussed.
Dose algorithm for EXTRAD 4100S extremity dosimeter for use at Sandia National Laboratories.
Potter, Charles Augustus
2011-05-01
An updated algorithm for the EXTRAD 4100S extremity dosimeter has been derived. This algorithm optimizes the binning of dosimeter element ratios and uses a quadratic function to determine the response factors for low response ratios. This results in lower systematic bias across all test categories and eliminates the need for the 'red strap' algorithm that was used for high energy beta/gamma emitting radionuclides. The Radiation Protection Dosimetry Program (RPDP) at Sandia National Laboratories uses the Thermo Fisher EXTRAD 4100S extremity dosimeter, shown in Fig 1.1 to determine shallow dose to the extremities of potentially exposed individuals. This dosimeter consists of two LiF TLD elements or 'chipstrates', one of TLD-700 ({sup 7}Li) and one of TLD-100 (natural Li) separated by a tin filter. Following readout and background subtraction, the ratio of the responses of the two elements is determined defining the penetrability of the incident radiation. While this penetrability approximates the incident energy of the radiation, X-rays and beta particles exist in energy distributions that make determination of dose conversion factors less straightforward in their determination.
NASA Technical Reports Server (NTRS)
Folta, David; Bauer, Frank H. (Technical Monitor)
2001-01-01
The autonomous formation flying control algorithm developed by the Goddard Space Flight Center (GSFC) for the New Millennium Program (NMP) Earth Observing-1 (EO-1) mission is investigated for applicability to libration point orbit formations. In the EO-1 formation-flying algorithm, control is accomplished via linearization about a reference transfer orbit with a state transition matrix (STM) computed from state inputs. The effect of libration point orbit dynamics on this algorithm architecture is explored via computation of STMs using the flight proven code, a monodromy matrix developed from a N-body model of a libration orbit, and a standard STM developed from the gravitational and coriolis effects as measured at the libration point. A comparison of formation flying Delta-Vs calculated from these methods is made to a standard linear quadratic regulator (LQR) method. The universal 3-D approach is optimal in the sense that it can be accommodated as an open-loop or closed-loop control using only state information.
NASA Astrophysics Data System (ADS)
Goldsmith, Bryan R.; Sanderson, Evan D.; Bean, Daniel; Peters, Baron
2013-05-01
Methods for modeling catalytic sites on amorphous supports lag far behind methods for modeling catalytic sites on metal surfaces, zeolites, and other crystalline materials. One typical strategy for amorphous supports uses cluster models with arbitrarily chosen constraints to model the rigid amorphous support, but these constraints arbitrarily influence catalyst site activity. An alternative strategy is to use no constraints, but this results in catalytic sites with unrealistic flexibility. We present a systematic ab initio method to model isolated active sites on insulating amorphous supports using small cluster models. A sequential quadratic programming framework helps us relate chemical properties, such as the activation energy, to active site structure. The algorithm is first illustrated on an empirical valence bond model energy landscape. We then use the algorithm to model an off-pathway kinetic trap in olefin metathesis by isolated Mo sites on amorphous SiO2. The cluster models were terminated with basis set deficient fluorine atoms to mimic the properties of an extended silica framework. We also discuss limitations of the current algorithm formulation and future directions for improvement.
Two linear time, low overhead algorithms for graph layout
2008-01-10
The software comprises two algorithms designed to perform a 2D layout of a graph structure in time linear with respect to the vertices and edges in the graph, whereas most other layout algorithms have a running time that is quadratic with respect to the number of vertices or greater. Although these layout algorithms run in a fraction of the time as their competitors, they provide competitive results when applied to most real-world graphs. These algorithmsmore » also have a low constant running time and small memory footprint, making them useful for small to large graphs.« less
NASA Astrophysics Data System (ADS)
Rossi, Francesco; Londrillo, Pasquale; Sgattoni, Andrea; Sinigardi, Stefano; Turchetti, Giorgio
2012-12-01
We present `jasmine', an implementation of a fully relativistic, 3D, electromagnetic Particle-In-Cell (PIC) code, capable of running simulations in various laser plasma acceleration regimes on Graphics-Processing-Units (GPUs) HPC clusters. Standard energy/charge preserving FDTD-based algorithms have been implemented using double precision and quadratic (or arbitrary sized) shape functions for the particle weighting. When porting a PIC scheme to the GPU architecture (or, in general, a shared memory environment), the particle-to-grid operations (e.g. the evaluation of the current density) require special care to avoid memory inconsistencies and conflicts. Here we present a robust implementation of this operation that is efficient for any number of particles per cell and particle shape function order. Our algorithm exploits the exposed GPU memory hierarchy and avoids the use of atomic operations, which can hurt performance especially when many particles lay on the same cell. We show the code multi-GPU scalability results and present a dynamic load-balancing algorithm. The code is written using a python-based C++ meta-programming technique which translates in a high level of modularity and allows for easy performance tuning and simple extension of the core algorithms to various simulation schemes.
NASA Astrophysics Data System (ADS)
Popescu, Mihai; Dumitrache, Alexandru
2011-05-01
This study refers to minimization of quadratic functionals in infinite time. The coefficients of the quadratic form are quadratic matrix, function of the state variable. Dynamic constraints are represented by bilinear differential systems of the form x˙=A(x)x+B(x)u,x(0)=x0. One selects an adequate factorization of A( x) such that the analyzed system should be controllable. Employing the Hamilton-Jacobi equation it results the matrix algebraic equation of Riccati associated to the optimum problem. The necessary extremum conditions determine the adjoint variables λ and the control variables u as functions of state variable, as well as the adjoint system corresponding to those functions. Thus one obtains a matrix differential equation where the solution representing the positive defined symmetric matrix P( x), verifies the Riccati algebraic equation. The stability analysis for the autonomous systems solution resulting for the determined feedback control is performed using the Liapunov function method. Finally we present certain significant cases.
Shafii, Mohammad Ali Meidianti, Rahma Wildian, Fitriyani, Dian; Tongkukut, Seni H. J.; Arkundato, Artoto
2014-09-30
Theoretical analysis of integral neutron transport equation using collision probability (CP) method with quadratic flux approach has been carried out. In general, the solution of the neutron transport using the CP method is performed with the flat flux approach. In this research, the CP method is implemented in the cylindrical nuclear fuel cell with the spatial of mesh being conducted into non flat flux approach. It means that the neutron flux at any point in the nuclear fuel cell are considered different each other followed the distribution pattern of quadratic flux. The result is presented here in the form of quadratic flux that is better understanding of the real condition in the cell calculation and as a starting point to be applied in computational calculation.
Resurrecting quadratic inflation in no-scale supergravity in light of BICEP2
Ellis, John; García, Marcos A.G.; Olive, Keith A.; Nanopoulos, Dimitri V. E-mail: garciagarcia@physics.umn.edu E-mail: olive@physics.umn.edu
2014-05-01
The magnitude of primordial tensor perturbations reported by the BICEP2 experiment is consistent with simple models of chaotic inflation driven by a single scalar field with a power-law potential ∝ φ{sup n} : n ≅ 2, in contrast to the WMAP and Planck results, which favored models resembling the Starobinsky R+R{sup 2} model if running of the scalar spectral index could be neglected. While models of inflation with a quadratic potential may be constructed in simple N = 1 supergravity, these constructions are more challenging in no-scale supergravity. We discuss here how quadratic inflation can be accommodated within supergravity, focusing primarily on the no-scale case. We also argue that the quadratic inflaton may be identified with the supersymmetric partner of a singlet (right-handed) neutrino, whose subsequent decay could have generated the baryon asymmetry via leptogenesis.
Van den Broek, W; Jiang, X; Koch, C T
2015-11-01
While the computational complexity of calculation of the projected potential in the multislice algorithm through reciprocal space scales quadratically with the number of atoms A per slice, a pure real-space calculation scales linearly with A. A hybrid strategy is introduced that has a theoretical complexity of O(AlogA), but that, when measured, outperforms both the reciprocal-space and the real-space approach by approximately an order in A and a large factor, respectively. This strategy is implemented in a new program, dubbed forward dynamical electron scattering (FDES), which simulates high resolution transmission electron microscopy images, diffraction patterns and convergent beam electron diffraction patterns. FDES attains a further increase in speed by running on a graphics processing unit and is made available to the community as open software. PMID:26233822
A note on the fundamental unit in some types of the real quadratic number fields
NASA Astrophysics Data System (ADS)
Özer, Ö.
2016-10-01
Let k =Q (√{d }) be a real quadratic numbefield where d > 0 is a positive square-free integer. The map d →Q (√{d }) is a bijection from the set off all square-free integers d ≠ 0, 1 to the set of all quadratic fields Q (√{d })={ x +y √{d }|x ,y ∈Q } . Furthermore, integral basis element of algebraic integer's ring in real quadratic fields is determined by either wd=√{d }=[ a0;a1,a2,⋯,aℓ (d)-1,2 a0 ¯ ] in the case of d ≡ 2,3(mod 4) or wd=1/+√{d } 2 =[ a0;a1,a2,⋯,aℓ (d)-1,2 a0-1 ¯ ] in the case of d ≡ 1(mod 4) where ℓ (d ) is the period length of continued fraction expansion. The purpose of this paper is to obtain classification of some types of real quadratic fields Q (√{d }) , which include the specific form of continued fraction expansion of integral basis element wd, for which has all partial quotient elements are equal to each other and written as ξs (except the last digit of the period) for ξ positive even integer where period length is ℓ =ℓ (d ) and d ≡ 2,3(mod 4) is a square free positive integer. Moreover, the present paper deals with determining new certain parametric formula of fundamental unit ɛd=t/d+ud√{d } 2 >1 with norm N (ɛd)=(-1) ℓ (d ) for such types of real quadratic fields. Besides, Yokoi's d-invariants nd and md in the relation to continued fraction expansion of wd are calculated by using coefficients of fundamental unit. All supported results are given in numerical tables. These new results and tables are not known in the literature of real quadratic fields.
Basic cluster compression algorithm
NASA Technical Reports Server (NTRS)
Hilbert, E. E.; Lee, J.
1980-01-01
Feature extraction and data compression of LANDSAT data is accomplished by BCCA program which reduces costs associated with transmitting, storing, distributing, and interpreting multispectral image data. Algorithm uses spatially local clustering to extract features from image data to describe spectral characteristics of data set. Approach requires only simple repetitive computations, and parallel processing can be used for very high data rates. Program is written in FORTRAN IV for batch execution and has been implemented on SEL 32/55.
Araújo, Ricardo; Mateus, Octávio
2015-01-01
The quadrate of reptiles and most other tetrapods plays an important morphofunctional role by allowing the articulation of the mandible with the cranium. In Theropoda, the morphology of the quadrate is particularly complex and varies importantly among different clades of non-avian theropods, therefore conferring a strong taxonomic potential. Inconsistencies in the notation and terminology used in discussions of the theropod quadrate anatomy have been noticed, including at least one instance when no less than eight different terms were given to the same structure. A standardized list of terms and notations for each quadrate anatomical entity is proposed here, with the goal of facilitating future descriptions of this important cranial bone. In addition, an overview of the literature on quadrate function and pneumaticity in non-avian theropods is presented, along with a discussion of the inferences that could be made from this research. Specifically, the quadrate of the large majority of non-avian theropods is akinetic but the diagonally oriented intercondylar sulcus of the mandibular articulation allowed both rami of the mandible to move laterally when opening the mouth in many of theropods. Pneumaticity of the quadrate is also present in most averostran clades and the pneumatic chamber—invaded by the quadrate diverticulum of the mandibular arch pneumatic system—was connected to one or several pneumatic foramina on the medial, lateral, posterior, anterior or ventral sides of the quadrate. PMID:26401455
Quadratic formula for determining the drop size in pressure-atomized sprays with and without swirl
NASA Astrophysics Data System (ADS)
Lee, T.-W.; An, Keju
2016-06-01
We use a theoretical framework based on the integral form of the conservation equations, along with a heuristic model of the viscous dissipation, to find a closed-form solution to the liquid atomization problem. The energy balance for the spray renders to a quadratic formula for the drop size as a function, primarily of the liquid velocity. The Sauter mean diameter found using the quadratic formula shows good agreements and physical trends, when compared with experimental observations. This approach is shown to be applicable toward specifying initial drop size in computational fluid dynamics of spray flows.
Nonadiabatic effects in ultracold molecules via anomalous linear and quadratic Zeeman shifts.
McGuyer, B H; Osborn, C B; McDonald, M; Reinaudi, G; Skomorowski, W; Moszynski, R; Zelevinsky, T
2013-12-13
Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound ultracold 88Sr2 molecules near the intercombination-line asymptote. Nonadiabatic Coriolis coupling and the nature of long-range molecular potentials explain how this effect arises and scales roughly cubically with the size of the molecule. The linear shifts yield nonadiabatic mixing angles of the molecular states. The quadratic shifts are sensitive to nearby opposite f-parity states and exhibit fourth-order corrections, providing a stringent test of a state-of-the-art ab initio model. PMID:24483652
Time evolution of two-dimensional quadratic Hamiltonians: A Lie algebraic approach
NASA Astrophysics Data System (ADS)
Sandoval-Santana, J. C.; Ibarra-Sierra, V. G.; Cardoso, J. L.; Kunold, A.
2016-04-01
We develop a Lie algebraic approach to systematically calculate the evolution operator of a system described by a generalized two-dimensional quadratic Hamiltonian with time-dependent coefficients. Although the development of the Lie algebraic approach presented here is mainly motivated by the two-dimensional quadratic Hamiltonian, it may be applied to investigate the evolution operators of any Hamiltonian having a dynamical algebra with a large number of elements. We illustrate the method by finding the propagator and the Heisenberg picture position and momentum operators for a two-dimensional charge subject to uniform and constant electro-magnetic fields.
Analytical solution of the Klein Gordon equation for a quadratic exponential-type potential
NASA Astrophysics Data System (ADS)
Ezzatpour, Somayyeh; Akbarieh, Amin Rezaei
2016-07-01
In this research study, analytical solutions of the Klein Gordon equation by considering the potential as a quadratic exponential will be presented. However, the potential is assumed to be within the framework of an approximation for the centrifugal potential in any state. The Nikiforov-Uvarov method is used to calculate the wave function, as well as corresponding exact energy equation, in bound states. We finally concluded that the quadratic exponential-type potential under which the results were deduced, led to outcomes that were comparable to the results obtained from the well-known potentials in some special cases.
Nonadiabatic effects in ultracold molecules via anomalous linear and quadratic Zeeman shifts.
McGuyer, B H; Osborn, C B; McDonald, M; Reinaudi, G; Skomorowski, W; Moszynski, R; Zelevinsky, T
2013-12-13
Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound ultracold 88Sr2 molecules near the intercombination-line asymptote. Nonadiabatic Coriolis coupling and the nature of long-range molecular potentials explain how this effect arises and scales roughly cubically with the size of the molecule. The linear shifts yield nonadiabatic mixing angles of the molecular states. The quadratic shifts are sensitive to nearby opposite f-parity states and exhibit fourth-order corrections, providing a stringent test of a state-of-the-art ab initio model.
OPTIMAL SHRINKAGE ESTIMATION OF MEAN PARAMETERS IN FAMILY OF DISTRIBUTIONS WITH QUADRATIC VARIANCE
Xie, Xianchao; Kou, S. C.; Brown, Lawrence
2015-01-01
This paper discusses the simultaneous inference of mean parameters in a family of distributions with quadratic variance function. We first introduce a class of semi-parametric/parametric shrinkage estimators and establish their asymptotic optimality properties. Two specific cases, the location-scale family and the natural exponential family with quadratic variance function, are then studied in detail. We conduct a comprehensive simulation study to compare the performance of the proposed methods with existing shrinkage estimators. We also apply the method to real data and obtain encouraging results. PMID:27041778
Newton equation for canonical, Lie-algebraic, and quadratic deformation of classical space
Daszkiewicz, Marcin; Walczyk, Cezary J.
2008-05-15
The Newton equation describing particle motion in a constant external field force on canonical, Lie-algebraic, and quadratic space-time is investigated. We show that for canonical deformation of space-time the dynamical effects are absent, while in the case of Lie-algebraic noncommutativity, when spatial coordinates commute to the time variable, the additional acceleration of the particle is generated. We also indicate that in the case of spatial coordinates commuting in a Lie-algebraic way, as well as for quadratic deformation, there appear additional velocity and position-dependent forces.
Optimal reservoir operation policies using novel nested algorithms
NASA Astrophysics Data System (ADS)
Delipetrev, Blagoj; Jonoski, Andreja; Solomatine, Dimitri
2015-04-01
Historically, the two most widely practiced methods for optimal reservoir operation have been dynamic programming (DP) and stochastic dynamic programming (SDP). These two methods suffer from the so called "dual curse" which prevents them to be used in reasonably complex water systems. The first one is the "curse of dimensionality" that denotes an exponential growth of the computational complexity with the state - decision space dimension. The second one is the "curse of modelling" that requires an explicit model of each component of the water system to anticipate the effect of each system's transition. We address the problem of optimal reservoir operation concerning multiple objectives that are related to 1) reservoir releases to satisfy several downstream users competing for water with dynamically varying demands, 2) deviations from the target minimum and maximum reservoir water levels and 3) hydropower production that is a combination of the reservoir water level and the reservoir releases. Addressing such a problem with classical methods (DP and SDP) requires a reasonably high level of discretization of the reservoir storage volume, which in combination with the required releases discretization for meeting the demands of downstream users leads to computationally expensive formulations and causes the curse of dimensionality. We present a novel approach, named "nested" that is implemented in DP, SDP and reinforcement learning (RL) and correspondingly three new algorithms are developed named nested DP (nDP), nested SDP (nSDP) and nested RL (nRL). The nested algorithms are composed from two algorithms: 1) DP, SDP or RL and 2) nested optimization algorithm. Depending on the way we formulate the objective function related to deficits in the allocation problem in the nested optimization, two methods are implemented: 1) Simplex for linear allocation problems, and 2) quadratic Knapsack method in the case of nonlinear problems. The novel idea is to include the nested
Data Structures and Algorithms.
ERIC Educational Resources Information Center
Wirth, Niklaus
1984-01-01
Built-in data structures are the registers and memory words where binary values are stored; hard-wired algorithms are the fixed rules, embodied in electronic logic circuits, by which stored data are interpreted as instructions to be executed. Various topics related to these two basic elements of every computer program are discussed. (JN)
Parker, G.G.; Eisler, G.R.; Feddema, J.T.
1994-09-01
Procedures for trajectory planning and control of flexible link robots are becoming increasingly important to satisfy performance requirements of hazardous waste removal efforts. It has been shown that utilizing link flexibility in designing open loop joint commands can result in improved performance as opposed to damping vibration throughout a trajectory. The efficient use of link compliance is exploited in this work. Specifically, experimental verification of minimum time, straight line tracking using a two-link planar flexible robot is presented. A numerical optimization process, using an experimentally verified modal model, is used for obtaining minimum time joint torque and angle histories. The optimal joint states are used as commands to the proportional-derivative servo actuated joints. These commands are precompensated for the nonnegligible joint servo actuator dynamics. Using the precompensated joint commands, the optimal joint angles are tracked with such fidelity that the tip tracking error is less than 2.5 cm.
Two Algorithms for Processing Electronic Nose Data
NASA Technical Reports Server (NTRS)
Young, Rebecca; Linnell, Bruce
2007-01-01
Two algorithms for processing the digitized readings of electronic noses, and computer programs to implement the algorithms, have been devised in a continuing effort to increase the utility of electronic noses as means of identifying airborne compounds and measuring their concentrations. One algorithm identifies the two vapors in a two-vapor mixture and estimates the concentration of each vapor (in principle, this algorithm could be extended to more than two vapors). The other algorithm identifies a single vapor and estimates its concentration.
Formalization of algorithms for relational database machines
Ryvkin, V.M.; Komarov, P.I.; Nazarov, A.S.
1986-11-01
This paper applies the apparatus of algorithmic algebras to formalize the mapping of the relational algebra language into the internal database processor language. The apparatus is a popular tool for formal structured description of parallel algorithms. The MUL'TIPROTSESSIST automatic parallel program design system using systems of algorithmic algebras may be applied to automate the design of database machine operating algorithms in experimental research and to formalize the parallel organization of interpretation algorithms for the relational algebraic operations.
A reliable algorithm for optimal control synthesis
NASA Technical Reports Server (NTRS)
Vansteenwyk, Brett; Ly, Uy-Loi
1992-01-01
In recent years, powerful design tools for linear time-invariant multivariable control systems have been developed based on direct parameter optimization. In this report, an algorithm for reliable optimal control synthesis using parameter optimization is presented. Specifically, a robust numerical algorithm is developed for the evaluation of the H(sup 2)-like cost functional and its gradients with respect to the controller design parameters. The method is specifically designed to handle defective degenerate systems and is based on the well-known Pade series approximation of the matrix exponential. Numerical test problems in control synthesis for simple mechanical systems and for a flexible structure with densely packed modes illustrate positively the reliability of this method when compared to a method based on diagonalization. Several types of cost functions have been considered: a cost function for robust control consisting of a linear combination of quadratic objectives for deterministic and random disturbances, and one representing an upper bound on the quadratic objective for worst case initial conditions. Finally, a framework for multivariable control synthesis has been developed combining the concept of closed-loop transfer recovery with numerical parameter optimization. The procedure enables designers to synthesize not only observer-based controllers but also controllers of arbitrary order and structure. Numerical design solutions rely heavily on the robust algorithm due to the high order of the synthesis model and the presence of near-overlapping modes. The design approach is successfully applied to the design of a high-bandwidth control system for a rotorcraft.
Not Available
1994-02-02
This report consists of three separate but related reports. They are (1) Human Resource Development, (2) Carbon-based Structural Materials Research Cluster, and (3) Data Parallel Algorithms for Scientific Computing. To meet the objectives of the Human Resource Development plan, the plan includes K--12 enrichment activities, undergraduate research opportunities for students at the state`s two Historically Black Colleges and Universities, graduate research through cluster assistantships and through a traineeship program targeted specifically to minorities, women and the disabled, and faculty development through participation in research clusters. One research cluster is the chemistry and physics of carbon-based materials. The objective of this cluster is to develop a self-sustaining group of researchers in carbon-based materials research within the institutions of higher education in the state of West Virginia. The projects will involve analysis of cokes, graphites and other carbons in order to understand the properties that provide desirable structural characteristics including resistance to oxidation, levels of anisotropy and structural characteristics of the carbons themselves. In the proposed cluster on parallel algorithms, research by four WVU faculty and three state liberal arts college faculty are: (1) modeling of self-organized critical systems by cellular automata; (2) multiprefix algorithms and fat-free embeddings; (3) offline and online partitioning of data computation; and (4) manipulating and rendering three dimensional objects. This cluster furthers the state Experimental Program to Stimulate Competitive Research plan by building on existing strengths at WVU in parallel algorithms.
FORTRAN Algorithm for Image Processing
NASA Technical Reports Server (NTRS)
Roth, Don J.; Hull, David R.
1987-01-01
FORTRAN computer algorithm containing various image-processing analysis and enhancement functions developed. Algorithm developed specifically to process images of developmental heat-engine materials obtained with sophisticated nondestructive evaluation instruments. Applications of program include scientific, industrial, and biomedical imaging for studies of flaws in materials, analyses of steel and ores, and pathology.
Closed-loop structural stability for linear-quadratic optimal systems
NASA Technical Reports Server (NTRS)
Wong, P. K.; Athans, M.
1975-01-01
This paper contains an explicit parameterization of a subclass of linear constant gain feedback maps that never destabilize an originally open-loop stable system. These results can then be used to obtain several new structural stability results for multi-input linear-quadratic feedback optimal designs.
Laplace-Gauss and Helmholtz-Gauss paraxial modes in media with quadratic refraction index.
Kiselev, Aleksei P; Plachenov, Alexandr B
2016-04-01
The scalar theory of paraxial wave propagation in an axisymmetric medium where the refraction index quadratically depends on transverse variables is addressed. Exact solutions of the corresponding parabolic equation are presented, generalizing the Laplace-Gauss and Helmholtz-Gauss modes earlier known for homogeneous media. Also, a generalization of a zero-order asymmetric Bessel-Gauss beam is given.
Graphical Description of Johnson-Neyman Outcomes for Linear and Quadratic Regression Surfaces.
ERIC Educational Resources Information Center
Schafer, William D.; Wang, Yuh-Yin
A modification of the usual graphical representation of heterogeneous regressions is described that can aid in interpreting significant regions for linear or quadratic surfaces. The standard Johnson-Neyman graph is a bivariate plot with the criterion variable on the ordinate and the predictor variable on the abscissa. Regression surfaces are drawn…
The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system
NASA Technical Reports Server (NTRS)
Yeon, Kyu Hwang; Um, Chung IN; George, T. F.
1994-01-01
The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.
A generalization of Baker's quadratic formulae for hyperelliptic ℘-functions
NASA Astrophysics Data System (ADS)
Athorne, Chris
2011-07-01
We present a generalization of a compact form, due to Baker, for quadratic identities satisfied by the three-index ℘-functions on curves of genus g=2, and a further generalization of a new result in genus g=3. The compact forms involve a bordered determinant containing 2(g-1)(g+1) free parameters.
A Comparison of Methods for Estimating Quadratic Effects in Nonlinear Structural Equation Models
ERIC Educational Resources Information Center
Harring, Jeffrey R.; Weiss, Brandi A.; Hsu, Jui-Chen
2012-01-01
Two Monte Carlo simulations were performed to compare methods for estimating and testing hypotheses of quadratic effects in latent variable regression models. The methods considered in the current study were (a) a 2-stage moderated regression approach using latent variable scores, (b) an unconstrained product indicator approach, (c) a latent…
Homogeneous systems with quadratic integrals, Lie-Poisson quasibrackets, and Kovalevskaya's method
NASA Astrophysics Data System (ADS)
Bizyaev, I. A.; Kozlov, V. V.
2015-12-01
We consider differential equations with quadratic right-hand sides that admit two quadratic first integrals, one of which is a positive-definite quadratic form. We indicate conditions of general nature under which a linear change of variables reduces this system to a certain 'canonical' form. Under these conditions, the system turns out to be divergenceless and can be reduced to a Hamiltonian form, but the corresponding linear Lie-Poisson bracket does not always satisfy the Jacobi identity. In the three-dimensional case, the equations can be reduced to the classical equations of the Euler top, and in four-dimensional space, the system turns out to be superintegrable and coincides with the Euler-Poincaré equations on some Lie algebra. In the five-dimensional case we find a reducing multiplier after multiplying by which the Poisson bracket satisfies the Jacobi identity. In the general case for n>5 we prove the absence of a reducing multiplier. As an example we consider a system of Lotka-Volterra type with quadratic right-hand sides that was studied by Kovalevskaya from the viewpoint of conditions of uniqueness of its solutions as functions of complex time. Bibliography: 38 titles.
ERIC Educational Resources Information Center
Didis, Makbule Gozde; Erbas, Ayhan Kursat
2015-01-01
This study attempts to investigate the performance of tenth-grade students in solving quadratic equations with one unknown, using symbolic equation and word-problem representations. The participants were 217 tenth-grade students, from three different public high schools. Data was collected through an open-ended questionnaire comprising eight…
Building Students' Understanding of Quadratic Equation Concept Using Naïve Geometry
ERIC Educational Resources Information Center
Fachrudin, Achmad Dhany; Putri, Ratu Ilma Indra; Darmawijoyo
2014-01-01
The purpose of this research is to know how Naïve Geometry method can support students' understanding about the concept of solving quadratic equations. In this article we will discuss one activities of the four activities we developed. This activity focused on how students linking the Naïve Geometry method with the solving of the quadratic…
Solution to Projectile Motion with Quadratic Drag and Graphing the Trajectory in Spreadsheets
ERIC Educational Resources Information Center
Benacka, Jan
2010-01-01
This note gives the analytical solution to projectile motion with quadratic drag by decomposing the velocity vector to "x," "y" coordinate directions. The solution is given by definite integrals. First, the impact angle is estimated from above, then the projectile coordinates are computed, and the trajectory is graphed at various launch angles and…
Graphical Representation of Complex Solutions of the Quadratic Equation in the "xy" Plane
ERIC Educational Resources Information Center
McDonald, Todd
2006-01-01
This paper presents a visual representation of complex solutions of quadratic equations in the xy plane. Rather than moving to the complex plane, students are able to experience a geometric interpretation of the solutions in the xy plane. I am also working on these types of representations with higher order polynomials with some success.
ERIC Educational Resources Information Center
Vial, Alexandre
2007-01-01
We investigate the problem of the horizontal distance travelled by a mobile experiencing a quadratic drag force. We show that by introducing a normalized distance, the problem can be greatly simplified. In order to parametrize this distance, we use the Pearson VII function, and we find that the optimal launch angle as a function of the initial…
ERIC Educational Resources Information Center
Kelava, Augustin; Werner, Christina S.; Schermelleh-Engel, Karin; Moosbrugger, Helfried; Zapf, Dieter; Ma, Yue; Cham, Heining; Aiken, Leona S.; West, Stephen G.
2011-01-01
Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x[superscript 2] [subscript 1], x[subscript 1]x[subscript 4]) to serve as indicators of each nonlinear latent construct. These approaches require the use of…
Optical synthetic-aperture radar processor archietecture with quadratic phase-error correction
Dickey, F.M.; Mason, J.J. )
1990-10-15
Uncompensated phase errors limit the image quality of synthetic-aperture radar. We present an acousto-optic synthetic-aperture radar processor architecture capable of measuring the quadratic phase error. This architecture allows for the error signal to be fed back to the processor to generate the corrected image.
Optical synthetic-aperture radar processor architecture with quadratic phase-error correction.
Dickey, F M; Mason, J J
1990-10-15
Uncompensated phase errors limit the image quality of synthetic-aperture radar. We present an acousto-optic synthetic-aperture radar processor architecture capable of measuring the quadratic phase error. This architecture allows for the error signal to be fed back to the processor to generate the corrected image.
A tutorial on the LQG/LTR method. [Linear Quadratic Gaussian/Loop Transfer Recovery
NASA Technical Reports Server (NTRS)
Athans, M.
1986-01-01
In this paper the so-called Linear-Quadratic-Gaussian method with Loop-Transfer-Recovery is surveyed. The objective is to provide a pragmatic exposition, with special emphasis on the step-by-step characteristics for designing multivariable feedback control systems.
Failures and Inabilities of High School Students about Quadratic Equations and Functions
ERIC Educational Resources Information Center
Memnun, Dilek Sezgin; Aydin, Bünyamin; Dinç, Emre; Çoban, Merve; Sevindik, Fatma
2015-01-01
In this research study, it was aimed to examine failures and inabilities of eleventh grade students about quadratic equations and functions. For this purpose, these students were asked ten open-ended questions. The analysis of the answers given by the students to these questions indicated that a significant part of these students had failures and…
Basis for a neuronal version of Grover's quantum algorithm.
Clark, Kevin B
2014-01-01
Grover's quantum (search) algorithm exploits principles of quantum information theory and computation to surpass the strong Church-Turing limit governing classical computers. The algorithm initializes a search field into superposed N (eigen)states to later execute nonclassical "subroutines" involving unitary phase shifts of measured states and to produce root-rate or quadratic gain in the algorithmic time (O(N (1/2))) needed to find some "target" solution m. Akin to this fast technological search algorithm, single eukaryotic cells, such as differentiated neurons, perform natural quadratic speed-up in the search for appropriate store-operated Ca(2+) response regulation of, among other processes, protein and lipid biosynthesis, cell energetics, stress responses, cell fate and death, synaptic plasticity, and immunoprotection. Such speed-up in cellular decision making results from spatiotemporal dynamics of networked intracellular Ca(2+)-induced Ca(2+) release and the search (or signaling) velocity of Ca(2+) wave propagation. As chemical processes, such as the duration of Ca(2+) mobilization, become rate-limiting over interstore distances, Ca(2+) waves quadratically decrease interstore-travel time from slow saltatory to fast continuous gradients proportional to the square-root of the classical Ca(2+) diffusion coefficient, D (1/2), matching the computing efficiency of Grover's quantum algorithm. In this Hypothesis and Theory article, I elaborate on these traits using a fire-diffuse-fire model of store-operated cytosolic Ca(2+) signaling valid for glutamatergic neurons. Salient model features corresponding to Grover's quantum algorithm are parameterized to meet requirements for the Oracle Hadamard transform and Grover's iteration. A neuronal version of Grover's quantum algorithm figures to benefit signal coincidence detection and integration, bidirectional synaptic plasticity, and other vital cell functions by rapidly selecting, ordering, and/or counting optional
Basis for a neuronal version of Grover's quantum algorithm
Clark, Kevin B.
2014-01-01
Grover's quantum (search) algorithm exploits principles of quantum information theory and computation to surpass the strong Church–Turing limit governing classical computers. The algorithm initializes a search field into superposed N (eigen)states to later execute nonclassical “subroutines” involving unitary phase shifts of measured states and to produce root-rate or quadratic gain in the algorithmic time (O(N1/2)) needed to find some “target” solution m. Akin to this fast technological search algorithm, single eukaryotic cells, such as differentiated neurons, perform natural quadratic speed-up in the search for appropriate store-operated Ca2+ response regulation of, among other processes, protein and lipid biosynthesis, cell energetics, stress responses, cell fate and death, synaptic plasticity, and immunoprotection. Such speed-up in cellular decision making results from spatiotemporal dynamics of networked intracellular Ca2+-induced Ca2+ release and the search (or signaling) velocity of Ca2+ wave propagation. As chemical processes, such as the duration of Ca2+ mobilization, become rate-limiting over interstore distances, Ca2+ waves quadratically decrease interstore-travel time from slow saltatory to fast continuous gradients proportional to the square-root of the classical Ca2+ diffusion coefficient, D1/2, matching the computing efficiency of Grover's quantum algorithm. In this Hypothesis and Theory article, I elaborate on these traits using a fire-diffuse-fire model of store-operated cytosolic Ca2+ signaling valid for glutamatergic neurons. Salient model features corresponding to Grover's quantum algorithm are parameterized to meet requirements for the Oracle Hadamard transform and Grover's iteration. A neuronal version of Grover's quantum algorithm figures to benefit signal coincidence detection and integration, bidirectional synaptic plasticity, and other vital cell functions by rapidly selecting, ordering, and/or counting optional response
The clinical algorithm nosology: a method for comparing algorithmic guidelines.
Pearson, S D; Margolis, C Z; Davis, S; Schreier, L K; Gottlieb, L K
1992-01-01
Concern regarding the cost and quality of medical care has led to a proliferation of competing clinical practice guidelines. No technique has been described for determining objectively the degree of similarity between alternative guidelines for the same clinical problem. The authors describe the development of the Clinical Algorithm Nosology (CAN), a new method to compare one form of guideline: the clinical algorithm. The CAN measures overall design complexity independent of algorithm content, qualitatively describes the clinical differences between two alternative algorithms, and then scores the degree of similarity between them. CAN algorithm design-complexity scores correlated highly with clinicians' estimates of complexity on an ordinal scale (r = 0.86). Five pairs of clinical algorithms addressing three topics (gallstone lithotripsy, thyroid nodule, and sinusitis) were selected for interrater reliability testing of the CAN clinical-similarity scoring system. Raters categorized the similarity of algorithm pathways in alternative algorithms as "identical," "similar," or "different." Interrater agreement was achieved on 85/109 scores (80%), weighted kappa statistic, k = 0.73. It is concluded that the CAN is a valid method for determining the structural complexity of clinical algorithms, and a reliable method for describing differences and scoring the similarity between algorithms for the same clinical problem. In the future, the CAN may serve to evaluate the reliability of algorithm development programs, and to support providers and purchasers in choosing among alternative clinical guidelines.
A quantum genetic algorithm with quantum crossover and mutation operations
NASA Astrophysics Data System (ADS)
SaiToh, Akira; Rahimi, Robabeh; Nakahara, Mikio
2013-11-01
In the context of evolutionary quantum computing in the literal meaning, a quantum crossover operation has not been introduced so far. Here, we introduce a novel quantum genetic algorithm that has a quantum crossover procedure performing crossovers among all chromosomes in parallel for each generation. A complexity analysis shows that a quadratic speedup is achieved over its classical counterpart in the dominant factor of the run time to handle each generation.
Technology Transfer Automated Retrieval System (TEKTRAN)
This historical dataset consists of a series of permanent 1-m2 quadrats located on the sagebrush steppe in eastern Idaho, USA. The key aspect of the data is that during each growing season, all individual plants in each quadrat were identified and mapped. The combination of a long time-series with f...
The Superior Lambert Algorithm
NASA Astrophysics Data System (ADS)
der, G.
2011-09-01
Lambert algorithms are used extensively for initial orbit determination, mission planning, space debris correlation, and missile targeting, just to name a few applications. Due to the significance of the Lambert problem in Astrodynamics, Gauss, Battin, Godal, Lancaster, Gooding, Sun and many others (References 1 to 15) have provided numerous formulations leading to various analytic solutions and iterative methods. Most Lambert algorithms and their computer programs can only work within one revolution, break down or converge slowly when the transfer angle is near zero or 180 degrees, and their multi-revolution limitations are either ignored or barely addressed. Despite claims of robustness, many Lambert algorithms fail without notice, and the users seldom have a clue why. The DerAstrodynamics lambert2 algorithm, which is based on the analytic solution formulated by Sun, works for any number of revolutions and converges rapidly at any transfer angle. It provides significant capability enhancements over every other Lambert algorithm in use today. These include improved speed, accuracy, robustness, and multirevolution capabilities as well as implementation simplicity. Additionally, the lambert2 algorithm provides a powerful tool for solving the angles-only problem without artificial singularities (pointed out by Gooding in Reference 16), which involves 3 lines of sight captured by optical sensors, or systems such as the Air Force Space Surveillance System (AFSSS). The analytic solution is derived from the extended Godal’s time equation by Sun, while the iterative method of solution is that of Laguerre, modified for robustness. The Keplerian solution of a Lambert algorithm can be extended to include the non-Keplerian terms of the Vinti algorithm via a simple targeting technique (References 17 to 19). Accurate analytic non-Keplerian trajectories can be predicted for satellites and ballistic missiles, while performing at least 100 times faster in speed than most
Mixed Integer Programming and Heuristic Scheduling for Space Communication Networks
NASA Technical Reports Server (NTRS)
Cheung, Kar-Ming; Lee, Charles H.
2012-01-01
We developed framework and the mathematical formulation for optimizing communication network using mixed integer programming. The design yields a system that is much smaller, in search space size, when compared to the earlier approach. Our constrained network optimization takes into account the dynamics of link performance within the network along with mission and operation requirements. A unique penalty function is introduced to transform the mixed integer programming into the more manageable problem of searching in a continuous space. The constrained optimization problem was proposed to solve in two stages: first using the heuristic Particle Swarming Optimization algorithm to get a good initial starting point, and then feeding the result into the Sequential Quadratic Programming algorithm to achieve the final optimal schedule. We demonstrate the above planning and scheduling methodology with a scenario of 20 spacecraft and 3 ground stations of a Deep Space Network site. Our approach and framework have been simple and flexible so that problems with larger number of constraints and network can be easily adapted and solved.
Power spectral estimation algorithms
NASA Technical Reports Server (NTRS)
Bhatia, Manjit S.
1989-01-01
Algorithms to estimate the power spectrum using Maximum Entropy Methods were developed. These algorithms were coded in FORTRAN 77 and were implemented on the VAX 780. The important considerations in this analysis are: (1) resolution, i.e., how close in frequency two spectral components can be spaced and still be identified; (2) dynamic range, i.e., how small a spectral peak can be, relative to the largest, and still be observed in the spectra; and (3) variance, i.e., how accurate the estimate of the spectra is to the actual spectra. The application of the algorithms based on Maximum Entropy Methods to a variety of data shows that these criteria are met quite well. Additional work in this direction would help confirm the findings. All of the software developed was turned over to the technical monitor. A copy of a typical program is included. Some of the actual data and graphs used on this data are also included.
NASA Astrophysics Data System (ADS)
Salvadori, A.; Fantoni, F.
2016-10-01
The present work frames the problem of three-dimensional quasi-static crack propagation in brittle materials into the theory of standard dissipative processes. Variational formulations are stated. They characterize the three dimensional crack front "quasi-static velocity" as minimizer of constrained quadratic functionals. An implicit in time crack tracking algorithm that computationally handles the constraint via the penalty method algorithm is introduced and proof of concept is provided.
Tada, K; Kishimoto, M; Omasa, T; Katakura, Y; Suga, K
2001-01-01
Constrained optimization for microbial fermentation was studied. For optimization, we used not the maximum principle but a nonlinear programming method because of the need to consider many metabolic reactions. In the case of L-lysine fermentation, the optimization problem in L-lysine production was formulated as a nonlinear programming problem. In general, the state equations based on material balances are represented as differential equations, but such equations which are dependent on time can not be applied to a nonlinear programming problem. Therefore, the state equations were made discrete in a time base, and a new single vector which is not dependent on time was substituted. From these formulae, the objective function and the constraints using nonlinear programming problem were defined as the amount of L-lysine produced, and as a metabolic reaction model and empirical equations, respectively. Computer program was developed to solve this constrained nonlinear programming problem. The applied algorithm of the computer programming was a sequential quadratic programming method (SQP method). When the constrained nonlinear programming problem is solved using the SQP method, the maximum amount of L-lysine produced and the optimal feeding rate of L-threonine could be calculated. From the calculated results, it was clear that introduction of the equality and inequality constraints was easy. L-Lysine at a concentration up to 75.3 g/l could be produced when the fermentation was carried out under optimal conditions.
In-Trail Procedure (ITP) Algorithm Design
NASA Technical Reports Server (NTRS)
Munoz, Cesar A.; Siminiceanu, Radu I.
2007-01-01
The primary objective of this document is to provide a detailed description of the In-Trail Procedure (ITP) algorithm, which is part of the Airborne Traffic Situational Awareness In-Trail Procedure (ATSA-ITP) application. To this end, the document presents a high level description of the ITP Algorithm and a prototype implementation of this algorithm in the programming language C.