On the Convergence Analysis of the Optimized Gradient Method.

PubMed

Kim, Donghwan; Fessler, Jeffrey A

2017-01-01

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

On the Convergence Analysis of the Optimized Gradient Method

PubMed Central

Kim, Donghwan; Fessler, Jeffrey A.

2016-01-01

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

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.

DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

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

NASA Technical Reports Server (NTRS)

Cooper, D. B.; Yalabik, N.

1975-01-01

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

Extending the accuracy of the SNAP interatomic potential form

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

Wood, Mitchell A.; Thompson, Aidan P.

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

Extending the accuracy of the SNAP interatomic potential form

DOE PAGES

Wood, Mitchell A.; Thompson, Aidan P.

2018-03-28

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

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

PubMed Central

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

2016-01-01

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

Stochastic Control of Energy Efficient Buildings: A Semidefinite Programming Approach

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

Ma, Xiao; Dong, Jin; Djouadi, Seddik M

2015-01-01

The key goal in energy efficient buildings is to reduce energy consumption of Heating, Ventilation, and Air- Conditioning (HVAC) systems while maintaining a comfortable temperature and humidity in the building. This paper proposes a novel stochastic control approach for achieving joint performance and power control of HVAC. We employ a constrained Stochastic Linear Quadratic Control (cSLQC) by minimizing a quadratic cost function with a disturbance assumed to be Gaussian. The problem is formulated to minimize the expected cost subject to a linear constraint and a probabilistic constraint. By using cSLQC, the problem is reduced to a semidefinite optimization problem, wheremore » the optimal control can be computed efficiently by Semidefinite programming (SDP). Simulation results are provided to demonstrate the effectiveness and power efficiency by utilizing the proposed control approach.« less

Terminal spacecraft rendezvous and capture with LASSO model predictive control

NASA Astrophysics Data System (ADS)

Hartley, Edward N.; Gallieri, Marco; Maciejowski, Jan M.

2013-11-01

The recently investigated ℓasso model predictive control (MPC) is applied to the terminal phase of a spacecraft rendezvous and capture mission. The interaction between the cost function and the treatment of minimum impulse bit is also investigated. The propellant consumption with ℓasso MPC for the considered scenario is noticeably less than with a conventional quadratic cost and control actions are sparser in time. Propellant consumption and sparsity are competitive with those achieved using a zone-based ℓ1 cost function, whilst requiring fewer decision variables in the optimisation problem than the latter. The ℓasso MPC is demonstrated to meet tighter specifications on control precision and also avoids the risk of undesirable behaviours often associated with pure ℓ1 stage costs.

Quadratic canonical transformation theory and higher order density matrices.

PubMed

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

2009-03-28

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

Digital robust active control law synthesis for large order flexible structure using parameter optimization

NASA Technical Reports Server (NTRS)

Mukhopadhyay, V.

1988-01-01

A generic procedure for the parameter optimization of a digital control law for a large-order flexible flight vehicle or large space structure modeled as a sampled data system is presented. A linear quadratic Guassian type cost function was minimized, while satisfying a set of constraints on the steady-state rms values of selected design responses, using a constrained optimization technique to meet multiple design requirements. Analytical expressions for the gradients of the cost function and the design constraints on mean square responses with respect to the control law design variables are presented.

A Factorization Approach to the Linear Regulator Quadratic Cost Problem

NASA Technical Reports Server (NTRS)

Milman, M. H.

1985-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Cost decomposition of linear systems with application to model reduction

NASA Technical Reports Server (NTRS)

Skelton, R. E.

1980-01-01

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

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

PubMed

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

2014-08-01

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

Exact solution for the optimal neuronal layout problem.

PubMed

Chklovskii, Dmitri B

2004-10-01

Evolution perfected brain design by maximizing its functionality while minimizing costs associated with building and maintaining it. Assumption that brain functionality is specified by neuronal connectivity, implemented by costly biological wiring, leads to the following optimal design problem. For a given neuronal connectivity, find a spatial layout of neurons that minimizes the wiring cost. Unfortunately, this problem is difficult to solve because the number of possible layouts is often astronomically large. We argue that the wiring cost may scale as wire length squared, reducing the optimal layout problem to a constrained minimization of a quadratic form. For biologically plausible constraints, this problem has exact analytical solutions, which give reasonable approximations to actual layouts in the brain. These solutions make the inverse problem of inferring neuronal connectivity from neuronal layout more tractable.

Lump solutions to nonlinear partial differential equations via Hirota bilinear forms

NASA Astrophysics Data System (ADS)

Ma, Wen-Xiu; Zhou, Yuan

2018-02-01

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

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.

Model reduction by weighted Component Cost Analysis

NASA Technical Reports Server (NTRS)

Kim, Jae H.; Skelton, Robert E.

1990-01-01

Component Cost Analysis considers any given system driven by a white noise process as an interconnection of different components, and assigns a metric called 'component cost' to each component. These component costs measure the contribution of each component to a predefined quadratic cost function. A reduced-order model of the given system may be obtained by deleting those components that have the smallest component costs. The theory of Component Cost Analysis is extended to include finite-bandwidth colored noises. The results also apply when actuators have dynamics of their own. Closed-form analytical expressions of component costs are also derived for a mechanical system described by its modal data. This is very useful to compute the modal costs of very high order systems. A numerical example for MINIMAST system is presented.

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

PubMed

Chen, Shyan-Shiou

2011-10-01

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

Decomposition method for zonal resource allocation problems in telecommunication networks

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

Discrete-time Markovian-jump linear quadratic optimal control

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

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

PubMed

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

2016-03-01

Policy-makers have long argued about the potential efficiency gains and cost savings from integrating HIV and sexual reproductive health (SRH) services, particularly in resource-constrained settings with generalised HIV epidemics. However, until now, little empirical evidence exists on whether the hypothesised efficiency gains associated with such integration can be achieved in practice. We estimated a quadratic cost function using data obtained from 40 health facilities, over a 2-year-period, in Kenya and Swaziland. The quadratic specification enables us to determine the existence of economies of scale and scope. The empirical results reveal that at the current output levels, only HIV counselling and testing services are characterised by service-specific economies of scale. However, no overall economies of scale exist as all outputs are increased. The results also indicate cost complementarities between cervical cancer screening and HIV care; post-natal care and HIV care and family planning and sexually transmitted infection treatment combinations only. The results from this analysis reveal that contrary to expectation, efficiency gains from the integration of HIV and SRH services, if any, are likely to be modest. Efficiency gains are likely to be most achievable in settings that are currently delivering HIV and SRH services at a low scale with high levels of fixed costs. The presence of cost complementarities for only three service combinations implies that careful consideration of setting-specific clinical practices and the extent to which they can be combined should be made when deciding which services to integrate. NCT01694862. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/

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

PubMed Central

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

2016-01-01

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

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

NASA Technical Reports Server (NTRS)

Rhee, Ihnseok; Speyer, Jason L.

1991-01-01

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

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

NASA Astrophysics Data System (ADS)

Cotar, Codina; Friesecke, Gero; Klüppelberg, Claudia

2018-06-01

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

Functional Data Approximation on Bounded Domains using Polygonal Finite Elements.

PubMed

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

2018-07-01

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

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

NASA Technical Reports Server (NTRS)

Stein, G.; Henke, A. H.

1972-01-01

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

On real-space Density Functional Theory for non-orthogonal crystal systems: Kronecker product formulation of the kinetic energy operator

NASA Astrophysics Data System (ADS)

Sharma, Abhiraj; Suryanarayana, Phanish

2018-05-01

We present an accurate and efficient real-space Density Functional Theory (DFT) framework for the ab initio study of non-orthogonal crystal systems. Specifically, employing a local reformulation of the electrostatics, we develop a novel Kronecker product formulation of the real-space kinetic energy operator that significantly reduces the number of operations associated with the Laplacian-vector multiplication, the dominant cost in practical computations. In particular, we reduce the scaling with respect to finite-difference order from quadratic to linear, thereby significantly bridging the gap in computational cost between non-orthogonal and orthogonal systems. We verify the accuracy and efficiency of the proposed methodology through selected examples.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

USGS Publications Warehouse

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

1986-01-01

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

Quadratic spline subroutine package

USGS Publications Warehouse

Rasmussen, Lowell A.

1982-01-01

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

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

ERIC Educational Resources Information Center

Ozaltun Celik, Aytug; Bukova Guzel, Esra

2017-01-01

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

Linear quadratic stochastic control of atomic hydrogen masers.

PubMed

Koppang, P; Leland, R

1999-01-01

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

Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing

NASA Technical Reports Server (NTRS)

Choi, Benjamin B.

2002-01-01

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

A study of parameter identification

NASA Technical Reports Server (NTRS)

Herget, C. J.; Patterson, R. E., III

1978-01-01

A set of definitions for deterministic parameter identification ability were proposed. Deterministic parameter identificability properties are presented based on four system characteristics: direct parameter recoverability, properties of the system transfer function, properties of output distinguishability, and uniqueness properties of a quadratic cost functional. Stochastic parameter identifiability was defined in terms of the existence of an estimation sequence for the unknown parameters which is consistent in probability. Stochastic parameter identifiability properties are presented based on the following characteristics: convergence properties of the maximum likelihood estimate, properties of the joint probability density functions of the observations, and properties of the information matrix.

Probabilistic dual heuristic programming-based adaptive critic

NASA Astrophysics Data System (ADS)

Herzallah, Randa

2010-02-01

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

The stability of quadratic-reciprocal functional equation

NASA Astrophysics Data System (ADS)

Song, Aimin; Song, Minwei

2018-04-01

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

Gain optimization with non-linear controls

NASA Technical Reports Server (NTRS)

Slater, G. L.; Kandadai, R. D.

1984-01-01

An algorithm has been developed for the analysis and design of controls for non-linear systems. The technical approach is to use statistical linearization to model the non-linear dynamics of a system by a quasi-Gaussian model. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this paper is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general, however, and numerical computation requires only that the specific non-linearity be considered in the analysis.

The generalized quadratic knapsack problem. A neuronal network approach.

PubMed

Talaván, Pedro M; Yáñez, Javier

2006-05-01

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

Finite Element Simulation of Articular Contact Mechanics with Quadratic Tetrahedral Elements

PubMed Central

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

2016-01-01

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

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

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2012-01-01

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

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

ERIC Educational Resources Information Center

Valahas, Theodoros; Boukas, Andreas

2011-01-01

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

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

NASA Astrophysics Data System (ADS)

Szederkényi, Gábor; Hangos, Katalin M.

2004-04-01

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

Regression model, artificial neural network, and cost estimation for biosorption of Ni(II)-ions from aqueous solutions by Potamogeton pectinatus.

PubMed

Fawzy, Manal; Nasr, Mahmoud; Adel, Samar; Helmi, Shacker

2018-03-21

This study investigated the application of Potamogeton pectinatus for Ni(II)-ions biosorption from aqueous solutions. FTIR spectra showed that the functional groups of -OH, C-H, -C = O, and -COO- could form an organometallic complex with Ni(II)-ions on the biomaterial surface. SEM/EDX analysis indicated that the voids on the biosorbent surface were blocked due to Ni(II)-ions uptake via an ion exchange mechanism. For Ni(II)-ions of 50 mg/L, the adsorption efficiency recorded 63.4% at pH: 5, biosorbent dosage: 10 g/L, and particle-diameter: 0.125-0.25 mm within 180 minutes. A quadratic model depicted that the plot of removal efficiency against pH or contact time caused quadratic-linear concave up curves, whereas the curve of initial Ni(II)-ions was quadratic-linear convex down. Artificial neural network with a structure of 5 - 6 - 1 was able to predict the adsorption efficiency (R 2 : 0.967). The relative importance of inputs was: initial Ni(II)-ions > pH > contact time > biosorbent dosage > particle-size. Freundlich isotherm described well the adsorption mechanism (R 2 : 0.974), which indicated a multilayer adsorption onto energetically heterogeneous surfaces. The net cost of using P. pectinatus for the removal of Ni(II)-ions (4.25 ± 1.26 mg/L) from real industrial effluents within 30 minutes was 3.4 $USD/m 3 .

An algorithm for the solution of dynamic linear programs

NASA Technical Reports Server (NTRS)

Psiaki, Mark L.

1989-01-01

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

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

NASA Technical Reports Server (NTRS)

Born, G. J.; Kai, T.

1975-01-01

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

Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

NASA Technical Reports Server (NTRS)

Milman, Mark H.

1987-01-01

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary systems. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

Biological effects and equivalent doses in radiotherapy: A software solution

PubMed Central

Voyant, Cyril; Julian, Daniel; Roustit, Rudy; Biffi, Katia; Lantieri, Céline

2013-01-01

Background The limits of TDF (time, dose, and fractionation) and linear quadratic models have been known for a long time. Medical physicists and physicians are required to provide fast and reliable interpretations regarding delivered doses or any future prescriptions relating to treatment changes. Aim We, therefore, propose a calculation interface under the GNU license to be used for equivalent doses, biological doses, and normal tumor complication probability (Lyman model). Materials and methods The methodology used draws from several sources: the linear-quadratic-linear model of Astrahan, the repopulation effects of Dale, and the prediction of multi-fractionated treatments of Thames. Results and conclusions The results are obtained from an algorithm that minimizes an ad-hoc cost function, and then compared to an equivalent dose computed using standard calculators in seven French radiotherapy centers. PMID:24936319

Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

NASA Technical Reports Server (NTRS)

Milman, Mark H.

1988-01-01

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary schemes. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

On the time-weighted quadratic sum of linear discrete systems

NASA Technical Reports Server (NTRS)

Jury, E. I.; Gutman, S.

1975-01-01

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

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

ERIC Educational Resources Information Center

Kenan, Kok Xiao-Feng

2017-01-01

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

Multibody model reduction by component mode synthesis and component cost analysis

NASA Technical Reports Server (NTRS)

Spanos, J. T.; Mingori, D. L.

1990-01-01

The classical assumed-modes method is widely used in modeling the dynamics of flexible multibody systems. According to the method, the elastic deformation of each component in the system is expanded in a series of spatial and temporal functions known as modes and modal coordinates, respectively. This paper focuses on the selection of component modes used in the assumed-modes expansion. A two-stage component modal reduction method is proposed combining Component Mode Synthesis (CMS) with Component Cost Analysis (CCA). First, each component model is truncated such that the contribution of the high frequency subsystem to the static response is preserved. Second, a new CMS procedure is employed to assemble the system model and CCA is used to further truncate component modes in accordance with their contribution to a quadratic cost function of the system output. The proposed method is demonstrated with a simple example of a flexible two-body system.

Guaranteed cost control of polynomial fuzzy systems via a sum of squares approach.

PubMed

Tanaka, Kazuo; Ohtake, Hiroshi; Wang, Hua O

2009-04-01

This paper presents the guaranteed cost control of polynomial fuzzy systems via a sum of squares (SOS) approach. First, we present a polynomial fuzzy model and controller that are more general representations of the well-known Takagi-Sugeno (T-S) fuzzy model and controller, respectively. Second, we derive a guaranteed cost control design condition based on polynomial Lyapunov functions. Hence, the design approach discussed in this paper is more general than the existing LMI approaches (to T-S fuzzy control system designs) based on quadratic Lyapunov functions. The design condition realizes a guaranteed cost control by minimizing the upper bound of a given performance function. In addition, the design condition in the proposed approach can be represented in terms of SOS and is numerically (partially symbolically) solved via the recent developed SOSTOOLS. To illustrate the validity of the design approach, two design examples are provided. The first example deals with a complicated nonlinear system. The second example presents micro helicopter control. Both the examples show that our approach provides more extensive design results for the existing LMI approach.

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

PubMed

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

2016-03-21

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

Fixed-point image orthorectification algorithms for reduced computational cost

NASA Astrophysics Data System (ADS)

French, Joseph Clinton

Imaging systems have been applied to many new applications in recent years. With the advent of low-cost, low-power focal planes and more powerful, lower cost computers, remote sensing applications have become more wide spread. Many of these applications require some form of geolocation, especially when relative distances are desired. However, when greater global positional accuracy is needed, orthorectification becomes necessary. Orthorectification is the process of projecting an image onto a Digital Elevation Map (DEM), which removes terrain distortions and corrects the perspective distortion by changing the viewing angle to be perpendicular to the projection plane. Orthorectification is used in disaster tracking, landscape management, wildlife monitoring and many other applications. However, orthorectification is a computationally expensive process due to floating point operations and divisions in the algorithm. To reduce the computational cost of on-board processing, two novel algorithm modifications are proposed. One modification is projection utilizing fixed-point arithmetic. Fixed point arithmetic removes the floating point operations and reduces the processing time by operating only on integers. The second modification is replacement of the division inherent in projection with a multiplication of the inverse. The inverse must operate iteratively. Therefore, the inverse is replaced with a linear approximation. As a result of these modifications, the processing time of projection is reduced by a factor of 1.3x with an average pixel position error of 0.2% of a pixel size for 128-bit integer processing and over 4x with an average pixel position error of less than 13% of a pixel size for a 64-bit integer processing. A secondary inverse function approximation is also developed that replaces the linear approximation with a quadratic. The quadratic approximation produces a more accurate approximation of the inverse, allowing for an integer multiplication calculation to be used in place of the traditional floating point division. This method increases the throughput of the orthorectification operation by 38% when compared to floating point processing. Additionally, this method improves the accuracy of the existing integer-based orthorectification algorithms in terms of average pixel distance, increasing the accuracy of the algorithm by more than 5x. The quadratic function reduces the pixel position error to 2% and is still 2.8x faster than the 128-bit floating point algorithm.

Piecewise linear approximation for hereditary control problems

NASA Technical Reports Server (NTRS)

Propst, Georg

1987-01-01

Finite dimensional approximations are presented for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in case the cost integral ranges over a finite time interval as well as in the case it ranges over an infinite time interval. The arguments in the latter case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space R(n) x L(2) and the favorable eigenvalue behavior of the piecewise linear approximations.

A Differential Evolution Algorithm Based on Nikaido-Isoda Function for Solving Nash Equilibrium in Nonlinear Continuous Games

PubMed Central

He, Feng; Zhang, Wei; Zhang, Guoqiang

2016-01-01

A differential evolution algorithm for solving Nash equilibrium in nonlinear continuous games is presented in this paper, called NIDE (Nikaido-Isoda differential evolution). At each generation, parent and child strategy profiles are compared one by one pairwisely, adapting Nikaido-Isoda function as fitness function. In practice, the NE of nonlinear game model with cubic cost function and quadratic demand function is solved, and this method could also be applied to non-concave payoff functions. Moreover, the NIDE is compared with the existing Nash Domination Evolutionary Multiplayer Optimization (NDEMO), the result showed that NIDE was significantly better than NDEMO with less iterations and shorter running time. These numerical examples suggested that the NIDE method is potentially useful. PMID:27589229

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

PubMed Central

Araújo, Ricardo; Mateus, Octávio

2015-01-01

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

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

NASA Astrophysics Data System (ADS)

Pan, Zhen; Anderes, Ethan; Knox, Lloyd

2018-05-01

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

Quadratic Optimisation with One Quadratic Equality Constraint

DTIC Science & Technology

2010-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

Microgravity vibration isolation: An optimal control law for the one-dimensional case

NASA Technical Reports Server (NTRS)

Hampton, Richard D.; Grodsinsky, Carlos M.; Allaire, Paul E.; Lewis, David W.; Knospe, Carl R.

1991-01-01

Certain experiments contemplated for space platforms must be isolated from the accelerations of the platform. An optimal active control is developed for microgravity vibration isolation, using constant state feedback gains (identical to those obtained from the Linear Quadratic Regulator (LQR) approach) along with constant feedforward gains. The quadratic cost function for this control algorithm effectively weights external accelerations of the platform disturbances by a factor proportional to (1/omega) exp 4. Low frequency accelerations are attenuated by greater than two orders of magnitude. The control relies on the absolute position and velocity feedback of the experiment and the absolute position and velocity feedforward of the platform, and generally derives the stability robustness characteristics guaranteed by the LQR approach to optimality. The method as derived is extendable to the case in which only the relative positions and velocities and the absolute accelerations of the experiment and space platform are available.

Microgravity vibration isolation: An optimal control law for the one-dimensional case

NASA Technical Reports Server (NTRS)

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

1991-01-01

Certain experiments contemplated for space platforms must be isolated from the accelerations of the platforms. An optimal active control is developed for microgravity vibration isolation, using constant state feedback gains (identical to those obtained from the Linear Quadratic Regulator (LQR) approach) along with constant feedforward (preview) gains. The quadratic cost function for this control algorithm effectively weights external accelerations of the platform disturbances by a factor proportional to (1/omega)(exp 4). Low frequency accelerations (less than 50 Hz) are attenuated by greater than two orders of magnitude. The control relies on the absolute position and velocity feedback of the experiment and the absolute position and velocity feedforward of the platform, and generally derives the stability robustness characteristics guaranteed by the LQR approach to optimality. The method as derived is extendable to the case in which only the relative positions and velocities and the absolute accelerations of the experiment and space platform are available.

Emotion suppression moderates the quadratic association between RSA and executive function

PubMed Central

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

2016-01-01

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

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…

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

NASA Astrophysics Data System (ADS)

Burns-Childers, Annie; Vidakovic, Draga

2018-07-01

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

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

PubMed Central

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

2015-01-01

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

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

PubMed

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

2015-01-01

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

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

PubMed Central

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

2013-01-01

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

Experimental and Theoretical Results in Output Trajectory Redesign for Flexible Structures

NASA Technical Reports Server (NTRS)

Dewey, J. S.; Leang, K.; Devasia, S.

1998-01-01

In this paper we study the optimal redesign of output trajectories for linear invertible systems. This is particularly important for tracking control of flexible structures because the input-state trajectores, that achieve tracking of the required output may cause excessive vibrations in the structure. We pose and solve this problem, in the context of linear systems, as the minimization of a quadratic cost function. The theory is developed and applied to the output tracking of a flexible structure and experimental results are presented.

Quadratic forms involving Green's and Robin functions

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

Dubinin, Vladimir N

2009-10-31

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

Students' Conceptions Supporting Their Symbolization and Meaning of Function Rules

ERIC Educational Resources Information Center

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

2016-01-01

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

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

PubMed

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

2017-01-01

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

Hyers-Ulam stability of a generalized Apollonius type quadratic mapping

NASA Astrophysics Data System (ADS)

Park, Chun-Gil; Rassias, Themistocles M.

2006-10-01

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

Ride comfort control in large flexible aircraft. M.S. Thesis

NASA Technical Reports Server (NTRS)

Warren, M. E.

1971-01-01

The problem of ameliorating the discomfort of passengers on a large air transport subject to flight disturbances is examined. The longitudinal dynamics of the aircraft, including effects of body flexing, are developed in terms of linear, constant coefficient differential equations in state variables. A cost functional, penalizing the rigid body displacements and flexure accelerations over the surface of the aircraft is formulated as a quadratic form. The resulting control problem, to minimize the cost subject to the state equation constraints, is of a class whose solutions are well known. The feedback gains for the optimal controller are calculated digitally, and the resulting autopilot is simulated on an analog computer and its performance evaluated.

Component Cost Analysis of Large Scale Systems

NASA Technical Reports Server (NTRS)

Skelton, R. E.; Yousuff, A.

1982-01-01

The ideas of cost decomposition is summarized to aid in the determination of the relative cost (or 'price') of each component of a linear dynamic system using quadratic performance criteria. In addition to the insights into system behavior that are afforded by such a component cost analysis CCA, these CCA ideas naturally lead to a theory for cost-equivalent realizations.

Digital robust active control law synthesis for large order systems using constrained optimization

NASA Technical Reports Server (NTRS)

Mukhopadhyay, Vivek

1987-01-01

This paper presents a direct digital control law synthesis procedure for a large order, sampled data, linear feedback system using constrained optimization techniques to meet multiple design requirements. A linear quadratic Gaussian type cost function is minimized while satisfying a set of constraints on the design loads and responses. General expressions for gradients of the cost function and constraints, with respect to the digital control law design variables are derived analytically and computed by solving a set of discrete Liapunov equations. The designer can choose the structure of the control law and the design variables, hence a stable classical control law as well as an estimator-based full or reduced order control law can be used as an initial starting point. Selected design responses can be treated as constraints instead of lumping them into the cost function. This feature can be used to modify a control law, to meet individual root mean square response limitations as well as minimum single value restrictions. Low order, robust digital control laws were synthesized for gust load alleviation of a flexible remotely piloted drone aircraft.

Integration of the Quadratic Function and Generalization

ERIC Educational Resources Information Center

Mitsuma, Kunio

2011-01-01

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

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

PubMed

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

2015-09-01

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

An Unexpected Influence on a Quadratic

ERIC Educational Resources Information Center

Davis, Jon D.

2013-01-01

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

Using ant colony optimization on the quadratic assignment problem to achieve low energy cost in geo-distributed data centers

NASA Astrophysics Data System (ADS)

Osei, Richard

There are many problems associated with operating a data center. Some of these problems include data security, system performance, increasing infrastructure complexity, increasing storage utilization, keeping up with data growth, and increasing energy costs. Energy cost differs by location, and at most locations fluctuates over time. The rising cost of energy makes it harder for data centers to function properly and provide a good quality of service. With reduced energy cost, data centers will have longer lasting servers/equipment, higher availability of resources, better quality of service, a greener environment, and reduced service and software costs for consumers. Some of the ways that data centers have tried to using to reduce energy costs include dynamically switching on and off servers based on the number of users and some predefined conditions, the use of environmental monitoring sensors, and the use of dynamic voltage and frequency scaling (DVFS), which enables processors to run at different combinations of frequencies with voltages to reduce energy cost. This thesis presents another method by which energy cost at data centers could be reduced. This method involves the use of Ant Colony Optimization (ACO) on a Quadratic Assignment Problem (QAP) in assigning user request to servers in geo-distributed data centers. In this paper, an effort to reduce data center energy cost involves the use of front portals, which handle users' requests, were used as ants to find cost effective ways to assign users requests to a server in heterogeneous geo-distributed data centers. The simulation results indicate that the ACO for Optimal Server Activation and Task Placement algorithm reduces energy cost on a small and large number of users' requests in a geo-distributed data center and its performance increases as the input data grows. In a simulation with 3 geo-distributed data centers, and user's resource request ranging from 25,000 to 25,000,000, the ACO algorithm was able to reduce energy cost on an average of $.70 per second. The ACO for Optimal Server Activation and Task Placement algorithm has proven to work as an alternative or improvement in reducing energy cost in geo-distributed data centers.

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

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

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

2010-12-15

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

Expected value analysis for integrated supplier selection and inventory control of multi-product inventory system with fuzzy cost

NASA Astrophysics Data System (ADS)

Sutrisno, Widowati, Tjahjana, R. Heru

2017-12-01

The future cost in many industrial problem is obviously uncertain. Then a mathematical analysis for a problem with uncertain cost is needed. In this article, we deals with the fuzzy expected value analysis to solve an integrated supplier selection and supplier selection problem with uncertain cost where the costs uncertainty is approached by a fuzzy variable. We formulate the mathematical model of the problems fuzzy expected value based quadratic optimization with total cost objective function and solve it by using expected value based fuzzy programming. From the numerical examples result performed by the authors, the supplier selection problem was solved i.e. the optimal supplier was selected for each time period where the optimal product volume of all product that should be purchased from each supplier for each time period was determined and the product stock level was controlled as decided by the authors i.e. it was followed the given reference level.

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

ERIC Educational Resources Information Center

Duarte, Jonathan T.

2010-01-01

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

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

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

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

2017-01-01

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

A non-linear programming approach to the computer-aided design of regulators using a linear-quadratic formulation

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.

An Algebraic Approach for Solving Quadratic Inequalities

ERIC Educational Resources Information Center

Mahmood, Munir; Al-Mirbati, Rudaina

2017-01-01

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

Integrated beam orientation and scanning-spot optimization in intensity-modulated proton therapy for brain and unilateral head and neck tumors.

PubMed

Gu, Wenbo; O'Connor, Daniel; Nguyen, Dan; Yu, Victoria Y; Ruan, Dan; Dong, Lei; Sheng, Ke

2018-04-01

Intensity-Modulated Proton Therapy (IMPT) is the state-of-the-art method of delivering proton radiotherapy. Previous research has been mainly focused on optimization of scanning spots with manually selected beam angles. Due to the computational complexity, the potential benefit of simultaneously optimizing beam orientations and spot pattern could not be realized. In this study, we developed a novel integrated beam orientation optimization (BOO) and scanning-spot optimization algorithm for intensity-modulated proton therapy (IMPT). A brain chordoma and three unilateral head-and-neck patients with a maximal target size of 112.49 cm 3 were included in this study. A total number of 1162 noncoplanar candidate beams evenly distributed across 4π steradians were included in the optimization. For each candidate beam, the pencil-beam doses of all scanning spots covering the PTV and a margin were calculated. The beam angle selection and spot intensity optimization problem was formulated to include three terms: a dose fidelity term to penalize the deviation of PTV and OAR doses from ideal dose distribution; an L1-norm sparsity term to reduce the number of active spots and improve delivery efficiency; a group sparsity term to control the number of active beams between 2 and 4. For the group sparsity term, convex L2,1-norm and nonconvex L2,1/2-norm were tested. For the dose fidelity term, both quadratic function and linearized equivalent uniform dose (LEUD) cost function were implemented. The optimization problem was solved using the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). The IMPT BOO method was tested on three head-and-neck patients and one skull base chordoma patient. The results were compared with IMPT plans created using column generation selected beams or manually selected beams. The L2,1-norm plan selected spatially aggregated beams, indicating potential degeneracy using this norm. L2,1/2-norm was able to select spatially separated beams and achieve smaller deviation from the ideal dose. In the L2,1/2-norm plans, the [mean dose, maximum dose] of OAR were reduced by an average of [2.38%, 4.24%] and[2.32%, 3.76%] of the prescription dose for the quadratic and LEUD cost function, respectively, compared with the IMPT plan using manual beam selection while maintaining the same PTV coverage. The L2,1/2 group sparsity plans were dosimetrically superior to the column generation plans as well. Besides beam orientation selection, spot sparsification was observed. Generally, with the quadratic cost function, 30%~60% spots in the selected beams remained active. With the LEUD cost function, the percentages of active spots were in the range of 35%~85%.The BOO-IMPT run time was approximately 20 min. This work shows the first IMPT approach integrating noncoplanar BOO and scanning-spot optimization in a single mathematical framework. This method is computationally efficient, dosimetrically superior and produces delivery-friendly IMPT plans. © 2018 American Association of Physicists in Medicine.

Experimental and Theoretical Results in Output-Trajectory Redesign for Flexible Structures

NASA Technical Reports Server (NTRS)

Dewey, J. S.; Devasia, Santosh

1996-01-01

In this paper we study the optimal redesign of output trajectory for linear invertible systems. This is particularly important for tracking control of flexible structures because the input-state trajectories that achieve the required output may cause excessive vibrations in the structure. A trade-off is then required between tracking and vibrations reduction. We pose and solve this problem as the minimization of a quadratic cost function. The theory is developed and applied to the output tracking of a flexible structure and experimental results are presented.

Using block pulse functions for seismic vibration semi-active control of structures with MR dampers

NASA Astrophysics Data System (ADS)

Rahimi Gendeshmin, Saeed; Davarnia, Daniel

2018-03-01

This article applied the idea of block pulse functions in the semi-active control of structures. The BP functions give effective tools to approximate complex problems. The applied control algorithm has a major effect on the performance of the controlled system and the requirements of the control devices. In control problems, it is important to devise an accurate analytical technique with less computational cost. It is proved that the BP functions are fundamental tools in approximation problems which have been applied in disparate areas in last decades. This study focuses on the employment of BP functions in control algorithm concerning reduction the computational cost. Magneto-rheological (MR) dampers are one of the well-known semi-active tools that can be used to control the response of civil Structures during earthquake. For validation purposes, numerical simulations of a 5-story shear building frame with MR dampers are presented. The results of suggested method were compared with results obtained by controlling the frame by the optimal control method based on linear quadratic regulator theory. It can be seen from simulation results that the suggested method can be helpful in reducing seismic structural responses. Besides, this method has acceptable accuracy and is in agreement with optimal control method with less computational costs.

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

NASA Astrophysics Data System (ADS)

Andries, Jesse

2010-11-01

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

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

NASA Astrophysics Data System (ADS)

Xu, Jiuping; Li, Jun

2002-09-01

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

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

NASA Astrophysics Data System (ADS)

Adhikari, Sam

2007-11-01

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

A neural network approach to job-shop scheduling.

PubMed

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

1991-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

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

ERIC Educational Resources Information Center

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

2015-01-01

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

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

ERIC Educational Resources Information Center

Dinç, Emre

2017-01-01

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

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

PubMed Central

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

2014-01-01

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

Low-rank separated representation surrogates of high-dimensional stochastic functions: Application in Bayesian inference

NASA Astrophysics Data System (ADS)

Validi, AbdoulAhad

2014-03-01

This study introduces a non-intrusive approach in the context of low-rank separated representation to construct a surrogate of high-dimensional stochastic functions, e.g., PDEs/ODEs, in order to decrease the computational cost of Markov Chain Monte Carlo simulations in Bayesian inference. The surrogate model is constructed via a regularized alternative least-square regression with Tikhonov regularization using a roughening matrix computing the gradient of the solution, in conjunction with a perturbation-based error indicator to detect optimal model complexities. The model approximates a vector of a continuous solution at discrete values of a physical variable. The required number of random realizations to achieve a successful approximation linearly depends on the function dimensionality. The computational cost of the model construction is quadratic in the number of random inputs, which potentially tackles the curse of dimensionality in high-dimensional stochastic functions. Furthermore, this vector-valued separated representation-based model, in comparison to the available scalar-valued case, leads to a significant reduction in the cost of approximation by an order of magnitude equal to the vector size. The performance of the method is studied through its application to three numerical examples including a 41-dimensional elliptic PDE and a 21-dimensional cavity flow.

Kullback-Leibler Divergence-Based Differential Evolution Markov Chain Filter for Global Localization of Mobile Robots.

PubMed

Martín, Fernando; Moreno, Luis; Garrido, Santiago; Blanco, Dolores

2015-09-16

One of the most important skills desired for a mobile robot is the ability to obtain its own location even in challenging environments. The information provided by the sensing system is used here to solve the global localization problem. In our previous work, we designed different algorithms founded on evolutionary strategies in order to solve the aforementioned task. The latest developments are presented in this paper. The engine of the localization module is a combination of the Markov chain Monte Carlo sampling technique and the Differential Evolution method, which results in a particle filter based on the minimization of a fitness function. The robot's pose is estimated from a set of possible locations weighted by a cost value. The measurements of the perceptive sensors are used together with the predicted ones in a known map to define a cost function to optimize. Although most localization methods rely on quadratic fitness functions, the sensed information is processed asymmetrically in this filter. The Kullback-Leibler divergence is the basis of a cost function that makes it possible to deal with different types of occlusions. The algorithm performance has been checked in a real map. The results are excellent in environments with dynamic and unmodeled obstacles, a fact that causes occlusions in the sensing area.

Kullback-Leibler Divergence-Based Differential Evolution Markov Chain Filter for Global Localization of Mobile Robots

PubMed Central

Martín, Fernando; Moreno, Luis; Garrido, Santiago; Blanco, Dolores

2015-01-01

One of the most important skills desired for a mobile robot is the ability to obtain its own location even in challenging environments. The information provided by the sensing system is used here to solve the global localization problem. In our previous work, we designed different algorithms founded on evolutionary strategies in order to solve the aforementioned task. The latest developments are presented in this paper. The engine of the localization module is a combination of the Markov chain Monte Carlo sampling technique and the Differential Evolution method, which results in a particle filter based on the minimization of a fitness function. The robot’s pose is estimated from a set of possible locations weighted by a cost value. The measurements of the perceptive sensors are used together with the predicted ones in a known map to define a cost function to optimize. Although most localization methods rely on quadratic fitness functions, the sensed information is processed asymmetrically in this filter. The Kullback-Leibler divergence is the basis of a cost function that makes it possible to deal with different types of occlusions. The algorithm performance has been checked in a real map. The results are excellent in environments with dynamic and unmodeled obstacles, a fact that causes occlusions in the sensing area. PMID:26389914

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

PubMed

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

2014-03-01

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

An optimized inverse modelling method for determining the location and strength of a point source releasing airborne material in urban environment

NASA Astrophysics Data System (ADS)

Efthimiou, George C.; Kovalets, Ivan V.; Venetsanos, Alexandros; Andronopoulos, Spyros; Argyropoulos, Christos D.; Kakosimos, Konstantinos

2017-12-01

An improved inverse modelling method to estimate the location and the emission rate of an unknown point stationary source of passive atmospheric pollutant in a complex urban geometry is incorporated in the Computational Fluid Dynamics code ADREA-HF and presented in this paper. The key improvement in relation to the previous version of the method lies in a two-step segregated approach. At first only the source coordinates are analysed using a correlation function of measured and calculated concentrations. In the second step the source rate is identified by minimizing a quadratic cost function. The validation of the new algorithm is performed by simulating the MUST wind tunnel experiment. A grid-independent flow field solution is firstly attained by applying successive refinements of the computational mesh and the final wind flow is validated against the measurements quantitatively and qualitatively. The old and new versions of the source term estimation method are tested on a coarse and a fine mesh. The new method appeared to be more robust, giving satisfactory estimations of source location and emission rate on both grids. The performance of the old version of the method varied between failure and success and appeared to be sensitive to the selection of model error magnitude that needs to be inserted in its quadratic cost function. The performance of the method depends also on the number and the placement of sensors constituting the measurement network. Of significant interest for the practical application of the method in urban settings is the number of concentration sensors required to obtain a ;satisfactory; determination of the source. The probability of obtaining a satisfactory solution - according to specified criteria -by the new method has been assessed as function of the number of sensors that constitute the measurement network.

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

PubMed

Liu, Xin; Shu, Xuewen

2017-08-20

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

An application of nonlinear programming to the design of regulators of a linear-quadratic formulation

NASA Technical Reports Server (NTRS)

Fleming, P.

1983-01-01

A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a nonlinear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer. One concerns helicopter longitudinal dynamics and the other the flight dynamics of an aerodynamically unstable aircraft.

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

NASA Astrophysics Data System (ADS)

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

2001-07-01

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

Exploring Quadratic Functions with Logger "Pro"

ERIC Educational Resources Information Center

Pope, Derek

2018-01-01

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

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

PubMed

Li, Shuai; Li, Yangming; Wang, Zheng

2013-03-01

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

Characterization of a Quadratic Function in Rn

ERIC Educational Resources Information Center

Xu, Conway

2010-01-01

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

Minitrack tracking function description, volume 2

NASA Technical Reports Server (NTRS)

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

1973-01-01

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

Fixed order dynamic compensation for multivariable linear systems

NASA Technical Reports Server (NTRS)

Kramer, F. S.; Calise, A. J.

1986-01-01

This paper considers the design of fixed order dynamic compensators for multivariable time invariant linear systems, minimizing a linear quadratic performance cost functional. Attention is given to robustness issues in terms of multivariable frequency domain specifications. An output feedback formulation is adopted by suitably augmenting the system description to include the compensator states. Either a controller or observer canonical form is imposed on the compensator description to reduce the number of free parameters to its minimal number. The internal structure of the compensator is prespecified by assigning a set of ascending feedback invariant indices, thus forming a Brunovsky structure for the nominal compensator.

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

USGS Publications Warehouse

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

1987-01-01

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

Topology Trivialization and Large Deviations for the Minimum in the Simplest Random Optimization

NASA Astrophysics Data System (ADS)

Fyodorov, Yan V.; Le Doussal, Pierre

2014-01-01

Finding the global minimum of a cost function given by the sum of a quadratic and a linear form in N real variables over (N-1)-dimensional sphere is one of the simplest, yet paradigmatic problems in Optimization Theory known as the "trust region subproblem" or "constraint least square problem". When both terms in the cost function are random this amounts to studying the ground state energy of the simplest spherical spin glass in a random magnetic field. We first identify and study two distinct large-N scaling regimes in which the linear term (magnetic field) leads to a gradual topology trivialization, i.e. reduction in the total number {N}_{tot} of critical (stationary) points in the cost function landscape. In the first regime {N}_{tot} remains of the order N and the cost function (energy) has generically two almost degenerate minima with the Tracy-Widom (TW) statistics. In the second regime the number of critical points is of the order of unity with a finite probability for a single minimum. In that case the mean total number of extrema (minima and maxima) of the cost function is given by the Laplace transform of the TW density, and the distribution of the global minimum energy is expected to take a universal scaling form generalizing the TW law. Though the full form of that distribution is not yet known to us, one of its far tails can be inferred from the large deviation theory for the global minimum. In the rest of the paper we show how to use the replica method to obtain the probability density of the minimum energy in the large-deviation approximation by finding both the rate function and the leading pre-exponential factor.

Understanding squeezing of quantum states with the Wigner function

NASA Technical Reports Server (NTRS)

Royer, Antoine

1994-01-01

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

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

PubMed

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

2007-09-01

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

On a stochastic control method for weakly coupled linear systems. M.S. Thesis

NASA Technical Reports Server (NTRS)

Kwong, R. H.

1972-01-01

The stochastic control of two weakly coupled linear systems with different controllers is considered. Each controller only makes measurements about his own system; no information about the other system is assumed to be available. Based on the noisy measurements, the controllers are to generate independently suitable control policies which minimize a quadratic cost functional. To account for the effects of weak coupling directly, an approximate model, which involves replacing the influence of one system on the other by a white noise process is proposed. Simple suboptimal control problem for calculating the covariances of these noises is solved using the matrix minimum principle. The overall system performance based on this scheme is analyzed as a function of the degree of intersystem coupling.

Approximate analytical relationships for linear optimal aeroelastic flight control laws

NASA Astrophysics Data System (ADS)

Kassem, Ayman Hamdy

1998-09-01

This dissertation introduces new methods to uncover functional relationships between design parameters of a contemporary control design technique and the resulting closed-loop properties. Three new methods are developed for generating such relationships through analytical expressions: the Direct Eigen-Based Technique, the Order of Magnitude Technique, and the Cost Function Imbedding Technique. Efforts concentrated on the linear-quadratic state-feedback control-design technique applied to an aeroelastic flight control task. For this specific application, simple and accurate analytical expressions for the closed-loop eigenvalues and zeros in terms of basic parameters such as stability and control derivatives, structural vibration damping and natural frequency, and cost function weights are generated. These expressions explicitly indicate how the weights augment the short period and aeroelastic modes, as well as the closed-loop zeros, and by what physical mechanism. The analytical expressions are used to address topics such as damping, nonminimum phase behavior, stability, and performance with robustness considerations, and design modifications. This type of knowledge is invaluable to the flight control designer and would be more difficult to formulate when obtained from numerical-based sensitivity analysis.

Analog "neuronal" networks in early vision.

PubMed Central

Koch, C; Marroquin, J; Yuille, A

1986-01-01

Many problems in early vision can be formulated in terms of minimizing a cost function. Examples are shape from shading, edge detection, motion analysis, structure from motion, and surface interpolation. As shown by Poggio and Koch [Poggio, T. & Koch, C. (1985) Proc. R. Soc. London, Ser. B 226, 303-323], quadratic variational problems, an important subset of early vision tasks, can be "solved" by linear, analog electrical, or chemical networks. However, in the presence of discontinuities, the cost function is nonquadratic, raising the question of designing efficient algorithms for computing the optimal solution. Recently, Hopfield and Tank [Hopfield, J. J. & Tank, D. W. (1985) Biol. Cybern. 52, 141-152] have shown that networks of nonlinear analog "neurons" can be effective in computing the solution of optimization problems. We show how these networks can be generalized to solve the nonconvex energy functionals of early vision. We illustrate this approach by implementing a specific analog network, solving the problem of reconstructing a smooth surface from sparse data while preserving its discontinuities. These results suggest a novel computational strategy for solving early vision problems in both biological and real-time artificial vision systems. PMID:3459172

Calculus Students' Understanding of the Vertex of the Quadratic Function in Relation to the Concept of Derivative

ERIC Educational Resources Information Center

Burns-Childers, Annie; Vidakovic, Draga

2018-01-01

The purpose of this study was to gain insight into 30, first year calculus students' understanding of the relationship between the concept of vertex of a quadratic function and the concept of the derivative. APOS (action-process-object-schema) theory was applied as a guiding framework of analysis on student written work, think-aloud and follow up…

Exploring quantum computing application to satellite data assimilation

NASA Astrophysics Data System (ADS)

Cheung, S.; Zhang, S. Q.

2015-12-01

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

Interaction phenomenon to dimensionally reduced p-gBKP equation

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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

NASA Astrophysics Data System (ADS)

Yu, Yong; Wang, Jun

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

A bivariate rational interpolation with a bi-quadratic denominator

NASA Astrophysics Data System (ADS)

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

2006-10-01

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

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

PubMed

Ginzburg, D; Mann, A

2014-03-10

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

Bottom friction optimization for a better barotropic tide modelling

NASA Astrophysics Data System (ADS)

Boutet, Martial; Lathuilière, Cyril; Son Hoang, Hong; Baraille, Rémy

2015-04-01

At a regional scale, barotropic tides are the dominant source of variability of currents and water heights. A precise representation of these processes is essential because of their great impacts on human activities (submersion risks, marine renewable energies, ...). Identified sources of error for tide modelling at a regional scale are the followings: bathymetry, boundary forcing and dissipation due to bottom friction. Nevertheless, bathymetric databases are nowadays known with a good accuracy, especially over shelves, and global tide models performances are better than ever. The most promising improvement is thus the bottom friction representation. The method used to estimate bottom friction is the simultaneous perturbation stochastic approximation (SPSA) which consists in the approximation of the gradient based on a fixed number of cost function measurements, regardless of the dimension of the vector to be estimated. Indeed, each cost function measurement is obtained by randomly perturbing every component of the parameter vector. An important feature of SPSA is its relative ease of implementation. In particular, the method does not require the development of tangent linear and adjoint version of the circulation model. Experiments are carried out to estimate bottom friction with the HYbrid Coordinate Ocean Model (HYCOM) in barotropic mode (one isopycnal layer). The study area is the Northeastern Atlantic margin which is characterized by strong currents and an intense dissipation. Bottom friction is parameterized with a quadratic term and friction coefficient is computed with the water height and the bottom roughness. The latter parameter is the one to be estimated. Assimilated data are the available tide gauge observations. First, the bottom roughness is estimated taking into account bottom sediment natures and bathymetric ranges. Then, it is estimated with geographical degrees of freedom. Finally, the impact of the estimation of a mixed quadratic/linear friction is evaluated.

Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows

PubMed Central

Wang, Di; Kleinberg, Robert D.

2009-01-01

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

Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows.

PubMed

Wang, Di; Kleinberg, Robert D

2009-11-28

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

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

NASA Astrophysics Data System (ADS)

Landsman, Zinoviy

2008-10-01

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

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.

A systematic way for the cost reduction of density fitting methods

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

Kállay, Mihály, E-mail: kallay@mail.bme.hu

2014-12-28

We present a simple approach for the reduction of the size of auxiliary basis sets used in methods exploiting the density fitting (resolution of identity) approximation for electron repulsion integrals. Starting out of the singular value decomposition of three-center two-electron integrals, new auxiliary functions are constructed as linear combinations of the original fitting functions. The new functions, which we term natural auxiliary functions (NAFs), are analogous to the natural orbitals widely used for the cost reduction of correlation methods. The use of the NAF basis enables the systematic truncation of the fitting basis, and thereby potentially the reduction of themore » computational expenses of the methods, though the scaling with the system size is not altered. The performance of the new approach has been tested for several quantum chemical methods. It is demonstrated that the most pronounced gain in computational efficiency can be expected for iterative models which scale quadratically with the size of the fitting basis set, such as the direct random phase approximation. The approach also has the promise of accelerating local correlation methods, for which the processing of three-center Coulomb integrals is a bottleneck.« less

Active distribution network planning considering linearized system loss

NASA Astrophysics Data System (ADS)

Li, Xiao; Wang, Mingqiang; Xu, Hao

2018-02-01

In this paper, various distribution network planning techniques with DGs are reviewed, and a new distribution network planning method is proposed. It assumes that the location of DGs and the topology of the network are fixed. The proposed model optimizes the capacities of DG and the optimal distribution line capacity simultaneously by a cost/benefit analysis and the benefit is quantified by the reduction of the expected interruption cost. Besides, the network loss is explicitly analyzed in the paper. For simplicity, the network loss is appropriately simplified as a quadratic function of difference of voltage phase angle. Then it is further piecewise linearized. In this paper, a piecewise linearization technique with different segment lengths is proposed. To validate its effectiveness and superiority, the proposed distribution network planning model with elaborate linearization technique is tested on the IEEE 33-bus distribution network system.

Optimal regulation in systems with stochastic time sampling

NASA Technical Reports Server (NTRS)

Montgomery, R. C.; Lee, P. S.

1980-01-01

An optimal control theory that accounts for stochastic variable time sampling in a distributed microprocessor based flight control system is presented. The theory is developed by using a linear process model for the airplane dynamics and the information distribution process is modeled as a variable time increment process where, at the time that information is supplied to the control effectors, the control effectors know the time of the next information update only in a stochastic sense. An optimal control problem is formulated and solved for the control law that minimizes the expected value of a quadratic cost function. The optimal cost obtained with a variable time increment Markov information update process where the control effectors know only the past information update intervals and the Markov transition mechanism is almost identical to that obtained with a known and uniform information update interval.

Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

A New Control Paradigm for Stochastic Differential Equations

NASA Astrophysics Data System (ADS)

Schmid, Matthias J. A.

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

Optimal orbit transfer suitable for large flexible structures

NASA Technical Reports Server (NTRS)

Chatterjee, Alok K.

1989-01-01

The problem of continuous low-thrust planar orbit transfer of large flexible structures is formulated as an optimal control problem with terminal state constraints. The dynamics of the spacecraft motion are treated as a point-mass central force field problem; the thrust-acceleration magnitude is treated as an additional state variable; and the rate of change of thrust-acceleration is treated as a control variable. To ensure smooth transfer, essential for flexible structures, an additional quadratic term is appended to the time cost functional. This term penalizes any abrupt change in acceleration. Numerical results are presented for the special case of a planar transfer.

Neuro-evolutionary computing paradigm for Painlevé equation-II in nonlinear optics

NASA Astrophysics Data System (ADS)

Ahmad, Iftikhar; Ahmad, Sufyan; Awais, Muhammad; Ul Islam Ahmad, Siraj; Asif Zahoor Raja, Muhammad

2018-05-01

The aim of this study is to investigate the numerical treatment of the Painlevé equation-II arising in physical models of nonlinear optics through artificial intelligence procedures by incorporating a single layer structure of neural networks optimized with genetic algorithms, sequential quadratic programming and active set techniques. We constructed a mathematical model for the nonlinear Painlevé equation-II with the help of networks by defining an error-based cost function in mean square sense. The performance of the proposed technique is validated through statistical analyses by means of the one-way ANOVA test conducted on a dataset generated by a large number of independent runs.

Development of a probabilistic analysis methodology for structural reliability estimation

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

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

NASA Technical Reports Server (NTRS)

Canavos, G. C.

1974-01-01

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

The effects of deregulation on rural electric distribution cooperatives: An empirical analysis

NASA Astrophysics Data System (ADS)

Greer, Monica Lynne

In 1996, the Federal Energy Regulatory Commission ("FERC") issued Orders 888 and 889, which were designed to promote competition in wholesale markets for electricity. While these Orders were predominantly meant to apply to vertically integrated investor-owned utilities ("IOUs"), FERC recently issued a Notice of Proposed Rulemaking that indicates its intent to make all transmission-owning entities, including those of cooperatively-owned utilities and the federal power administrations subject to FERC jurisdiction. Cooperatively owned utilities ("coops"), the focus of this paper, are organized as either generation and transmission ("G&T") or distribution only. And, although there are typically long-term contracts between the G&T and the distribution coops (thus rendering them quasi-vertically-integrated), they are very different from their investor-owned counterparts. It is because of these differences that the economic viability of these entities is being questioned in a deregulated environment. This dissertation examines the ability of coops to continue operating in their present form in a restructured electricity market. More specifically, using 1996 data for 831 distribution coops I estimate both quadratic and translogarithmic cost specifications so as to ascertain whether these firms are operating in such a fashion as to minimize costs. I find evidence that they are not. When delivered power is modeled as a single-output translogarithmic cost equation, I find that the majority of firms in the sample were operating in the increasing returns to scale portion of the average cost curve in 1996. This result reveals that coops delivered far less electricity to all customer classes than was necessary to attain the minimum efficient scale. And, upon estimating a multiple-output quadratic cost function, I find that there are ray economies, product specific returns to scale, and economies of scope in the distribution of electricity to the various customer classes that are not being captured. This occurs because each coop is too small in terms of the quantity of electricity distributed. As a result, horizontal mergers between these firms (especially contiguous ones) could yield substantial cost savings and help to ensure their survival in a deregulated market.

Quantum superintegrable system with a novel chain structure of quadratic algebras

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Two Car-Buying Strategies: An Old Problem Revisited with a New Analysis.

ERIC Educational Resources Information Center

Sen, Tapan; And Others

1996-01-01

Demonstrates the application of spreadsheet analysis in solving equations beyond quadratics. Considers the costs of interest, gasoline, and maintenance in deciding how long it pays to keep a car. (MKR)

Nonlinear Associations between Plasma Cholesterol Levels and Neuropsychological Function

PubMed Central

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

2016-01-01

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

Optimally stopped variational quantum algorithms

NASA Astrophysics Data System (ADS)

Vinci, Walter; Shabani, Alireza

2018-04-01

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

Stochastic sampling of quadrature grids for the evaluation of vibrational expectation values

NASA Astrophysics Data System (ADS)

López Ríos, Pablo; Monserrat, Bartomeu; Needs, Richard J.

2018-02-01

The thermal lines method for the evaluation of vibrational expectation values of electronic observables [B. Monserrat, Phys. Rev. B 93, 014302 (2016), 10.1103/PhysRevB.93.014302] was recently proposed as a physically motivated approximation offering balance between the accuracy of direct Monte Carlo integration and the low computational cost of using local quadratic approximations. In this paper we reformulate thermal lines as a stochastic implementation of quadrature-grid integration, analyze the analytical form of its bias, and extend the method to multiple-point quadrature grids applicable to any factorizable harmonic or anharmonic nuclear wave function. The bias incurred by thermal lines is found to depend on the local form of the expectation value, and we demonstrate that the use of finer quadrature grids along selected modes can eliminate this bias, while still offering an ˜30 % lower computational cost than direct Monte Carlo integration in our tests.

Swarm based mean-variance mapping optimization (MVMOS) for solving economic dispatch

NASA Astrophysics Data System (ADS)

Khoa, T. H.; Vasant, P. M.; Singh, M. S. Balbir; Dieu, V. N.

2014-10-01

The economic dispatch (ED) is an essential optimization task in the power generation system. It is defined as the process of allocating the real power output of generation units to meet required load demand so as their total operating cost is minimized while satisfying all physical and operational constraints. This paper introduces a novel optimization which named as Swarm based Mean-variance mapping optimization (MVMOS). The technique is the extension of the original single particle mean-variance mapping optimization (MVMO). Its features make it potentially attractive algorithm for solving optimization problems. The proposed method is implemented for three test power systems, including 3, 13 and 20 thermal generation units with quadratic cost function and the obtained results are compared with many other methods available in the literature. Test results have indicated that the proposed method can efficiently implement for solving economic dispatch.

Optimized Quasi-Interpolators for Image Reconstruction.

PubMed

Sacht, Leonardo; Nehab, Diego

2015-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

An Alternative Method to the Classical Partial Fraction Decomposition

ERIC Educational Resources Information Center

Cherif, Chokri

2007-01-01

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

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

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

1999-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

What makes a reach movement effortful? Physical effort discounting supports common minimization principles in decision making and motor control

PubMed Central

Ulbrich, Philipp; Gail, Alexander

2017-01-01

When deciding between alternative options, a rational agent chooses on the basis of the desirability of each outcome, including associated costs. As different options typically result in different actions, the effort associated with each action is an essential cost parameter. How do humans discount physical effort when deciding between movements? We used an action-selection task to characterize how subjective effort depends on the parameters of arm transport movements and controlled for potential confounding factors such as delay discounting and performance. First, by repeatedly asking subjects to choose between 2 arm movements of different amplitudes or durations, performed against different levels of force, we identified parameter combinations that subjects experienced as identical in effort (isoeffort curves). Movements with a long duration were judged more effortful than short-duration movements against the same force, while movement amplitudes did not influence effort. Biomechanics of the movements also affected effort, as movements towards the body midline were preferred to movements away from it. Second, by introducing movement repetitions, we further determined that the cost function for choosing between effortful movements had a quadratic relationship with force, while choices were made on the basis of the logarithm of these costs. Our results show that effort-based action selection during reaching cannot easily be explained by metabolic costs. Instead, force-loaded reaches, a widely occurring natural behavior, imposed an effort cost for decision making similar to cost functions in motor control. Our results thereby support the idea that motor control and economic choice are governed by partly overlapping optimization principles. PMID:28586347

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

PubMed

Kobayashi, Seiji

2002-05-10

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

Digital robust control law synthesis using constrained optimization

NASA Technical Reports Server (NTRS)

Mukhopadhyay, Vivekananda

1989-01-01

Development of digital robust control laws for active control of high performance flexible aircraft and large space structures is a research area of significant practical importance. The flexible system is typically modeled by a large order state space system of equations in order to accurately represent the dynamics. The active control law must satisy multiple conflicting design requirements and maintain certain stability margins, yet should be simple enough to be implementable on an onboard digital computer. Described here is an application of a generic digital control law synthesis procedure for such a system, using optimal control theory and constrained optimization technique. A linear quadratic Gaussian type cost function is minimized by updating the free parameters of the digital control law, while trying to satisfy a set of constraints on the design loads, responses and stability margins. Analytical expressions for the gradients of the cost function and the constraints with respect to the control law design variables are used to facilitate rapid numerical convergence. These gradients can be used for sensitivity study and may be integrated into a simultaneous structure and control optimization scheme.

Retrospective Cost Adaptive Control with Concurrent Closed-Loop Identification

NASA Astrophysics Data System (ADS)

Sobolic, Frantisek M.

Retrospective cost adaptive control (RCAC) is a discrete-time direct adaptive control algorithm for stabilization, command following, and disturbance rejection. RCAC is known to work on systems given minimal modeling information which is the leading numerator coefficient and any nonminimum-phase (NMP) zeros of the plant transfer function. This information is normally needed a priori and is key in the development of the filter, also known as the target model, within the retrospective performance variable. A novel approach to alleviate the need for prior modeling of both the leading coefficient of the plant transfer function as well as any NMP zeros is developed. The extension to the RCAC algorithm is the use of concurrent optimization of both the target model and the controller coefficients. Concurrent optimization of the target model and controller coefficients is a quadratic optimization problem in the target model and controller coefficients separately. However, this optimization problem is not convex as a joint function of both variables, and therefore nonconvex optimization methods are needed. Finally, insights within RCAC that include intercalated injection between the controller numerator and the denominator, unveil the workings of RCAC fitting a specific closed-loop transfer function to the target model. We exploit this interpretation by investigating several closed-loop identification architectures in order to extract this information for use in the target model.

Advanced Energy Storage Management in Distribution Network

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

Liu, Guodong; Ceylan, Oguzhan; Xiao, Bailu

2016-01-01

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

On reliable control system designs. Ph.D. Thesis; [actuators

NASA Technical Reports Server (NTRS)

Birdwell, J. D.

1978-01-01

A mathematical model for use in the design of reliable multivariable control systems is discussed with special emphasis on actuator failures and necessary actuator redundancy levels. The model consists of a linear time invariant discrete time dynamical system. Configuration changes in the system dynamics are governed by a Markov chain that includes transition probabilities from one configuration state to another. The performance index is a standard quadratic cost functional, over an infinite time interval. The actual system configuration can be deduced with a one step delay. The calculation of the optimal control law requires the solution of a set of highly coupled Riccati-like matrix difference equations. Results can be used for off-line studies relating the open loop dynamics, required performance, actuator mean time to failure, and functional or identical actuator redundancy, with and without feedback gain reconfiguration strategies.

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

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

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

2016-06-15

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

Linear-quadratic-Gaussian synthesis with reduced parameter sensitivity

NASA Technical Reports Server (NTRS)

Lin, J. Y.; Mingori, D. L.

1992-01-01

We present a method for improving the tolerance of a conventional LQG controller to parameter errors in the plant model. The improvement is achieved by introducing additional terms reflecting the structure of the parameter errors into the LQR cost function, and also the process and measurement noise models. Adjusting the sizes of these additional terms permits a trade-off between robustness and nominal performance. Manipulation of some of the additional terms leads to high gain controllers while other terms lead to low gain controllers. Conditions are developed under which the high-gain approach asymptotically recovers the robustness of the corresponding full-state feedback design, and the low-gain approach makes the closed-loop poles asymptotically insensitive to parameter errors.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Nonlinear associations between plasma cholesterol levels and neuropsychological function.

PubMed

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

2016-11-01

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

Statistical distribution sampling

NASA Technical Reports Server (NTRS)

Johnson, E. S.

1975-01-01

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

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

PubMed

Zhang, Zhongheng; Ji, Xuqing

2016-10-13

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

A General Method for Solving Systems of Non-Linear Equations

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

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

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

Keller, Jaime

2008-09-17

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

Uniform sparse bounds for discrete quadratic phase Hilbert transforms

NASA Astrophysics Data System (ADS)

Kesler, Robert; Arias, Darío Mena

2017-09-01

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

Learning graph matching.

PubMed

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

2009-06-01

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

QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.

PubMed

Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

2014-01-01

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

Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother

NASA Astrophysics Data System (ADS)

Fillion, Anthony; Bocquet, Marc; Gratton, Serge

2018-04-01

The analysis in nonlinear variational data assimilation is the solution of a non-quadratic minimization. Thus, the analysis efficiency relies on its ability to locate a global minimum of the cost function. If this minimization uses a Gauss-Newton (GN) method, it is critical for the starting point to be in the attraction basin of a global minimum. Otherwise the method may converge to a local extremum, which degrades the analysis. With chaotic models, the number of local extrema often increases with the temporal extent of the data assimilation window, making the former condition harder to satisfy. This is unfortunate because the assimilation performance also increases with this temporal extent. However, a quasi-static (QS) minimization may overcome these local extrema. It accomplishes this by gradually injecting the observations in the cost function. This method was introduced by Pires et al. (1996) in a 4D-Var context. We generalize this approach to four-dimensional strong-constraint nonlinear ensemble variational (EnVar) methods, which are based on both a nonlinear variational analysis and the propagation of dynamical error statistics via an ensemble. This forces one to consider the cost function minimizations in the broader context of cycled data assimilation algorithms. We adapt this QS approach to the iterative ensemble Kalman smoother (IEnKS), an exemplar of nonlinear deterministic four-dimensional EnVar methods. Using low-order models, we quantify the positive impact of the QS approach on the IEnKS, especially for long data assimilation windows. We also examine the computational cost of QS implementations and suggest cheaper algorithms.

Optimum profit model considering production, quality and sale problem

NASA Astrophysics Data System (ADS)

Chen, Chung-Ho; Lu, Chih-Lun

2011-12-01

Chen and Liu ['Procurement Strategies in the Presence of the Spot Market-an Analytical Framework', Production Planning and Control, 18, 297-309] presented the optimum profit model between the producers and the purchasers for the supply chain system with a pure procurement policy. However, their model with a simple manufacturing cost did not consider the used cost of the customer. In this study, the modified Chen and Liu's model will be addressed for determining the optimum product and process parameters. The authors propose a modified Chen and Liu's model under the two-stage screening procedure. The surrogate variable having a high correlation with the measurable quality characteristic will be directly measured in the first stage. The measurable quality characteristic will be directly measured in the second stage when the product decision cannot be determined in the first stage. The used cost of the customer will be measured by adopting Taguchi's quadratic quality loss function. The optimum purchaser's order quantity, the producer's product price and the process quality level will be jointly determined by maximising the expected profit between them.

PSQP: Puzzle Solving by Quadratic Programming.

PubMed

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

2017-02-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

An exponential decay model for mediation.

PubMed

Fritz, Matthew S

2014-10-01

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

An Exponential Decay Model for Mediation

PubMed Central

Fritz, Matthew S.

2013-01-01

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

Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

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

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

2016-06-15

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

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

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

Meng, Ziyang; Yang, Tao; Li, Guoqi

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

On Volterra quadratic stochastic operators with continual state space

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

Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

2015-05-15

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

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

PubMed

Ricotta, Carlo; Szeidl, Laszlo

2006-11-01

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

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

DOE PAGES

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

2017-09-18

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Incentive schemes in development of socio-economic systems

NASA Astrophysics Data System (ADS)

Grachev, V. V.; Ivushkin, K. A.; Myshlyaev, L. P.

2018-05-01

The paper is devoted to the study of incentive schemes when developing socio-economic systems. The article analyzes the existing incentive schemes. It is established that the traditional incentive mechanisms do not fully take into account the specifics of the creation of each socio-economic system and, as a rule, are difficult to implement. The incentive schemes based on the full-scale simulation approach, which allow the most complete information from the existing projects of creation of socio-economic systems to be extracted, are proposed. The statement of the problem is given, the method and algorithm of the full-scale simulation study of the efficiency of incentive functions is developed. The results of the study are presented. It is shown that the use of quadratic and piecewise linear functions of incentive allows the time and costs for creating social and economic systems to be reduced by 10%-15%.

Combined control-structure optimization

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

Quadratic constrained mixed discrete optimization with an adiabatic quantum optimizer

NASA Astrophysics Data System (ADS)

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

2014-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Adaptive control of stochastic linear systems with unknown parameters. M.S. Thesis

NASA Technical Reports Server (NTRS)

Ku, R. T.

1972-01-01

The problem of optimal control of linear discrete-time stochastic dynamical system with unknown and, possibly, stochastically varying parameters is considered on the basis of noisy measurements. It is desired to minimize the expected value of a quadratic cost functional. Since the simultaneous estimation of the state and plant parameters is a nonlinear filtering problem, the extended Kalman filter algorithm is used. Several qualitative and asymptotic properties of the open loop feedback optimal control and the enforced separation scheme are discussed. Simulation results via Monte Carlo method show that, in terms of the performance measure, for stable systems the open loop feedback optimal control system is slightly better than the enforced separation scheme, while for unstable systems the latter scheme is far better.

Extensions to PIFCGT: Multirate output feedback and optimal disturbance suppression

NASA Technical Reports Server (NTRS)

Broussard, J. R.

1986-01-01

New control synthesis procedures for digital flight control systems were developed. The theoretical developments are the solution to the problem of optimal disturbance suppression in the presence of windshear. Control synthesis is accomplished using a linear quadratic cost function, the command generator tracker for trajectory following and the proportional-integral-filter control structure for practical implementation. Extensions are made to the optimal output feedback algorithm for computing feedback gains so that the multirate and optimal disturbance control designs are computed and compared for the advanced transport operating system (ATOPS). The performance of the designs is demonstrated by closed-loop poles, frequency domain multiinput sigma and eigenvalue plots and detailed nonlinear 6-DOF aircraft simulations in the terminal area in the presence of windshear.

A quantum heuristic algorithm for the traveling salesman problem

NASA Astrophysics Data System (ADS)

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

2012-12-01

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

The shadow price of CO2 emissions in China's iron and steel industry.

PubMed

Wang, Ke; Che, Linan; Ma, Chunbo; Wei, Yi-Ming

2017-11-15

As China becomes the world's largest energy consumer and CO 2 emitter, there has been a rapidly emerging literature on estimating China's abatement cost for CO 2 using a distance function approach. However, the existing studies have mostly focused on the cost estimates at macro levels (provinces or industries) with few examining firm-level abatement costs. No work has attempted to estimate the abatement cost of CO 2 emissions in the iron and steel industry. Although some have argued that the directional distance function (DDF) is more appropriate in the presence of bad output under regulation, the choice of directions is largely arbitrary. This study provides the most up-to-date estimate of the shadow price of CO 2 using a unique dataset of China's major iron and steel enterprises in 2014. The paper uses output quadratic DDF and investigates the impact of using different directional vectors representing different carbon mitigation strategies. The results show that the mean CO 2 shadow price of China's iron and steel enterprises is very sensitive to the choice of direction vectors. The average shadow prices of CO 2 are 407, 1226 and 6058Yuan/tonne respectively for the three different direction vectors. We also find substantial heterogeneity in the shadow prices of CO 2 emissions among China's major iron and steel enterprises. Larger, listed enterprises are found to be associated lower CO 2 shadow prices than smaller, unlisted enterprises. Copyright © 2017 Elsevier B.V. All rights reserved.

DE and NLP Based QPLS Algorithm

NASA Astrophysics Data System (ADS)

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

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

The GUP and quantum Raychaudhuri equation

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Quadratic grating apodized photon sieves for simultaneous multiplane microscopy

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Comparison of joint space versus task force load distribution optimization for a multiarm manipulator system

NASA Technical Reports Server (NTRS)

Soloway, Donald I.; Alberts, Thomas E.

1989-01-01

It is often proposed that the redundancy in choosing a force distribution for multiple arms grasping a single object should be handled by minimizing a quadratic performance index. The performance index may be formulated in terms of joint torques or in terms of the Cartesian space force/torque applied to the body by the grippers. The former seeks to minimize power consumption while the latter minimizes body stresses. Because the cost functions are related to each other by a joint angle dependent transformation on the weight matrix, it might be argued that either method tends to reduce power consumption, but clearly the joint space minimization is optimal. A comparison of these two options is presented with consideration given to computational cost and power consumption. Simulation results using a two arm robot system are presented to show the savings realized by employing the joint space optimization. These savings are offset by additional complexity, computation time and in some cases processor power consumption.

The marriage problem and the fate of bachelors

NASA Astrophysics Data System (ADS)

Nieuwenhuizen, Th. M.

In the marriage problem, a variant of the bi-parted matching problem, each member has a “wish-list” expressing his/her preference for all possible partners; this list consists of random, positive real numbers drawn from a certain distribution. One searches the lowest cost for the society, at the risk of breaking up pairs in the course of time. Minimization of a global cost function (Hamiltonian) is performed with statistical mechanics techniques at a finite fictitious temperature. The problem is generalized to include bachelors, needed in particular when the groups have different size, and polygamy. Exact solutions are found for the optimal solution ( T=0). The entropy is found to vanish quadratically in T. Also, other evidence is found that the replica symmetric solution is exact, implying at most a polynomial degeneracy of the optimal solution. Whether bachelors occur or not, depends not only on their intrinsic qualities, or lack thereof, but also on global aspects of the chance for pair formation in society.

LQ optimal and reaching law-based sliding modes for inventory management systems

NASA Astrophysics Data System (ADS)

Ignaciuk, Przemysław; Bartoszewicz, Andrzej

2012-01-01

In this article, the theory of discrete sliding-mode control is used to design new supply strategies for periodic-review inventory systems. In the considered systems, the stock used to fulfil an unknown, time-varying demand can be replenished from a single supply source or from multiple suppliers procuring orders with different delays. The proposed strategies guarantee that demand is always entirely satisfied from the on-hand stock (yielding the maximum service level), and the warehouse capacity is not exceeded (which eliminates the cost of emergency storage). In contrast to the classical, stochastic approaches, in this article, we focus on optimising the inventory system dynamics. The parameters of the first control strategy are selected by minimising a quadratic cost functional. Next, it is shown how the system dynamical performance can be improved by applying the concept of a reaching law with the appropriately adjusted reaching phase. The stable, nonoscillatory behaviour of the closed-loop system is demonstrated and the properties of the designed controllers are discussed and strictly proved.

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

NASA Astrophysics Data System (ADS)

Ohlson Timoudas, Thomas

2017-12-01

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

Elegant Ince-Gaussian beams in a quadratic-index medium

NASA Astrophysics Data System (ADS)

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

2011-09-01

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

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

A Site Density Functional Theory for Water: Application to Solvation of Amino Acid Side Chains.

PubMed

Liu, Yu; Zhao, Shuangliang; Wu, Jianzhong

2013-04-09

We report a site density functional theory (SDFT) based on the conventional atomistic models of water and the universality ansatz of the bridge functional. The excess Helmholtz energy functional is formulated in terms of a quadratic expansion with respect to the local density deviation from that of a uniform system and a universal functional for all higher-order terms approximated by that of a reference hard-sphere system. With the atomistic pair direct correlation functions of the uniform system calculated from MD simulation and an analytical expression for the bridge functional from the modified fundamental measure theory, the SDFT can be used to predict the structure and thermodynamic properties of water under inhomogeneous conditions with a computational cost negligible in comparison to that of brute-force simulations. The numerical performance of the SDFT has been demonstrated with the predictions of the solvation free energies of 15 molecular analogs of amino acid side chains in water represented by SPC/E, SPC, and TIP3P models. For theTIP3P model, a comparison of the theoretical predictions with MD simulation and experimental data shows agreement within 0.64 and 1.09 kcal/mol on average, respectively.

Quantum Quench of the Sachdev-Ye-Kitaev Model

NASA Astrophysics Data System (ADS)

Steinberg, Julia; Eberlein, Andreas; Sachdev, Subir

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

QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES

PubMed Central

RAND, ALEXANDER; GILLETTE, ANDREW; BAJAJ, CHANDRAJIT

2013-01-01

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

Evaluation of single and two-stage adaptive sampling designs for estimation of density and abundance of freshwater mussels in a large river

USGS Publications Warehouse

Smith, D.R.; Rogala, J.T.; Gray, B.R.; Zigler, S.J.; Newton, T.J.

2011-01-01

Reliable estimates of abundance are needed to assess consequences of proposed habitat restoration and enhancement projects on freshwater mussels in the Upper Mississippi River (UMR). Although there is general guidance on sampling techniques for population assessment of freshwater mussels, the actual performance of sampling designs can depend critically on the population density and spatial distribution at the project site. To evaluate various sampling designs, we simulated sampling of populations, which varied in density and degree of spatial clustering. Because of logistics and costs of large river sampling and spatial clustering of freshwater mussels, we focused on adaptive and non-adaptive versions of single and two-stage sampling. The candidate designs performed similarly in terms of precision (CV) and probability of species detection for fixed sample size. Both CV and species detection were determined largely by density, spatial distribution and sample size. However, designs did differ in the rate that occupied quadrats were encountered. Occupied units had a higher probability of selection using adaptive designs than conventional designs. We used two measures of cost: sample size (i.e. number of quadrats) and distance travelled between the quadrats. Adaptive and two-stage designs tended to reduce distance between sampling units, and thus performed better when distance travelled was considered. Based on the comparisons, we provide general recommendations on the sampling designs for the freshwater mussels in the UMR, and presumably other large rivers.

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

PubMed

Sutherland, John C

2014-09-07

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

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

PubMed

Frings, Christian; Wühr, Peter

2014-11-01

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

Intelligent, Robust Control of Deteriorated Turbofan Engines via Linear Parameter Varying Quadratic Lyapunov Function Design

NASA Technical Reports Server (NTRS)

Turso, James A.; Litt, Jonathan S.

2004-01-01

A method for accommodating engine deterioration via a scheduled Linear Parameter Varying Quadratic Lyapunov Function (LPVQLF)-Based controller is presented. The LPVQLF design methodology provides a means for developing unconditionally stable, robust control of Linear Parameter Varying (LPV) systems. The controller is scheduled on the Engine Deterioration Index, a function of estimated parameters that relate to engine health, and is computed using a multilayer feedforward neural network. Acceptable thrust response and tight control of exhaust gas temperature (EGT) is accomplished by adjusting the performance weights on these parameters for different levels of engine degradation. Nonlinear simulations demonstrate that the controller achieves specified performance objectives while being robust to engine deterioration as well as engine-to-engine variations.

Robust Control of Uncertain Systems via Dissipative LQG-Type Controllers

NASA Technical Reports Server (NTRS)

Joshi, Suresh M.

2000-01-01

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

Computation and analysis for a constrained entropy optimization problem in finance

NASA Astrophysics Data System (ADS)

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

2008-12-01

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

Development of Analysis Tools for Certification of Flight Control Laws

DTIC Science & Technology

2009-03-31

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

Data Assimilation on a Quantum Annealing Computer: Feasibility and Scalability

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

Constrained ℋ∞ control for low bandwidth active suspensions

NASA Astrophysics Data System (ADS)

Wasiwitono, Unggul; Sutantra, I. Nyoman

2017-08-01

Low Bandwidth Active Suspension (LBAS) is shown to be more competitive to High Bandwidth Active Suspension (HBAS) when energy and cost aspects are taken into account. In this paper, the constrained ℋ∞ control scheme is applied for LBAS system. The ℋ∞ performance is used to measure ride comfort while the concept of reachable set in a state-space ellipsoid defined by a quadratic storage function is used to capture the time domain constraint that representing the requirements for road holding, suspension deflection limitation and actuator saturation. Then, the control problem is derived in the framework of Linear Matrix Inequality (LMI) optimization. The simulation is conducted considering the road disturbance as a stationary random process. The achievable performance of LBAS is analyzed for different values of bandwidth and damping ratio.

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

NASA Astrophysics Data System (ADS)

Kawamoto, Shigeru; Takamoto, Masanori; Kobayashi, Yasuhiro

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

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

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1984-01-01

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

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

NASA Technical Reports Server (NTRS)

Ito, Kazufumi; Teglas, Russell

1987-01-01

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

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

DTIC Science & Technology

1987-01-01

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

Estimating economic value of agricultural water under changing conditions and the effects of spatial aggregation.

PubMed

Medellín-Azuara, Josué; Harou, Julien J; Howitt, Richard E

2010-11-01

Given the high proportion of water used for agriculture in certain regions, the economic value of agricultural water can be an important tool for water management and policy development. This value is quantified using economic demand curves for irrigation water. Such demand functions show the incremental contribution of water to agricultural production. Water demand curves are estimated using econometric or optimisation techniques. Calibrated agricultural optimisation models allow the derivation of demand curves using smaller datasets than econometric models. This paper introduces these subject areas then explores the effect of spatial aggregation (upscaling) on the valuation of water for irrigated agriculture. A case study from the Rio Grande-Rio Bravo Basin in North Mexico investigates differences in valuation at farm and regional aggregated levels under four scenarios: technological change, warm-dry climate change, changes in agricultural commodity prices, and water costs for agriculture. The scenarios consider changes due to external shocks or new policies. Positive mathematical programming (PMP), a calibrated optimisation method, is the deductive valuation method used. An exponential cost function is compared to the quadratic cost functions typically used in PMP. Results indicate that the economic value of water at the farm level and the regionally aggregated level are similar, but that the variability and distributional effects of each scenario are affected by aggregation. Moderately aggregated agricultural production models are effective at capturing average-farm adaptation to policy changes and external shocks. Farm-level models best reveal the distribution of scenario impacts. Copyright © 2009 Elsevier B.V. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Henriksson, Johan; Saue, Trond; Norman, Patrick

2008-01-01

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

Sharing Teaching Ideas.

ERIC Educational Resources Information Center

Touval, Ayana

1992-01-01

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

Constrained multiple indicator kriging using sequential quadratic programming

NASA Astrophysics Data System (ADS)

Soltani-Mohammadi, Saeed; Erhan Tercan, A.

2012-11-01

Multiple indicator kriging (MIK) is a nonparametric method used to estimate conditional cumulative distribution functions (CCDF). Indicator estimates produced by MIK may not satisfy the order relations of a valid CCDF which is ordered and bounded between 0 and 1. In this paper a new method has been presented that guarantees the order relations of the cumulative distribution functions estimated by multiple indicator kriging. The method is based on minimizing the sum of kriging variances for each cutoff under unbiasedness and order relations constraints and solving constrained indicator kriging system by sequential quadratic programming. A computer code is written in the Matlab environment to implement the developed algorithm and the method is applied to the thickness data.

High-Speed Numeric Function Generator Using Piecewise Quadratic Approximations

DTIC Science & Technology

2007-09-01

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

Factorization method of quadratic template

NASA Astrophysics Data System (ADS)

Kotyrba, Martin

2017-07-01

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

Linear parameter varying representations for nonlinear control design

NASA Astrophysics Data System (ADS)

Carter, Lance Huntington

Linear parameter varying (LPV) systems are investigated as a framework for gain-scheduled control design and optimal hybrid control. An LPV system is defined as a linear system whose dynamics depend upon an a priori unknown but measurable exogenous parameter. A gain-scheduled autopilot design is presented for a bank-to-turn (BTT) missile. The method is novel in that the gain-scheduled design does not involve linearizations about operating points. Instead, the missile dynamics are brought to LPV form via a state transformation. This idea is applied to the design of a coupled longitudinal/lateral BTT missile autopilot. The pitch and yaw/roll dynamics are separately transformed to LPV form, where the cross axis states are treated as "exogenous" parameters. These are actually endogenous variables, so such a plant is called "quasi-LPV." Once in quasi-LPV form, a family of robust controllers using mu synthesis is designed for both the pitch and yaw/roll channels, using angle-of-attack and roll rate as the scheduling variables. The closed-loop time response is simulated using the original nonlinear model and also using perturbed aerodynamic coefficients. Modeling and control of engine idle speed is investigated using LPV methods. It is shown how generalized discrete nonlinear systems may be transformed into quasi-LPV form. A discrete nonlinear engine model is developed and expressed in quasi-LPV form with engine speed as the scheduling variable. An example control design is presented using linear quadratic methods. Simulations are shown comparing the LPV based controller performance to that using PID control. LPV representations are also shown to provide a setting for hybrid systems. A hybrid system is characterized by control inputs consisting of both analog signals and discrete actions. A solution is derived for the optimal control of hybrid systems with generalized cost functions. This is shown to be computationally intensive, so a suboptimal strategy is proposed that neglects a subset of possible parameter trajectories. A computational algorithm is constructed for this suboptimal solution applied to a class of linear non-quadratic cost functions.

Effects of build parameters on linear wear loss in plastic part produced by fused deposition modeling

NASA Astrophysics Data System (ADS)

Mohamed, Omar Ahmed; Masood, Syed Hasan; Bhowmik, Jahar Lal

2017-07-01

Fused Deposition Modeling (FDM) is one of the prominent additive manufacturing technologies for producing polymer products. FDM is a complex additive manufacturing process that can be influenced by many process conditions. The industrial demands required from the FDM process are increasing with higher level product functionality and properties. The functionality and performance of FDM manufactured parts are greatly influenced by the combination of many various FDM process parameters. Designers and researchers always pay attention to study the effects of FDM process parameters on different product functionalities and properties such as mechanical strength, surface quality, dimensional accuracy, build time and material consumption. However, very limited studies have been carried out to investigate and optimize the effect of FDM build parameters on wear performance. This study focuses on the effect of different build parameters on micro-structural and wear performance of FDM specimens using definitive screening design based quadratic model. This would reduce the cost and effort of additive manufacturing engineer to have a systematic approachto make decision among the manufacturing parameters to achieve the desired product quality.

A topological proof of chaos for two nonlinear heterogeneous triopoly game models

NASA Astrophysics Data System (ADS)

Pireddu, Marina

2016-08-01

We rigorously prove the existence of chaotic dynamics for two nonlinear Cournot triopoly game models with heterogeneous players, for which in the existing literature the presence of complex phenomena and strange attractors has been shown via numerical simulations. In the first model that we analyze, costs are linear but the demand function is isoelastic, while, in the second model, the demand function is linear and production costs are quadratic. As concerns the decisional mechanisms adopted by the firms, in both models one firm adopts a myopic adjustment mechanism, considering the marginal profit of the last period; the second firm maximizes its own expected profit under the assumption that the competitors' production levels will not vary with respect to the previous period; the third firm acts adaptively, changing its output proportionally to the difference between its own output in the previous period and the naive expectation value. The topological method we employ in our analysis is the so-called "Stretching Along the Paths" technique, based on the Poincaré-Miranda Theorem and the properties of the cutting surfaces, which allows to prove the existence of a semi-conjugacy between the system under consideration and the Bernoulli shift, so that the former inherits from the latter several crucial chaotic features, among which a positive topological entropy.

A topological proof of chaos for two nonlinear heterogeneous triopoly game models.

PubMed

Pireddu, Marina

2016-08-01

We rigorously prove the existence of chaotic dynamics for two nonlinear Cournot triopoly game models with heterogeneous players, for which in the existing literature the presence of complex phenomena and strange attractors has been shown via numerical simulations. In the first model that we analyze, costs are linear but the demand function is isoelastic, while, in the second model, the demand function is linear and production costs are quadratic. As concerns the decisional mechanisms adopted by the firms, in both models one firm adopts a myopic adjustment mechanism, considering the marginal profit of the last period; the second firm maximizes its own expected profit under the assumption that the competitors' production levels will not vary with respect to the previous period; the third firm acts adaptively, changing its output proportionally to the difference between its own output in the previous period and the naive expectation value. The topological method we employ in our analysis is the so-called "Stretching Along the Paths" technique, based on the Poincaré-Miranda Theorem and the properties of the cutting surfaces, which allows to prove the existence of a semi-conjugacy between the system under consideration and the Bernoulli shift, so that the former inherits from the latter several crucial chaotic features, among which a positive topological entropy.

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

PubMed

Dinpajooh, Mohammadhasan; Matyushov, Dmitry V

2014-07-17

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

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

NASA Astrophysics Data System (ADS)

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

2015-11-01

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

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

PubMed

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

2013-01-01

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

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

PubMed Central

Wang, Xiao-Lin; Duan, Zuo-Liang

2013-01-01

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

Accelerating large scale Kohn-Sham density functional theory calculations with semi-local functionals and hybrid functionals

NASA Astrophysics Data System (ADS)

Lin, Lin

The computational cost of standard Kohn-Sham density functional theory (KSDFT) calculations scale cubically with respect to the system size, which limits its use in large scale applications. In recent years, we have developed an alternative procedure called the pole expansion and selected inversion (PEXSI) method. The PEXSI method solves KSDFT without solving any eigenvalue and eigenvector, and directly evaluates physical quantities including electron density, energy, atomic force, density of states, and local density of states. The overall algorithm scales as at most quadratically for all materials including insulators, semiconductors and the difficult metallic systems. The PEXSI method can be efficiently parallelized over 10,000 - 100,000 processors on high performance machines. The PEXSI method has been integrated into a number of community electronic structure software packages such as ATK, BigDFT, CP2K, DGDFT, FHI-aims and SIESTA, and has been used in a number of applications with 2D materials beyond 10,000 atoms. The PEXSI method works for LDA, GGA and meta-GGA functionals. The mathematical structure for hybrid functional KSDFT calculations is significantly different. I will also discuss recent progress on using adaptive compressed exchange method for accelerating hybrid functional calculations. DOE SciDAC Program, DOE CAMERA Program, LBNL LDRD, Sloan Fellowship.

Growth Points in Linking Representations of Function: A Research-Based Framework

ERIC Educational Resources Information Center

Ronda, Erlina

2015-01-01

This paper describes five growth points in linking representations of function developed from a study of secondary school learners. Framed within the cognitivist perspective and process-object conception of function, the growth points were identified and described based on linear and quadratic function tasks learners can do and their strategies…

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

PubMed Central

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

2010-01-01

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

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

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

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

2016-03-15

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

The identification of high potential archers based on fitness and motor ability variables: A Support Vector Machine approach.

PubMed

Taha, Zahari; Musa, Rabiu Muazu; P P Abdul Majeed, Anwar; Alim, Muhammad Muaz; Abdullah, Mohamad Razali

2018-02-01

Support Vector Machine (SVM) has been shown to be an effective learning algorithm for classification and prediction. However, the application of SVM for prediction and classification in specific sport has rarely been used to quantify/discriminate low and high-performance athletes. The present study classified and predicted high and low-potential archers from a set of fitness and motor ability variables trained on different SVMs kernel algorithms. 50 youth archers with the mean age and standard deviation of 17.0 ± 0.6 years drawn from various archery programmes completed a six arrows shooting score test. Standard fitness and ability measurements namely hand grip, vertical jump, standing broad jump, static balance, upper muscle strength and the core muscle strength were also recorded. Hierarchical agglomerative cluster analysis (HACA) was used to cluster the archers based on the performance variables tested. SVM models with linear, quadratic, cubic, fine RBF, medium RBF, as well as the coarse RBF kernel functions, were trained based on the measured performance variables. The HACA clustered the archers into high-potential archers (HPA) and low-potential archers (LPA), respectively. The linear, quadratic, cubic, as well as the medium RBF kernel functions models, demonstrated reasonably excellent classification accuracy of 97.5% and 2.5% error rate for the prediction of the HPA and the LPA. The findings of this investigation can be valuable to coaches and sports managers to recognise high potential athletes from a combination of the selected few measured fitness and motor ability performance variables examined which would consequently save cost, time and effort during talent identification programme. Copyright © 2017 Elsevier B.V. All rights reserved.

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

PubMed Central

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

2016-01-01

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

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

PubMed

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

2016-09-01

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

Information distribution in distributed microprocessor based flight control systems

NASA Technical Reports Server (NTRS)

Montgomery, R. C.; Lee, P. S.

1977-01-01

This paper presents an optimal control theory that accounts for variable time intervals in the information distribution to control effectors in a distributed microprocessor based flight control system. The theory is developed using a linear process model for the aircraft dynamics and the information distribution process is modeled as a variable time increment process where, at the time that information is supplied to the control effectors, the control effectors know the time of the next information update only in a stochastic sense. An optimal control problem is formulated and solved that provides the control law that minimizes the expected value of a quadratic cost function. An example is presented where the theory is applied to the control of the longitudinal motions of the F8-DFBW aircraft. Theoretical and simulation results indicate that, for the example problem, the optimal cost obtained using a variable time increment Markov information update process where the control effectors know only the past information update intervals and the Markov transition mechanism is almost identical to that obtained using a known uniform information update interval.

Stochastic resonance in a fractional oscillator driven by multiplicative quadratic noise

NASA Astrophysics Data System (ADS)

Ren, Ruibin; Luo, Maokang; Deng, Ke

2017-02-01

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

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

NASA Technical Reports Server (NTRS)

Cavalli, D.

1978-01-01

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

Optimal solution and optimality condition of the Hunter-Saxton equation

NASA Astrophysics Data System (ADS)

Shen, Chunyu

2018-02-01

This paper is devoted to the optimal distributed control problem governed by the Hunter-Saxton equation with constraints on the control. We first investigate the existence and uniqueness of weak solution for the controlled system with appropriate initial value and boundary conditions. In contrast with our previous research, the proof of solution mapping is local Lipschitz continuous, which is one big improvement. Second, based on the well-posedness result, we find a unique optimal control and optimal solution for the controlled system with the quadratic cost functional. Moreover, we establish the sufficient and necessary optimality condition of an optimal control by means of the optimal control theory, not limited to the necessary condition, which is another major novelty of this paper. We also discuss the optimality conditions corresponding to two physical meaningful distributed observation cases.

Suboptimal LQR-based spacecraft full motion control: Theory and experimentation

NASA Astrophysics Data System (ADS)

Guarnaccia, Leone; Bevilacqua, Riccardo; Pastorelli, Stefano P.

2016-05-01

This work introduces a real time suboptimal control algorithm for six-degree-of-freedom spacecraft maneuvering based on a State-Dependent-Algebraic-Riccati-Equation (SDARE) approach and real-time linearization of the equations of motion. The control strategy is sub-optimal since the gains of the linear quadratic regulator (LQR) are re-computed at each sample time. The cost function of the proposed controller has been compared with the one obtained via a general purpose optimal control software, showing, on average, an increase in control effort of approximately 15%, compensated by real-time implementability. Lastly, the paper presents experimental tests on a hardware-in-the-loop six-degree-of-freedom spacecraft simulator, designed for testing new guidance, navigation, and control algorithms for nano-satellites in a one-g laboratory environment. The tests show the real-time feasibility of the proposed approach.

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

NASA Technical Reports Server (NTRS)

Barnett, T. L. (Principal Investigator)

1981-01-01

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

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

NASA Astrophysics Data System (ADS)

Faribault, Alexandre; Tschirhart, Hugo; Muller, Nicolas

2016-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Quadratic integrand double-hybrid made spin-component-scaled

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

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

2016-03-28

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

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

NASA Technical Reports Server (NTRS)

Lehtinen, B.; Geyser, L. C.

1984-01-01

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

Quadrat Data for Fermilab Prairie Plant Survey

Science.gov Websites

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

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

PubMed

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

2010-12-01

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

Production and optimization of polyhydroxyalkanoates from non-edible Calophyllum inophyllum oil using Cupriavidus necator.

PubMed

Arumugam, A; Senthamizhan, S G; Ponnusami, V; Sudalai, S

2018-06-01

Polyhydroxyalkanoates (PHA) are biodegradable polymers found in the cellular masses of a wide range of bacterial species and the demand for PHA is steadily growing. In this work we have produced PHA from a low-cost substrate, Calophyllum inophyllum oil, using Cupriavidus necator. Effects of various process parameters such as Oil concentration, Nitrogen source and inoculum size on the production of PHA were studied using Response Surface Methodology. A quadratic equation was used in the model to fit the experimental data. It was found that the model could satisfactorily predict the PHA yield (R 2 =99.17%). Linear, quadratic and interaction terms used in the model were found to be statistically significant. Maximum PHA yield of 10.6gL -1 was obtained under the optimized conditions of oil concentration - 17.5%, inoculum concentration - 50mL/L and nitrogen content - 1.125gL -1 , respectively. The product obtained was characterized using FTIR and NMR to confirm that it was PHA. The results demonstrate that C. inophyllum oil, a non-edible oil, can be potentially used as a low-cost substrate for the production of PHA. Copyright © 2018 Elsevier B.V. All rights reserved.

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

Huang, Kuo -Ling; Mehrotra, Sanjay

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

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

Three Lessons on Parabolas--What, Where, Why

ERIC Educational Resources Information Center

Ceyanes, Ben; Lockwood, Pamela; Gill, Kristina

2014-01-01

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

Optimization of Cubic Polynomial Functions without Calculus

ERIC Educational Resources Information Center

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

2008-01-01

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

Circulant Matrices and Affine Equivalence of Monomial Rotation Symmetric Boolean Functions

DTIC Science & Technology

2015-01-01

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

Towards the automatization of the Foucault knife-edge quantitative test

NASA Astrophysics Data System (ADS)

Rodríguez, G.; Villa, J.; Martínez, G.; de la Rosa, I.; Ivanov, R.

2017-08-01

Given the increasing necessity of simple, economical and reliable methods and instruments for performing quality tests of optical surfaces such as mirrors and lenses, in the recent years we resumed the study of the long forgotten Foucault knife-edge test from the point of view of the physical optics, ultimately achieving a closed mathematical expression that directly relates the knife-edge position along the displacement paraxial axis with the observable irradiance pattern, which later allowed us to propose a quantitative methodology for estimating the wavefront error of an aspherical mirror with precision akin to interferometry. In this work, we present a further improved digital image processing algorithm in which the sigmoidal cost-function for calculating the transient slope-point of each associated intensity-illumination profile is replaced for a simplified version of it, thus making the whole process of estimating the wavefront gradient remarkably more stable and efficient, at the same time, the Fourier based algorithm employed for gradient integration has been replaced as well for a regularized quadratic cost-function that allows a considerably easier introduction of the region of interest (ROI) of the function, which solved by means of a linear gradient conjugate method largely increases the overall accuracy and efficiency of the algorithm. This revised approach of our methodology can be easily implemented and handled by most single-board microcontrollers in the market, hence enabling the implementation of a full-integrated automatized test apparatus, opening a realistic path for even the proposal of a stand-alone optical mirror analyzer prototype.

Pulmonary rehabilitation coupled with negative pressure ventilation decreases decline in lung function, hospitalizations, and medical cost in COPD

PubMed Central

Huang, Hung-Yu; Chou, Pai-Chien; Joa, Wen-Ching; Chen, Li-Fei; Sheng, Te-Fang; Lin, Horng-Chyuan; Yang, Lan-Yan; Pan, Yu-Bin; Chung, Fu-Tsai; Wang, Chun-Hua; Kuo, Han-Pin

2016-01-01

Abstract Pulmonary rehabilitation (PR) brings benefits to patients with chronic obstructive pulmonary disease (COPD). Negative pressure ventilation (NPV) increases ventilation and decreases hyperinflation as well as breathing work in COPD. We evaluated the long-term effects of a hospital-based PR program coupled with NPV support in patients with COPD on clinical outcomes. One hundred twenty-nine patients with COPD were followed up for more than 5 years, with the NPV group (n = 63) receiving the support of NPV (20–30 cm H2O delivery pressure for 60 min) and unsupervised home exercise program of 20 to 30 min daily walk, while the control group (n = 6) only received unsupervised home exercise program. Pulmonary function tests and 6 min walk tests (6MWT) were performed every 3 to 6 months. Emergency room (ER) visits and hospitalization with medical costs were recorded. A significant time-by-group interaction in the yearly decline of forced expiratory volume in 1 s in the control group analyzed by mixed-model repeated-measure analysis was found (P = 0.048). The 6MWT distance of the NPV group was significantly increased during the first 4 years, with the interaction of time and group (P = 0.003), the time alone (P = 0.014), and the quadratic time (P < 0.001) being significant between the 2 groups. ER exacerbations and hospitalizations decreased by 66% (P < 0.0001) and 54% (P < 0.0001) in the NPV group, respectively. Patients on PR program coupled with NPV had a significant reduction of annual medical costs (P = 0.022). Our hospital-based multidisciplinary PR coupled with NPV reduced yearly decline of lung function, exacerbations, and hospitalization rates, and improved walking distance and medical costs in patients with COPD during a 5-year observation PMID:27741132

Pulmonary rehabilitation coupled with negative pressure ventilation decreases decline in lung function, hospitalizations, and medical cost in COPD: A 5-year study.

PubMed

Huang, Hung-Yu; Chou, Pai-Chien; Joa, Wen-Ching; Chen, Li-Fei; Sheng, Te-Fang; Lin, Horng-Chyuan; Yang, Lan-Yan; Pan, Yu-Bin; Chung, Fu-Tsai; Wang, Chun-Hua; Kuo, Han-Pin

2016-10-01

Pulmonary rehabilitation (PR) brings benefits to patients with chronic obstructive pulmonary disease (COPD). Negative pressure ventilation (NPV) increases ventilation and decreases hyperinflation as well as breathing work in COPD. We evaluated the long-term effects of a hospital-based PR program coupled with NPV support in patients with COPD on clinical outcomes.One hundred twenty-nine patients with COPD were followed up for more than 5 years, with the NPV group (n = 63) receiving the support of NPV (20-30 cm H2O delivery pressure for 60 min) and unsupervised home exercise program of 20 to 30 min daily walk, while the control group (n = 6) only received unsupervised home exercise program. Pulmonary function tests and 6 min walk tests (6MWT) were performed every 3 to 6 months. Emergency room (ER) visits and hospitalization with medical costs were recorded.A significant time-by-group interaction in the yearly decline of forced expiratory volume in 1 s in the control group analyzed by mixed-model repeated-measure analysis was found (P = 0.048). The 6MWT distance of the NPV group was significantly increased during the first 4 years, with the interaction of time and group (P = 0.003), the time alone (P = 0.014), and the quadratic time (P < 0.001) being significant between the 2 groups. ER exacerbations and hospitalizations decreased by 66% (P < 0.0001) and 54% (P < 0.0001) in the NPV group, respectively. Patients on PR program coupled with NPV had a significant reduction of annual medical costs (P = 0.022).Our hospital-based multidisciplinary PR coupled with NPV reduced yearly decline of lung function, exacerbations, and hospitalization rates, and improved walking distance and medical costs in patients with COPD during a 5-year observation.

Application of Lagrangian blending functions for grid generation around airplane geometries

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

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

PubMed

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

2016-01-01

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

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

PubMed

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

2017-08-01

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

Quadratic electroabsorption studies of molecular motion in dye-doped polymers

NASA Astrophysics Data System (ADS)

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

1993-02-01

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

A Converse of a Result about the Floor Function by Hermite

ERIC Educational Resources Information Center

Mortici, Cristinel

2012-01-01

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

Quadratic semiparametric Von Mises calculus

PubMed Central

Robins, James; Li, Lingling; Tchetgen, Eric

2009-01-01

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

Applications of Lagrangian blending functions for grid generation around airplane geometries

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Slushy weightings for the optimal pilot model. [considering visual tracking task

NASA Technical Reports Server (NTRS)

Dillow, J. D.; Picha, D. G.; Anderson, R. O.

1975-01-01

A pilot model is described which accounts for the effect of motion cues in a well defined visual tracking task. The effect of visual and motion cues are accounted for in the model in two ways. First, the observation matrix in the pilot model is structured to account for the visual and motion inputs presented to the pilot. Secondly, the weightings in the quadratic cost function associated with the pilot model are modified to account for the pilot's perception of the variables he considers important in the task. Analytic results obtained using the pilot model are compared to experimental results and in general good agreement is demonstrated. The analytic model yields small improvements in tracking performance with the addition of motion cues for easily controlled task dynamics and large improvements in tracking performance with the addition of motion cues for difficult task dynamics.

Entanglement-assisted quantum feedback control

NASA Astrophysics Data System (ADS)

Yamamoto, Naoki; Mikami, Tomoaki

2017-07-01

The main advantage of quantum metrology relies on the effective use of entanglement, which indeed allows us to achieve strictly better estimation performance over the standard quantum limit. In this paper, we propose an analogous method utilizing entanglement for the purpose of feedback control. The system considered is a general linear dynamical quantum system, where the control goal can be systematically formulated as a linear quadratic Gaussian control problem based on the quantum Kalman filtering method; in this setting, an entangled input probe field is effectively used to reduce the estimation error and accordingly the control cost function. In particular, we show that, in the problem of cooling an opto-mechanical oscillator, the entanglement-assisted feedback control can lower the stationary occupation number of the oscillator below the limit attainable by the controller with a coherent probe field and furthermore beats the controller with an optimized squeezed probe field.

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

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.

2012-01-01

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

Feature to prototype transition in neural networks

NASA Astrophysics Data System (ADS)

Krotov, Dmitry; Hopfield, John

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

Multi-Party Privacy-Preserving Set Intersection with Quasi-Linear Complexity

NASA Astrophysics Data System (ADS)

Cheon, Jung Hee; Jarecki, Stanislaw; Seo, Jae Hong

Secure computation of the set intersection functionality allows n parties to find the intersection between their datasets without revealing anything else about them. An efficient protocol for such a task could have multiple potential applications in commerce, health care, and security. However, all currently known secure set intersection protocols for n>2 parties have computational costs that are quadratic in the (maximum) number of entries in the dataset contributed by each party, making secure computation of the set intersection only practical for small datasets. In this paper, we describe the first multi-party protocol for securely computing the set intersection functionality with both the communication and the computation costs that are quasi-linear in the size of the datasets. For a fixed security parameter, our protocols require O(n2k) bits of communication and Õ(n2k) group multiplications per player in the malicious adversary setting, where k is the size of each dataset. Our protocol follows the basic idea of the protocol proposed by Kissner and Song, but we gain efficiency by using different representations of the polynomials associated with users' datasets and careful employment of algorithms that interpolate or evaluate polynomials on multiple points more efficiently. Moreover, the proposed protocol is robust. This means that the protocol outputs the desired result even if some corrupted players leave during the execution of the protocol.

A topological proof of chaos for two nonlinear heterogeneous triopoly game models

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

Pireddu, Marina, E-mail: marina.pireddu@unimib.it

We rigorously prove the existence of chaotic dynamics for two nonlinear Cournot triopoly game models with heterogeneous players, for which in the existing literature the presence of complex phenomena and strange attractors has been shown via numerical simulations. In the first model that we analyze, costs are linear but the demand function is isoelastic, while, in the second model, the demand function is linear and production costs are quadratic. As concerns the decisional mechanisms adopted by the firms, in both models one firm adopts a myopic adjustment mechanism, considering the marginal profit of the last period; the second firm maximizesmore » its own expected profit under the assumption that the competitors' production levels will not vary with respect to the previous period; the third firm acts adaptively, changing its output proportionally to the difference between its own output in the previous period and the naive expectation value. The topological method we employ in our analysis is the so-called “Stretching Along the Paths” technique, based on the Poincaré-Miranda Theorem and the properties of the cutting surfaces, which allows to prove the existence of a semi-conjugacy between the system under consideration and the Bernoulli shift, so that the former inherits from the latter several crucial chaotic features, among which a positive topological entropy.« less

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

PubMed

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

2013-10-01

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

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

NASA Astrophysics Data System (ADS)

Şen, R.; Aygün, S.

2017-02-01

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

Discrete Element Method Simulation of a Boulder Extraction From an Asteroid

NASA Technical Reports Server (NTRS)

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

2014-01-01

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

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

PubMed

Howard, Robert W

2014-09-01

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

Optimization of actuator arrays for aircraft interior noise control

NASA Technical Reports Server (NTRS)

Cabell, R. H.; Lester, H. C.; Mathur, G. P.; Tran, B. N.

1993-01-01

A numerical procedure for grouping actuators in order to reduce the number of degrees of freedom in an active noise control system is evaluated using experimental data. Piezoceramic actuators for reducing aircraft interior noise are arranged into groups using a nonlinear optimization routine and clustering algorithm. An actuator group is created when two or more actuators are driven with the same control input. This procedure is suitable for active control applications where actuators are already mounted on a structure. The feasibility of this technique is demonstrated using measured data from the aft cabin of a Douglas DC-9 fuselage. The measured data include transfer functions between 34 piezoceramic actuators and 29 interior microphones and microphone responses due to the primary noise produced by external speakers. Control inputs for the grouped actuators were calculated so that a cost function, defined as a quadratic pressure term and a penalty term, was a minimum. The measured transfer functions and microphone responses are checked by comparing calculated noise reductions with measured noise reductions for four frequencies. The grouping procedure is then used to determine actuator groups that improve overall interior noise reductions by 5.3 to 15 dB, compared to the baseline experimental configuration.

Plasticity Tool for Predicting Shear Nonlinearity of Unidirectional Laminates Under Multiaxial Loading

NASA Technical Reports Server (NTRS)

Wang, John T.; Bomarito, Geoffrey F.

2016-01-01

This study implements a plasticity tool to predict the nonlinear shear behavior of unidirectional composite laminates under multiaxial loadings, with an intent to further develop the tool for use in composite progressive damage analysis. The steps for developing the plasticity tool include establishing a general quadratic yield function, deriving the incremental elasto-plastic stress-strain relations using the yield function with associated flow rule, and integrating the elasto-plastic stress-strain relations with a modified Euler method and a substepping scheme. Micromechanics analyses are performed to obtain normal and shear stress-strain curves that are used in determining the plasticity parameters of the yield function. By analyzing a micromechanics model, a virtual testing approach is used to replace costly experimental tests for obtaining stress-strain responses of composites under various loadings. The predicted elastic moduli and Poisson's ratios are in good agreement with experimental data. The substepping scheme for integrating the elasto-plastic stress-strain relations is suitable for working with displacement-based finite element codes. An illustration problem is solved to show that the plasticity tool can predict the nonlinear shear behavior for a unidirectional laminate subjected to multiaxial loadings.

Jerk Minimization Method for Vibration Control in Buildings

NASA Technical Reports Server (NTRS)

Abatan, Ayo O.; Yao, Leummim

1997-01-01

In many vibration minimization control problems for high rise buildings subject to strong earthquake loads, the emphasis has been on a combination of minimizing the displacement, the velocity and the acceleration of the motion of the building. In most cases, the accelerations that are involved are not necessarily large but the change in them (jerk) are abrupt. These changes in magnitude or direction are responsible for most building damage and also create discomfort like motion sickness for inhabitants of these structures because of the element of surprise. We propose a method of minimizing also the jerk which is the sudden change in acceleration or the derivative of the acceleration using classical linear quadratic optimal controls. This was done through the introduction of a quadratic performance index involving the cost due to the jerk; a special change of variable; and using the jerk as a control variable. The values of the optimal control are obtained using the Riccati equation.

Data Modeling Using Finite Differences

ERIC Educational Resources Information Center

Rhoads, Kathryn; Mendoza Epperson, James A.

2017-01-01

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

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

ERIC Educational Resources Information Center

What Works Clearinghouse, 2009

2009-01-01

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

Non-fragile observer-based output feedback control for polytopic uncertain system under distributed model predictive control approach

NASA Astrophysics Data System (ADS)

Zhu, Kaiqun; Song, Yan; Zhang, Sunjie; Zhong, Zhaozhun

2017-07-01

In this paper, a non-fragile observer-based output feedback control problem for the polytopic uncertain system under distributed model predictive control (MPC) approach is discussed. By decomposing the global system into some subsystems, the computation complexity is reduced, so it follows that the online designing time can be saved.Moreover, an observer-based output feedback control algorithm is proposed in the framework of distributed MPC to deal with the difficulties in obtaining the states measurements. In this way, the presented observer-based output-feedback MPC strategy is more flexible and applicable in practice than the traditional state-feedback one. What is more, the non-fragility of the controller has been taken into consideration in favour of increasing the robustness of the polytopic uncertain system. After that, a sufficient stability criterion is presented by using Lyapunov-like functional approach, meanwhile, the corresponding control law and the upper bound of the quadratic cost function are derived by solving an optimisation subject to convex constraints. Finally, some simulation examples are employed to show the effectiveness of the method.

Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.

PubMed

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.

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

PubMed

Skariah, Deepak G; Arigovindan, Muthuvel

2017-06-19

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

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

PubMed

Wang, Chunhua; Liu, Xiaoming; Xia, Hu

2017-03-01

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

Linear Approximation SAR Azimuth Processing Study

NASA Technical Reports Server (NTRS)

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

1979-01-01

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

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

PubMed Central

Zhu, Yun; Fan, Ruzong; Xiong, Momiao

2017-01-01

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

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

PubMed

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

1982-01-01

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

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

PubMed

Kendal, W S

2000-04-01

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

Polarimetric image reconstruction algorithms

NASA Astrophysics Data System (ADS)

Valenzuela, John R.

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

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

PubMed

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

2018-06-01

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

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

PubMed

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

2018-02-01

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

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

DTIC Science & Technology

2010-06-01

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

The Factorability of Quadratics: Motivation for More Techniques

ERIC Educational Resources Information Center

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

2005-01-01

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

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

DOE PAGES

Huang, Kuo -Ling; Mehrotra, Sanjay

2016-11-08

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

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

PubMed

Hoover, Brian G; Gamiz, Victor L

2006-02-01

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

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

PubMed

Uchida, Teruhisa; Nakaune, Naoko

2004-12-01

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

High-order Newton-penalty algorithms

NASA Astrophysics Data System (ADS)

Dussault, Jean-Pierre

2005-10-01

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

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

NASA Astrophysics Data System (ADS)

Bochkarev, S. V.

2014-02-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

AESOP- INTERACTIVE DESIGN OF LINEAR QUADRATIC REGULATORS AND KALMAN FILTERS

NASA Technical Reports Server (NTRS)

Lehtinen, B.

1994-01-01

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

Interpolation and Polynomial Curve Fitting

ERIC Educational Resources Information Center

Yang, Yajun; Gordon, Sheldon P.

2014-01-01

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

The Inverted Student Density and Test Scores.

ERIC Educational Resources Information Center

Boldt, Robert F.

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

State Spending on Higher Education Capital Outlays

ERIC Educational Resources Information Center

Delaney, Jennifer A.; Doyle, William R.

2014-01-01

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

An Authentic Task That Models Quadratics

ERIC Educational Resources Information Center

Baron, Lorraine M.

2015-01-01

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

Use of nonlinear programming to optimize performance response to energy density in broiler feed formulation.

PubMed

Guevara, V R

2004-02-01

A nonlinear programming optimization model was developed to maximize margin over feed cost in broiler feed formulation and is described in this paper. The model identifies the optimal feed mix that maximizes profit margin. Optimum metabolizable energy level and performance were found by using Excel Solver nonlinear programming. Data from an energy density study with broilers were fitted to quadratic equations to express weight gain, feed consumption, and the objective function income over feed cost in terms of energy density. Nutrient:energy ratio constraints were transformed into equivalent linear constraints. National Research Council nutrient requirements and feeding program were used for examining changes in variables. The nonlinear programming feed formulation method was used to illustrate the effects of changes in different variables on the optimum energy density, performance, and profitability and was compared with conventional linear programming. To demonstrate the capabilities of the model, I determined the impact of variation in prices. Prices for broiler, corn, fish meal, and soybean meal were increased and decreased by 25%. Formulations were identical in all other respects. Energy density, margin, and diet cost changed compared with conventional linear programming formulation. This study suggests that nonlinear programming can be more useful than conventional linear programming to optimize performance response to energy density in broiler feed formulation because an energy level does not need to be set.

Quadratic Forms and Semiclassical Eigenfunction Hypothesis for Flat Tori

NASA Astrophysics Data System (ADS)

T. Sardari, Naser

2018-03-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-08-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-08-01

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

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

PubMed

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

2010-04-01

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

Robust guaranteed cost tracking control of quadrotor UAV with uncertainties.

PubMed

Xu, Zhiwei; Nian, Xiaohong; Wang, Haibo; Chen, Yinsheng

2017-07-01

In this paper, a robust guaranteed cost controller (RGCC) is proposed for quadrotor UAV system with uncertainties to address set-point tracking problem. A sufficient condition of the existence for RGCC is derived by Lyapunov stability theorem. The designed RGCC not only guarantees the whole closed-loop system asymptotically stable but also makes the quadratic performance level built for the closed-loop system have an upper bound irrespective to all admissible parameter uncertainties. Then, an optimal robust guaranteed cost controller is developed to minimize the upper bound of performance level. Simulation results verify the presented control algorithms possess small overshoot and short setting time, with which the quadrotor has ability to perform set-point tracking task well. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Reducing Formation-Keeping Maneuver Costs for Formation Flying Satellites in Low-Earth Orbit

NASA Technical Reports Server (NTRS)

Hamilton, Nicholas

2001-01-01

Several techniques are used to synthesize the formation-keeping control law for a three-satellite formation in low-earth orbit. The objective is to minimize maneuver cost and position tracking error. Initial reductions are found for a one-satellite case by tuning the state-weighting matrix within the linear-quadratic-Gaussian framework. Further savings come from adjusting the maneuver interval. Scenarios examined include cases with and without process noise. These results are then applied to a three-satellite formation. For both the one-satellite and three-satellite cases, increasing the maneuver interval yields a decrease in maneuver cost and an increase in position tracking error. A maneuver interval of 8-10 minutes provides a good trade-off between maneuver cost and position tracking error. An analysis of the closed-loop poles with respect to varying maneuver intervals explains the effectiveness of the chosen maneuver interval.

On-line adaptive battery impedance parameter and state estimation considering physical principles in reduced order equivalent circuit battery models. Part 1. Requirements, critical review of methods and modeling

NASA Astrophysics Data System (ADS)

Fleischer, Christian; Waag, Wladislaw; Heyn, Hans-Martin; Sauer, Dirk Uwe

2014-08-01

Lithium-ion battery systems employed in high power demanding systems such as electric vehicles require a sophisticated monitoring system to ensure safe and reliable operation. Three major states of the battery are of special interest and need to be constantly monitored, these include: battery state of charge (SoC), battery state of health (capcity fade determination, SoH), and state of function (power fade determination, SoF). In a series of two papers, we propose a system of algorithms based on a weighted recursive least quadratic squares parameter estimator, that is able to determine the battery impedance and diffusion parameters for accurate state estimation. The functionality was proven on different battery chemistries with different aging conditions. The first paper investigates the general requirements on BMS for HEV/EV applications. In parallel, the commonly used methods for battery monitoring are reviewed to elaborate their strength and weaknesses in terms of the identified requirements for on-line applications. Special emphasis will be placed on real-time capability and memory optimized code for cost-sensitive industrial or automotive applications in which low-cost microcontrollers must be used. Therefore, a battery model is presented which includes the influence of the Butler-Volmer kinetics on the charge-transfer process. Lastly, the mass transport process inside the battery is modeled in a novel state-space representation.

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

PubMed

Culpepper, Steven Andrew

2016-06-01

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

Validation of drift and diffusion coefficients from experimental data

NASA Astrophysics Data System (ADS)

Riera, R.; Anteneodo, C.

2010-04-01

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

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

PubMed

Hajian-Tilaki, Karimollah; Heidari, Behzad

2015-01-01

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

A wavelet-based adaptive fusion algorithm of infrared polarization imaging

NASA Astrophysics Data System (ADS)

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

2011-08-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Seven Wonders of the Ancient and Modern Quadratic World.

ERIC Educational Resources Information Center

Taylor, Sharon E.; Mittag, Kathleen Cage

2001-01-01

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

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

NASA Astrophysics Data System (ADS)

Andrews, Mark

2018-05-01

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

THE EFFECTIVENESS OF QUADRATS FOR MEASURING VASCULAR PLANT DIVERSITY

EPA Science Inventory

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

Waste management under multiple complexities: inexact piecewise-linearization-based fuzzy flexible programming.

PubMed

Sun, Wei; Huang, Guo H; Lv, Ying; Li, Gongchen

2012-06-01

To tackle nonlinear economies-of-scale (EOS) effects in interval-parameter constraints for a representative waste management problem, an inexact piecewise-linearization-based fuzzy flexible programming (IPFP) model is developed. In IPFP, interval parameters for waste amounts and transportation/operation costs can be quantified; aspiration levels for net system costs, as well as tolerance intervals for both capacities of waste treatment facilities and waste generation rates can be reflected; and the nonlinear EOS effects transformed from objective function to constraints can be approximated. An interactive algorithm is proposed for solving the IPFP model, which in nature is an interval-parameter mixed-integer quadratically constrained programming model. To demonstrate the IPFP's advantages, two alternative models are developed to compare their performances. One is a conventional linear-regression-based inexact fuzzy programming model (IPFP2) and the other is an IPFP model with all right-hand-sides of fussy constraints being the corresponding interval numbers (IPFP3). The comparison results between IPFP and IPFP2 indicate that the optimized waste amounts would have the similar patterns in both models. However, when dealing with EOS effects in constraints, the IPFP2 may underestimate the net system costs while the IPFP can estimate the costs more accurately. The comparison results between IPFP and IPFP3 indicate that their solutions would be significantly different. The decreased system uncertainties in IPFP's solutions demonstrate its effectiveness for providing more satisfactory interval solutions than IPFP3. Following its first application to waste management, the IPFP can be potentially applied to other environmental problems under multiple complexities. Copyright © 2012 Elsevier Ltd. All rights reserved.

Reduction potential, shadow prices, and pollution costs of agricultural pollutants in China.

PubMed

Tang, Kai; Gong, Chengzhu; Wang, Dong

2016-01-15

This paper analyses the reduction potential, shadow prices, and pollution costs of agricultural pollutants in China based on provincial panel data for 2001-2010. Using a parameterized quadratic form for the directional output distance function, we find that if agricultural sectors in all provinces were to produce on the production frontier, China could potentially reduce agricultural emissions of chemical oxygen demand (COD), total nitrogen (TN), and total phosphorus (TP) by 16.0%, 16.2%, and 20.4%, respectively. Additionally, our results show that the shadow price of TN increased rapidly and continuously, while that of COD and TP fluctuated for the whole period. For the whole country, the average shadow price of COD, TN, and TP are 8266 Yuan/tonne, 25,560 Yuan/tonne, and 10,160 Yuan/tonne, respectively. The regional shadow prices of agricultural pollutants are unbalanced. Furthermore, we show that the pollution costs from emissions of COD, TN, and TP are 6.09% of the annual gross output value of the agricultural sector and are highest in the Western and lowest in the Eastern provinces. Our estimates suggest that there is scope for further pollution abatement and simultaneous output expansion for China's agriculture if farmers promote greater efficiency in their production process. Policymakers are required to dynamically adjust the pollution tax rates and ascertain the initial permit price in an emission trading system. Policymakers should also consider the different pollution costs for each province when making the reduction allocations within the agricultural sector. Copyright © 2015 Elsevier B.V. All rights reserved.

Reducing the metabolic cost of walking with an ankle exoskeleton: interaction between actuation timing and power.

PubMed

Galle, Samuel; Malcolm, Philippe; Collins, Steven Hartley; De Clercq, Dirk

2017-04-27

Powered ankle-foot exoskeletons can reduce the metabolic cost of human walking to below normal levels, but optimal assistance properties remain unclear. The purpose of this study was to test the effects of different assistance timing and power characteristics in an experiment with a tethered ankle-foot exoskeleton. Ten healthy female subjects walked on a treadmill with bilateral ankle-foot exoskeletons in 10 different assistance conditions. Artificial pneumatic muscles assisted plantarflexion during ankle push-off using one of four actuation onset timings (36, 42, 48 and 54% of the stride) and three power levels (average positive exoskeleton power over a stride, summed for both legs, of 0.2, 0.4 and 0.5 W∙kg -1 ). We compared metabolic rate, kinematics and electromyography (EMG) between conditions. Optimal assistance was achieved with an onset of 42% stride and average power of 0.4 W∙kg -1 , leading to 21% reduction in metabolic cost compared to walking with the exoskeleton deactivated and 12% reduction compared to normal walking without the exoskeleton. With suboptimal timing or power, the exoskeleton still reduced metabolic cost, but substantially less so. The relationship between timing, power and metabolic rate was well-characterized by a two-dimensional quadratic function. The assistive mechanisms leading to these improvements included reducing muscular activity in the ankle plantarflexors and assisting leg swing initiation. These results emphasize the importance of optimizing exoskeleton actuation properties when assisting or augmenting human locomotion. Our optimal assistance onset timing and average power levels could be used for other exoskeletons to improve assistance and resulting benefits.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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

PubMed

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

2016-10-17

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

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

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

Murray, W.; Prieto, F.J.

1993-05-01

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

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

NASA Astrophysics Data System (ADS)

Matsushima, Masatomo; Ohmiya, Mayumi

2009-09-01

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

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

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

A review of spatio-temporal modelling of quadrat count data with application to striga occurrence in a pearl millet field

NASA Astrophysics Data System (ADS)

Hess, Dale; van Lieshout, Marie-Colette; Payne, Bill; Stein, Alfred

This paper describes how spatial statistical techniques may be used to analyse weed occurrence in tropical fields. Quadrat counts of weed numbers are available over a series of years, as well as data on explanatory variables, and the aim is to smooth the data and assess spatial and temporal trends. We review a range of models for correlated count data. As an illustration, we consider data on striga infestation of a 60 × 24 m 2 millet field in Niger collected from 1985 until 1991, modelled by independent Poisson counts and a prior auto regression term enforcing spatial coherence. The smoothed fields show the presence of a seed bank, the estimated model parameters indicate a decay in the striga numbers over time, as well as a clear correlation with the amount of rainfall in 15 consecutive days following the sowing date. Such results could contribute to precision agriculture as a guide to more cost-effective striga control strategies.

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

NASA Astrophysics Data System (ADS)

Liao, Haitao; Wu, Wenwang; Fang, Daining

2018-07-01

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

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

DTIC Science & Technology

1990-02-01

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

Command Generator Tracker Synthesis Methods Using an LQG (Linear System Model, Quadratic Cost, and Gaussian Noise Process) Derived Proportional Plus Integral Controller Based on the Integral of the Regulation Error.

DTIC Science & Technology

1983-12-01

34 M4 + + Z + + + E + ass + + Z + + + osi " " + + Z + + + + 9tr"- + t + Z + ++ +" + + L + Z + +0+ + : :L:+: • +: E. . :ce + L+ Z+ + E+ 9 " + L z + K...this guide.) The truth model description is identified by the heading "TRUTH MODELO . The matrices of the continuous-time system are listed first. The

Electron-beam conditioning by thomson scattering.

PubMed

Schroeder, C B; Esarey, E; Leemans, W P

2004-11-05

A method is proposed for conditioning electron beams via Thomson scattering. The conditioning provides a quadratic correlation between the electron energy deviation and the betatron amplitude of the electrons, which results in enhanced gain in free-electron lasers. Quantum effects imply conditioning must occur at high laser fluence and moderate electron energy. Conditioning of x-ray free-electron lasers should be achievable with present laser technology, leading to significant size and cost reductions of these large-scale facilities.

Sparse Regression as a Sparse Eigenvalue Problem

NASA Technical Reports Server (NTRS)

Moghaddam, Baback; Gruber, Amit; Weiss, Yair; Avidan, Shai

2008-01-01

We extend the l0-norm "subspectral" algorithms for sparse-LDA [5] and sparse-PCA [6] to general quadratic costs such as MSE in linear (kernel) regression. The resulting "Sparse Least Squares" (SLS) problem is also NP-hard, by way of its equivalence to a rank-1 sparse eigenvalue problem (e.g., binary sparse-LDA [7]). Specifically, for a general quadratic cost we use a highly-efficient technique for direct eigenvalue computation using partitioned matrix inverses which leads to dramatic x103 speed-ups over standard eigenvalue decomposition. This increased efficiency mitigates the O(n4) scaling behaviour that up to now has limited the previous algorithms' utility for high-dimensional learning problems. Moreover, the new computation prioritizes the role of the less-myopic backward elimination stage which becomes more efficient than forward selection. Similarly, branch-and-bound search for Exact Sparse Least Squares (ESLS) also benefits from partitioned matrix inverse techniques. Our Greedy Sparse Least Squares (GSLS) generalizes Natarajan's algorithm [9] also known as Order-Recursive Matching Pursuit (ORMP). Specifically, the forward half of GSLS is exactly equivalent to ORMP but more efficient. By including the backward pass, which only doubles the computation, we can achieve lower MSE than ORMP. Experimental comparisons to the state-of-the-art LARS algorithm [3] show forward-GSLS is faster, more accurate and more flexible in terms of choice of regularization

The period function of the generalized Lotka-Volterra centers

NASA Astrophysics Data System (ADS)

Villadelprat, J.

2008-05-01

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

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

ERIC Educational Resources Information Center

Hohensee, Charles

2014-01-01

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

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

NASA Astrophysics Data System (ADS)

Long, Kai; Wang, Xuan; Gu, Xianguang

2017-09-01

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

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

PubMed

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

2017-09-22

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

Effect of Evolutionary Anisotropy on Earing Prediction in Cylindrical Cup Drawing

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

Hypersonic Vehicle Trajectory Optimization and Control

NASA Technical Reports Server (NTRS)

Balakrishnan, S. N.; Shen, J.; Grohs, J. R.

1997-01-01

Two classes of neural networks have been developed for the study of hypersonic vehicle trajectory optimization and control. The first one is called an 'adaptive critic'. The uniqueness and main features of this approach are that: (1) they need no external training; (2) they allow variability of initial conditions; and (3) they can serve as feedback control. This is used to solve a 'free final time' two-point boundary value problem that maximizes the mass at the rocket burn-out while satisfying the pre-specified burn-out conditions in velocity, flightpath angle, and altitude. The second neural network is a recurrent network. An interesting feature of this network formulation is that when its inputs are the coefficients of the dynamics and control matrices, the network outputs are the Kalman sequences (with a quadratic cost function); the same network is also used for identifying the coefficients of the dynamics and control matrices. Consequently, we can use it to control a system whose parameters are uncertain. Numerical results are presented which illustrate the potential of these methods.

Modified optimal control pilot model for computer-aided design and analysis

NASA Technical Reports Server (NTRS)

Davidson, John B.; Schmidt, David K.

1992-01-01

This paper presents the theoretical development of a modified optimal control pilot model based upon the optimal control model (OCM) of the human operator developed by Kleinman, Baron, and Levison. This model is input compatible with the OCM and retains other key aspects of the OCM, such as a linear quadratic solution for the pilot gains with inclusion of control rate in the cost function, a Kalman estimator, and the ability to account for attention allocation and perception threshold effects. An algorithm designed for each implementation in current dynamic systems analysis and design software is presented. Example results based upon the analysis of a tracking task using three basic dynamic systems are compared with measured results and with similar analyses performed with the OCM and two previously proposed simplified optimal pilot models. The pilot frequency responses and error statistics obtained with this modified optimal control model are shown to compare more favorably to the measured experimental results than the other previously proposed simplified models evaluated.

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

NASA Technical Reports Server (NTRS)

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

2003-01-01

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

Development of BEM for ceramic composites

NASA Technical Reports Server (NTRS)

Henry, D. P.; Banerjee, P. K.; Dargush, G. F.

1990-01-01

Details on the progress made during the first three years of a five-year program towards the development of a boundary element code are presented. This code was designed for the micromechanical studies of advance ceramic composites. Additional effort was made in generalizing the implementation to allow the program to be applicable to real problems in the aerospace industry. The ceramic composite formulations developed were implemented in the three-dimensional boundary element computer code BEST3D. BEST3D was adopted as the base for the ceramic composite program, so that many of the enhanced features of this general purpose boundary element code could by utilized. Some of these facilities include sophisticated numerical integration, the capability of local definition of boundary conditions, and the use of quadratic shape functions for modeling geometry and field variables on the boundary. The multi-region implementation permits a body to be modeled in substructural parts; thus dramatically reducing the cost of the analysis. Furthermore, it allows a body consisting of regions of different ceramic matrices and inserts to be studied.

Design Optimization for a Maglev System Employing Flux Eliminating Coils

NASA Technical Reports Server (NTRS)

Davey, Kent R.

1996-01-01

Flux eliminating coils have received no little attention over the past thirty years as an alternative for realizing lift in a MAGLEV system. When the magnets on board the vehicle are displaced from the equilibrium or null flux point of these coils, they induce current in those coils which act to restore the coil to its null flux or centerline position. The question being addressed in this paper is that of how to choose the best coil for a given system. What appears at first glance to be an innocent question is in fact one that is actually quite involved, encompassing both the global economics and physics of the system. The real key in analyzing that question is to derive an optimization index or functional which represents the cost of the system subject to constraints, the primary constraint being that the vehicle lift itself at a certain threshold speed. Outlined in this paper is one scenario for realizing a total system design which uses sequential quadratic programming techniques.

Multirate sampled-data yaw-damper and modal suppression system design

NASA Technical Reports Server (NTRS)

Berg, Martin C.; Mason, Gregory S.

1990-01-01

A multirate control law synthesized algorithm based on an infinite-time quadratic cost function, was developed along with a method for analyzing the robustness of multirate systems. A generalized multirate sampled-data control law structure (GMCLS) was introduced. A new infinite-time-based parameter optimization multirate sampled-data control law synthesis method and solution algorithm were developed. A singular-value-based method for determining gain and phase margins for multirate systems was also developed. The finite-time-based parameter optimization multirate sampled-data control law synthesis algorithm originally intended to be applied to the aircraft problem was instead demonstrated by application to a simpler problem involving the control of the tip position of a two-link robot arm. The GMCLS, the infinite-time-based parameter optimization multirate control law synthesis method and solution algorithm, and the singular-value based method for determining gain and phase margins were all demonstrated by application to the aircraft control problem originally proposed for this project.

Linear model for fast background subtraction in oligonucleotide microarrays.

PubMed

Kroll, K Myriam; Barkema, Gerard T; Carlon, Enrico

2009-11-16

One important preprocessing step in the analysis of microarray data is background subtraction. In high-density oligonucleotide arrays this is recognized as a crucial step for the global performance of the data analysis from raw intensities to expression values. We propose here an algorithm for background estimation based on a model in which the cost function is quadratic in a set of fitting parameters such that minimization can be performed through linear algebra. The model incorporates two effects: 1) Correlated intensities between neighboring features in the chip and 2) sequence-dependent affinities for non-specific hybridization fitted by an extended nearest-neighbor model. The algorithm has been tested on 360 GeneChips from publicly available data of recent expression experiments. The algorithm is fast and accurate. Strong correlations between the fitted values for different experiments as well as between the free-energy parameters and their counterparts in aqueous solution indicate that the model captures a significant part of the underlying physical chemistry.

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

PubMed

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

2010-01-01

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

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

DTIC Science & Technology

2011-04-01

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

Mathematics in the Real World.

ERIC Educational Resources Information Center

Borenstein, Matt

1997-01-01

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

Nonconvex model predictive control for commercial refrigeration

NASA Astrophysics Data System (ADS)

Gybel Hovgaard, Tobias; Boyd, Stephen; Larsen, Lars F. S.; Bagterp Jørgensen, John

2013-08-01

We consider the control of a commercial multi-zone refrigeration system, consisting of several cooling units that share a common compressor, and is used to cool multiple areas or rooms. In each time period we choose cooling capacity to each unit and a common evaporation temperature. The goal is to minimise the total energy cost, using real-time electricity prices, while obeying temperature constraints on the zones. We propose a variation on model predictive control to achieve this goal. When the right variables are used, the dynamics of the system are linear, and the constraints are convex. The cost function, however, is nonconvex due to the temperature dependence of thermodynamic efficiency. To handle this nonconvexity we propose a sequential convex optimisation method, which typically converges in fewer than 5 or so iterations. We employ a fast convex quadratic programming solver to carry out the iterations, which is more than fast enough to run in real time. We demonstrate our method on a realistic model, with a full year simulation and 15-minute time periods, using historical electricity prices and weather data, as well as random variations in thermal load. These simulations show substantial cost savings, on the order of 30%, compared to a standard thermostat-based control system. Perhaps more important, we see that the method exhibits sophisticated response to real-time variations in electricity prices. This demand response is critical to help balance real-time uncertainties in generation capacity associated with large penetration of intermittent renewable energy sources in a future smart grid.

Estimating population size with correlated sampling unit estimates

Treesearch

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

2003-01-01

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

Quadratic soliton self-reflection at a quadratically nonlinear interface

NASA Astrophysics Data System (ADS)

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

2003-11-01

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

Self-Replicating Quadratics

ERIC Educational Resources Information Center

Withers, Christopher S.; Nadarajah, Saralees

2012-01-01

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

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

PubMed

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

2018-04-01

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

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

PubMed

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

2007-03-01

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

Orthogonality preserving infinite dimensional quadratic stochastic operators

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

Akın, Hasan; Mukhamedov, Farrukh

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

Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

ERIC Educational Resources Information Center

Laine, A. D.

2015-01-01

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

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

NASA Astrophysics Data System (ADS)

Boehm, M.

1985-09-01

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

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

NASA Technical Reports Server (NTRS)

Natarajan, R.; Brown, R. A.

1986-01-01

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

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

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1984-01-01

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

Unsteady Propeller Hydrodynamics

DTIC Science & Technology

2001-06-01

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

Penalized Weighted Least-Squares Approach to Sinogram Noise Reduction and Image Reconstruction for Low-Dose X-Ray Computed Tomography

PubMed Central

Wang, Jing; Li, Tianfang; Lu, Hongbing; Liang, Zhengrong

2006-01-01

Reconstructing low-dose X-ray CT (computed tomography) images is a noise problem. This work investigated a penalized weighted least-squares (PWLS) approach to address this problem in two dimensions, where the WLS considers first- and second-order noise moments and the penalty models signal spatial correlations. Three different implementations were studied for the PWLS minimization. One utilizes a MRF (Markov random field) Gibbs functional to consider spatial correlations among nearby detector bins and projection views in sinogram space and minimizes the PWLS cost function by iterative Gauss-Seidel algorithm. Another employs Karhunen-Loève (KL) transform to de-correlate data signals among nearby views and minimizes the PWLS adaptively to each KL component by analytical calculation, where the spatial correlation among nearby bins is modeled by the same Gibbs functional. The third one models the spatial correlations among image pixels in image domain also by a MRF Gibbs functional and minimizes the PWLS by iterative successive over-relaxation algorithm. In these three implementations, a quadratic functional regularization was chosen for the MRF model. Phantom experiments showed a comparable performance of these three PWLS-based methods in terms of suppressing noise-induced streak artifacts and preserving resolution in the reconstructed images. Computer simulations concurred with the phantom experiments in terms of noise-resolution tradeoff and detectability in low contrast environment. The KL-PWLS implementation may have the advantage in terms of computation for high-resolution dynamic low-dose CT imaging. PMID:17024831

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

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook

1988-01-01

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

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

DOE PAGES

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

2015-06-16

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

Robust Stabilization of Uncertain Systems Based on Energy Dissipation Concepts

NASA Technical Reports Server (NTRS)

Gupta, Sandeep

1996-01-01

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

Optimization of Fish Protection System to Increase Technosphere Safety

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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

NASA Technical Reports Server (NTRS)

Thompson, P. M.

1979-01-01

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

Using Visualization to Generalize on Quadratic Patterning Tasks

ERIC Educational Resources Information Center

Kirwan, J. Vince

2017-01-01

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

Solution of Thermoelectricity Problems Energy Method

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

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

PubMed

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

2016-12-01

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

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

PubMed

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

2012-11-01

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

Functional properties of models for direction selectivity in the retina.

PubMed

Grzywacz, N M; Koch, C

1987-01-01

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

Cost-Sharing of Ecological Construction Based on Trapezoidal Intuitionistic Fuzzy Cooperative Games.

PubMed

Liu, Jiacai; Zhao, Wenjian

2016-11-08

There exist some fuzziness and uncertainty in the process of ecological construction. The aim of this paper is to develop a direct and an effective simplified method for obtaining the cost-sharing scheme when some interested parties form a cooperative coalition to improve the ecological environment of Min River together. Firstly, we propose the solution concept of the least square prenucleolus of cooperative games with coalition values expressed by trapezoidal intuitionistic fuzzy numbers. Then, based on the square of the distance in the numerical value between two trapezoidal intuitionistic fuzzy numbers, we establish a corresponding quadratic programming model to obtain the least square prenucleolus, which can effectively avoid the information distortion and uncertainty enlargement brought about by the subtraction of trapezoidal intuitionistic fuzzy numbers. Finally, we give a numerical example about the cost-sharing of ecological construction in Fujian Province in China to show the validity, applicability, and advantages of the proposed model and method.

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

ERIC Educational Resources Information Center

Todorova, Teodora; Alexiev, Valentin; Weber, Thomas

2006-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

Dynamical correlation functions of the quadratic coupling spin-Boson model

NASA Astrophysics Data System (ADS)

Zheng, Da-Chuan; Tong, Ning-Hua

2017-06-01

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

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

NASA Technical Reports Server (NTRS)

Lei, Ning; Xiong, Xiaoxiong

2016-01-01

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

Lyapunov functions for a class of nonlinear systems using Caputo derivative

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

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

PubMed

Chalal, Hocine; Abed-Meraim, Farid

2018-06-20

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

Securing Digital Audio using Complex Quadratic Map

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Regions of absolute ultimate boundedness for discrete-time systems.

NASA Technical Reports Server (NTRS)

Siljak, D. D.; Weissenberger, S.

1972-01-01

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

Prediction of infection risk of hop by Pseudoperonspora humuli

USDA-ARS?s Scientific Manuscript database

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

The Shock and Vibration Digest. Volume 18, Number 6

DTIC Science & Technology

1986-06-01

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

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

ERIC Educational Resources Information Center

Wood, Eric

1992-01-01

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

Interactive Spreadsheets in JCE Webware

ERIC Educational Resources Information Center

Coleman, William F.; Fedosky, Edward W.

2005-01-01

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

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

ERIC Educational Resources Information Center

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

2015-01-01

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

On Partial Fraction Decompositions by Repeated Polynomial Divisions

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2017-01-01

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

Electrochemical oxidation of ampicillin antibiotic at boron-doped diamond electrodes and process optimization using response surface methodology.

PubMed

Körbahti, Bahadır K; Taşyürek, Selin

2015-03-01

Electrochemical oxidation and process optimization of ampicillin antibiotic at boron-doped diamond electrodes (BDD) were investigated in a batch electrochemical reactor. The influence of operating parameters, such as ampicillin concentration, electrolyte concentration, current density, and reaction temperature, on ampicillin removal, COD removal, and energy consumption was analyzed in order to optimize the electrochemical oxidation process under specified cost-driven constraints using response surface methodology. Quadratic models for the responses satisfied the assumptions of the analysis of variance well according to normal probability, studentized residuals, and outlier t residual plots. Residual plots followed a normal distribution, and outlier t values indicated that the approximations of the fitted models to the quadratic response surfaces were very good. Optimum operating conditions were determined at 618 mg/L ampicillin concentration, 3.6 g/L electrolyte concentration, 13.4 mA/cm(2) current density, and 36 °C reaction temperature. Under response surface optimized conditions, ampicillin removal, COD removal, and energy consumption were obtained as 97.1 %, 92.5 %, and 71.7 kWh/kg CODr, respectively.

Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential

NASA Astrophysics Data System (ADS)

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

2006-07-01

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

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

NASA Astrophysics Data System (ADS)

Jeanmairet, Guillaume; Levesque, Maximilien; Borgis, Daniel

2013-10-01

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

Parametric optimal control of uncertain systems under an optimistic value criterion

NASA Astrophysics Data System (ADS)

Li, Bo; Zhu, Yuanguo

2018-01-01

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

Dolan Grady relations and noncommutative quasi-exactly solvable systems

NASA Astrophysics Data System (ADS)

Klishevich, Sergey M.; Plyushchay, Mikhail S.

2003-11-01

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

Effects of Unstable Shoes on Energy Cost During Treadmill Walking at Various Speeds

PubMed Central

Koyama, Keiji; Naito, Hisashi; Ozaki, Hayao; Yanagiya, Toshio

2012-01-01

In recent years, shoes having rounded soles in the anterior-posterior direction have been commercially introduced, which are commonly known as unstable shoes (US). However, physiological responses during walking in US, particularly at various speeds, have not been extensively studied to date. The purpose of this study was to investigate the effect of wearing unstable shoes while walking at low to high speeds on the rate of perceived exertion (RPE), muscle activation, oxygen consumption (VO2), and optimum speed. Healthy male adults wore US or normal walking shoes (WS), and walked at various speeds on a treadmill with no inclination. In experiment 1, subjects walked at 3, 4, 5, 6, and 7 km·h-1 (duration, 3 min for all speeds) and were recorded on video from the right sagittal plane to calculate the step length and cadence. Simultaneously, electromyogram (EMG) was recorded from six different thigh and calf muscles, and the integrated EMG (iEMG) was calculated. In experiment 2, RPE, heart rate and VO2 were measured with the walking speed being increased from 3.6 to 7.2 km·h-1 incrementally by 0.9 km·h-1 every 6 min. The optimum speed, defined by the least oxygen cost, was calculated from the fitted quadratic relationship between walking speed and oxygen cost. Wearing US resulted in significantly longer step length and lower cadence compared with WS condition at any given speed. For all speeds, iEMG in the medial gastrocnemius and soleus muscles, heart rate, and VO2 were significantly higher in US than WS. However, RPE and optimum speed (US, 4.75 ± 0.32 km·h-1; WS, 4. 79 ± 0.18 km·h-1) did not differ significantly between the two conditions. These results suggest that unstable shoes can increase muscle activity of lower legs and energy cost without influencing RPE and optimum speed during walking at various speeds. Key points During walking at various speeds, wearing unstable shoes results in longer step length and lower cadence compared with wearing WS. Wearing unstable shoes increases muscle activities of lower leg. Wearing unstable shoes shifts the quadratic relationship between walking speed and oxygen cost upward and increases energy cost about 4% without changes in RPE and optimum speed. PMID:24150072

Geometric Approaches to Quadratic Equations from Other Times and Places.

ERIC Educational Resources Information Center

Allaire, Patricia R.; Bradley, Robert E.

2001-01-01

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

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

NASA Technical Reports Server (NTRS)

Haddad, Wassim M.; Bernstein, Dennis S.

1991-01-01

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

Adaptiveness in monotone pseudo-Boolean optimization and stochastic neural computation.

PubMed

Grossi, Giuliano

2009-08-01

Hopfield neural network (HNN) is a nonlinear computational model successfully applied in finding near-optimal solutions of several difficult combinatorial problems. In many cases, the network energy function is obtained through a learning procedure so that its minima are states falling into a proper subspace (feasible region) of the search space. However, because of the network nonlinearity, a number of undesirable local energy minima emerge from the learning procedure, significantly effecting the network performance. In the neural model analyzed here, we combine both a penalty and a stochastic process in order to enhance the performance of a binary HNN. The penalty strategy allows us to gradually lead the search towards states representing feasible solutions, so avoiding oscillatory behaviors or asymptotically instable convergence. Presence of stochastic dynamics potentially prevents the network to fall into shallow local minima of the energy function, i.e., quite far from global optimum. Hence, for a given fixed network topology, the desired final distribution on the states can be reached by carefully modulating such process. The model uses pseudo-Boolean functions both to express problem constraints and cost function; a combination of these two functions is then interpreted as energy of the neural network. A wide variety of NP-hard problems fall in the class of problems that can be solved by the model at hand, particularly those having a monotonic quadratic pseudo-Boolean function as constraint function. That is, functions easily derived by closed algebraic expressions representing the constraint structure and easy (polynomial time) to maximize. We show the asymptotic convergence properties of this model characterizing its state space distribution at thermal equilibrium in terms of Markov chain and give evidence of its ability to find high quality solutions on benchmarks and randomly generated instances of two specific problems taken from the computational graph theory.

On non-autonomous dynamical systems

NASA Astrophysics Data System (ADS)

Anzaldo-Meneses, A.

2015-04-01

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

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

NASA Astrophysics Data System (ADS)

Henebry, Geoffrey; Tomaszewska, Monika; Kelgenbaeva, Kamilya

2017-04-01

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

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

Climate Intervention as an Optimization Problem

NASA Astrophysics Data System (ADS)

Caldeira, Ken; Ban-Weiss, George A.

2010-05-01

Typically, climate models simulations of intentional intervention in the climate system have taken the approach of imposing a change (eg, in solar flux, aerosol concentrations, aerosol emissions) and then predicting how that imposed change might affect Earth's climate or chemistry. Computations proceed from cause to effect. However, humans often proceed from "What do I want?" to "How do I get it?" One approach to thinking about intentional intervention in the climate system ("geoengineering") is to ask "What kind of climate do we want?" and then ask "What pattern of radiative forcing would come closest to achieving that desired climate state?" This involves defining climate goals and a cost function that measures how closely those goals are attained. (An important next step is to ask "How would we go about producing these desired patterns of radiative forcing?" However, this question is beyond the scope of our present study.) We performed a variety of climate simulations in NCAR's CAM3.1 atmospheric general circulation model with a slab ocean model and thermodynamic sea ice model. We then evaluated, for a specific set of climate forcing basis functions (ie, aerosol concentration distributions), the extent to which the climate response to a linear combination of those basis functions was similar to a linear combination of the climate response to each basis function taken individually. We then developed several cost functions (eg, relative to the 1xCO2 climate, minimize rms difference in zonal and annual mean land temperature, minimize rms difference in zonal and annual mean runoff, minimize rms difference in a combination of these temperature and runoff indices) and then predicted optimal combinations of our basis functions that would minimize these cost functions. Lastly, we produced forward simulations of the predicted optimal radiative forcing patterns and compared these with our expected results. Obviously, our climate model is much simpler than reality and predictions from individual models do not provide a sound basis for action; nevertheless, our model results indicate that the general approach outlined here can lead to patterns of radiative forcing that make the zonal annual mean climate of a high CO2 world markedly more similar to that of a low CO2 world simultaneously for both temperature and hydrological indices, where degree of similarity is measured using our explicit cost functions. We restricted ourselves to zonally uniform aerosol concentrations distributions that can be defined in terms of a positive-definite quadratic equation on the sine of latitude. Under this constraint, applying an aerosol distribution in a 2xCO2 climate that minimized a combination of rms difference in zonal and annual mean land temperature and runoff relative to the 1xCO2 climate, the rms difference in zonal and annual mean temperatures was reduced by ~90% and the rms difference in zonal and annual mean runoff was reduced by ~80%. This indicates that there may be potential for stratospheric aerosols to diminish simultaneously both temperature and hydrological cycle changes caused by excess CO2 in the atmosphere. Clearly, our model does not include many factors (eg, socio-political consequences, chemical consequences, ocean circulation changes, aerosol transport and microphysics) so we do not argue strongly for our specific climate model results, however, we do argue strongly in favor of our methodological approach. The proposed approach is general, in the sense that cost functions can be developed that represent different valuations. While the choice of appropriate cost functions is inherently a value judgment, evaluating those functions for a specific climate simulation is a quantitative exercise. Thus, the use of explicit cost functions in evaluating model results for climate intervention scenarios is a clear way of separating value judgments from purely scientific and technical issues.

Effects of using ground redberry juniper and dried distillers grains with solubles in lamb feedlot diets: growth, blood serum, fecal, and wool characteristics.

PubMed

Whitney, T R; Lupton, C J; Muir, J P; Adams, R P; Stewart, W C

2014-03-01

Effects of using ground redberry juniper and dried distillers grains with solubles (DDGS) in Rambouillet lamb (n = 45) feedlot diets on growth, blood serum, fecal, and wool characteristics were evaluated. In a randomized design study with 2 feeding periods (Period 1 = 64% concentrate diet, 35 d; Period 2 = 85% concentrate diet, 56 d), lambs were individually fed 5 isonitrogenous diets: a control diet (CNTL) that contained oat hay but not DDGS or juniper or DDGS-based diets in which 0 (0JUN), 33 (33JUN), 66 (66JUN), or 100% (100JUN) of the oat hay was replaced by juniper. During Period 1, lambs fed CNTL had greater (P < 0.05) DMI and ADG and tended to have greater (P < 0.10) G:F than lambs fed 0JUN or lambs fed DDGS-based diets. Lamb DMI, ADG, and G:F quadratically increased (P < 0.008) as juniper increased in the DDGS-based diets. During Period 2, lambs fed CNTL had greater (P < 0.05) DMI than lambs fed 0JUN or lambs fed DDGS-based diets, but ADG was similar (P > 0.41). Compared to 0JUN, lambs fed CNTL had similar (P = 0.12) G:F and tended to have less G:F (P = 0.07) than lambs fed DDGS-based diets. Among lambs fed DDGS-based diets, DMI was similar (P > 0.19), ADG increased linearly (P = 0.03), and G:F tended to decrease quadratically (P = 0.06) as juniper increased in the diet. Serum IGF-1, serum urea N (SUN), and fecal N were greater (P < 0.05) and serum Ca and P and fecal P were similar (P > 0.13) for lambs fed CNTL vs. lambs fed DDGS-based diets (CNTL). Within lambs fed DDGS-based diets, SUN increased quadratically (P = 0.01) and fecal N increased linearly (P = 0.004), which can partially be attributed to increased dietary urea and condensed tannin intake. Most wool characteristics were not affected, but wool growth per kilogram of BW decreased quadratically (P = 0.04) as percentage of juniper increased in the DDGS-based diets. When evaluating the entire 91-d feeding trial, results indicated that replacing all of the ground oat hay with ground juniper leaves and stems in lamb growing and finishing diets is not detrimental to animal performance and that DDGS-based diets can reduce total feedlot costs, as compared to sorghum grain and cottonseed meal-based diets. However, compared to using juniper or oat hay as the sole roughage source, using both during the growing period (Period 1) enhanced growth performance and further reduced total feedlot costs.

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

NASA Technical Reports Server (NTRS)

Burken, John J.

2005-01-01

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

A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints.

PubMed

Liang, X B; Wang, J

2000-01-01

This paper presents a continuous-time recurrent neural-network model for nonlinear optimization with any continuously differentiable objective function and bound constraints. Quadratic optimization with bound constraints is a special problem which can be solved by the recurrent neural network. The proposed recurrent neural network has the following characteristics. 1) It is regular in the sense that any optimum of the objective function with bound constraints is also an equilibrium point of the neural network. If the objective function to be minimized is convex, then the recurrent neural network is complete in the sense that the set of optima of the function with bound constraints coincides with the set of equilibria of the neural network. 2) The recurrent neural network is primal and quasiconvergent in the sense that its trajectory cannot escape from the feasible region and will converge to the set of equilibria of the neural network for any initial point in the feasible bound region. 3) The recurrent neural network has an attractivity property in the sense that its trajectory will eventually converge to the feasible region for any initial states even at outside of the bounded feasible region. 4) For minimizing any strictly convex quadratic objective function subject to bound constraints, the recurrent neural network is globally exponentially stable for almost any positive network parameters. Simulation results are given to demonstrate the convergence and performance of the proposed recurrent neural network for nonlinear optimization with bound constraints.

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

NASA Technical Reports Server (NTRS)

Thompson, Kyle B.; Gnoffo, Peter A.

2016-01-01

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

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

NASA Astrophysics Data System (ADS)

Hassan Mohammed, Mohammed Ahmed

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

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

ERIC Educational Resources Information Center

Joe, Harry; Maydeu-Olivares, Alberto

2010-01-01

Maydeu-Olivares and Joe (J. Am. Stat. Assoc. 100:1009-1020, "2005"; Psychometrika 71:713-732, "2006") introduced classes of chi-square tests for (sparse) multidimensional multinomial data based on low-order marginal proportions. Our extension provides general conditions under which quadratic forms in linear functions of cell residuals are…

Using Challenging Tasks for Formative Assessment on Quadratic Functions with Senior Secondary Students

ERIC Educational Resources Information Center

Wilkie, Karina J.

2016-01-01

Senior secondary mathematics students who develop conceptual understanding that moves them beyond "rules without reasons" to connections between related concepts are in a strong place to tackle the more difficult mathematics application problems. Current research is examining how the use of challenging tasks at different levels of…

Polynomial Graphs and Symmetry

ERIC Educational Resources Information Center

Goehle, Geoff; Kobayashi, Mitsuo

2013-01-01

Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…

Learning Mathematics with Interactive Whiteboards and Computer-Based Graphing Utility

ERIC Educational Resources Information Center

Erbas, Ayhan Kursat; Ince, Muge; Kaya, Sukru

2015-01-01

The purpose of this study was to explore the effect of a technology-supported learning environment utilizing an interactive whiteboard (IWB) and NuCalc graphing software compared to a traditional direct instruction-based environment on student achievement in graphs of quadratic functions and attitudes towards mathematics and technology. Sixty-five…

A Historical Perspective from "a" to "c"

ERIC Educational Resources Information Center

Edwards, Thomas G.; Ozgun-Koca, S. Asli

2010-01-01

Evolving technology has played an important part in a common quadratic-function lesson. Having been mentioned repeatedly in numerous reform documents, a recurring lesson has involved changing the parameters in f(x) = ax[superscript 2] + bx + c and studying the effects on the graph. In both NCTM Yearbooks and NCTM Standards documents, technology is…

Bicycles, Birds, Bats and Balloons: New Applications for Algebra Classes.

ERIC Educational Resources Information Center

Yoshiwara, Bruce; Yoshiwara, Kathy

This collection of activities is intended to enhance the teaching of college algebra through the use of modeling. The problems use real data and involve the representation and interpretation of the data. The concepts addressed include rates of change, linear and quadratic regression, and functions. The collection consists of eight problems, four…

Self-Efficacy and Interest: Experimental Studies of Optimal Incompetence.

ERIC Educational Resources Information Center

Silvia, Paul J.

2003-01-01

To test the optimal incompetence hypothesis (high self-efficacy lowers task interest), 30 subjects rated interest, perceived difficulty, and confidence of success in different tasks. In study 2, 33 subjects completed a dart-game task in easy, moderate, and difficult conditions. In both, interest was a quadratic function of self-efficacy,…

Effect of Cabri-Assisted Instruction on Secondary School Students' Misconceptions about Graphs of Quadratic Functions

ERIC Educational Resources Information Center

Koklu, Oguz; Topcu, Abdullah

2012-01-01

Pre-existing misconceptions are serious impediments to learning in mathematics. Means for detecting and correcting them have received much attention in the literature of educational research. Dynamic geometry software has been tried at different grade levels. This quasi-experimental study investigates the effect of Cabri-assisted instruction on…

Deriving the Quadratic Regression Equation Using Algebra

ERIC Educational Resources Information Center

Gordon, Sheldon P.; Gordon, Florence S.

2004-01-01

In discussions with leading educators from many different fields, MAA's CRAFTY (Curriculum Renewal Across the First Two Years) committee found that one of the most common mathematical themes in those other disciplines is the idea of fitting a function to a set of data in the least squares sense. The representatives of those partner disciplines…

Synchronization of Lienard-Type Oscillators in Uniform Electrical Networks

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

Sinha, Mohit; Dorfler, Florian; Johnson, Brian B.

2016-08-01

This paper presents a condition for global asymptotic synchronization of Lienard-type nonlinear oscillators in uniform LTI electrical networks with series R-L circuits modeling interconnections. By uniform electrical networks, we mean that the per-unit-length impedances are identical for the interconnecting lines. We derive conditions for global asymptotic synchronization for a particular feedback architecture where the derivative of the oscillator output current supplements the innate current feedback induced by simply interconnecting the oscillator to the network. Our proof leverages a coordinate transformation to a set of differential coordinates that emphasizes signal differences and the particular form of feedback permits the formulation ofmore » a quadratic Lyapunov function for this class of networks. This approach is particularly interesting since synchronization conditions are difficult to obtain by means of quadratic Lyapunov functions when only current feedback is used and for networks composed of series R-L circuits. Our synchronization condition depends on the algebraic connectivity of the underlying network, and reiterates the conventional wisdom from Lyapunov- and passivity-based arguments that strong coupling is required to ensure synchronization.« less

Offline handwritten word recognition using MQDF-HMMs

NASA Astrophysics Data System (ADS)

Ramachandrula, Sitaram; Hambarde, Mangesh; Patial, Ajay; Sahoo, Dushyant; Kochar, Shaivi

2015-01-01

We propose an improved HMM formulation for offline handwriting recognition (HWR). The main contribution of this work is using modified quadratic discriminant function (MQDF) [1] within HMM framework. In an MQDF-HMM the state observation likelihood is calculated by a weighted combination of MQDF likelihoods of individual Gaussians of GMM (Gaussian Mixture Model). The quadratic discriminant function (QDF) of a multivariate Gaussian can be rewritten by avoiding the inverse of covariance matrix by using the Eigen values and Eigen vectors of it. The MQDF is derived from QDF by substituting few of badly estimated lower-most Eigen values by an appropriate constant. The estimation errors of non-dominant Eigen vectors and Eigen values of covariance matrix for which the training data is insufficient can be controlled by this approach. MQDF has been successfully shown to improve the character recognition performance [1]. The usage of MQDF in HMM improves the computation, storage and modeling power of HMM when there is limited training data. We have got encouraging results on offline handwritten character (NIST database) and word recognition in English using MQDF HMMs.

Calculation of the electron wave function in a graded-channel double-heterojunction modulation-doped field-effect transistor

NASA Technical Reports Server (NTRS)

Mui, D. S. L.; Patil, M. B.; Morkoc, H.

1989-01-01

Three double-heterojunction modulation-doped field-effect transistor structures with different channel composition are investigated theoretically. All of these transistors have an In(x)Ga(1-x)As channel sandwiched between two doped Al(0.3)Ga(0.7)As barriers with undoped spacer layers. In one of the structures, x varies from 0 from either heterojunction to 0.15 at the center of the channel quadratically; in the other two, constant values of x of 0 and 0.15 are used. The Poisson and Schroedinger equations are solved self-consistently for the electron wave function in all three cases. The results showed that the two-dimensional electron gas (2DEG) concentration in the channel of the quadratically graded structure is higher than the x = 0 one and slightly lower than the x = 0.15 one, and the mean distance of the 2DEG is closer to the center of the channel for this transistor than the other two. These two effects have important implications on the electron mobility in the channel.

Battle for Climate and Scarcity Rents: Beyond the Linear-Quadratic Case.

PubMed

Kagan, Mark; van der Ploeg, Frederick; Withagen, Cees

Industria imports oil, produces final goods and wishes to mitigate global warming. Oilrabia exports oil and buys final goods from the other country. Industria uses the carbon tax to impose an import tariff on oil and steal some of Oilrabia's scarcity rent. Conversely, Oilrabia has monopoly power and sets the oil price to steal some of Industria's climate rent. We analyze the relative speeds of oil extraction and carbon accumulation under these strategic interactions for various production function specifications and compare these with the efficient and competitive outcomes. We prove that for the class of HARA production functions, the oil price is initially higher and subsequently lower in the open-loop Nash equilibrium than in the efficient outcome. The oil extraction rate is thus initially too low and in later stages too high. The HARA class includes linear, loglinear and semi-loglinear demand functions as special cases. For non-HARA production functions, Oilrabia may in the open-loop Nash equilibrium initially price oil lower than the efficient level, thus resulting in more oil extraction and climate damages. We also contrast the open-loop Nash and efficient outcomes numerically with the feedback Nash outcomes. We find that the optimal carbon tax path in the feedback Nash equilibrium is flatter than in the open-loop Nash equilibrium. It turns out that for certain demand functions using the carbon tax as an import tariff may hurt consumers' welfare as the resulting user cost of oil is so high that the fall in welfare wipes out the gain from higher tariff revenues.

Richness in Functional Connectivity Depends on the Neuronal Integrity within the Posterior Cingulate Cortex

PubMed Central

Lord, Anton R.; Li, Meng; Demenescu, Liliana R.; van den Meer, Johan; Borchardt, Viola; Krause, Anna Linda; Heinze, Hans-Jochen; Breakspear, Michael; Walter, Martin

2017-01-01

The brain's connectivity skeleton—a rich club of strongly interconnected members—was initially shown to exist in human structural networks, but recent evidence suggests a functional counterpart. This rich club typically includes key regions (or hubs) from multiple canonical networks, reducing the cost of inter-network communication. The posterior cingulate cortex (PCC), a hub node embedded within the default mode network, is known to facilitate communication between brain networks and is a key member of the “rich club.” Here, we assessed how metabolic signatures of neuronal integrity and cortical thickness influence the global extent of a functional rich club as measured using the functional rich club coefficient (fRCC). Rich club estimation was performed on functional connectivity of resting state brain signals acquired at 3T in 48 healthy adult subjects. Magnetic resonance spectroscopy was measured in the same session using a point resolved spectroscopy sequence. We confirmed convergence of functional rich club with a previously established structural rich club. N-acetyl aspartate (NAA) in the PCC is significantly correlated with age (p = 0.001), while the rich club coefficient showed no effect of age (p = 0.106). In addition, we found a significant quadratic relationship between fRCC and NAA concentration in PCC (p = 0.009). Furthermore, cortical thinning in the PCC was correlated with a reduced rich club coefficient after accounting for age and NAA. In conclusion, we found that the fRCC is related to a marker of neuronal integrity in a key region of the cingulate cortex. Furthermore, cortical thinning in the same area was observed, suggesting that both cortical thinning and neuronal integrity in the hub regions influence functional integration of at a whole brain level. PMID:28439224

Richness in Functional Connectivity Depends on the Neuronal Integrity within the Posterior Cingulate Cortex.

PubMed

Lord, Anton R; Li, Meng; Demenescu, Liliana R; van den Meer, Johan; Borchardt, Viola; Krause, Anna Linda; Heinze, Hans-Jochen; Breakspear, Michael; Walter, Martin

2017-01-01

The brain's connectivity skeleton-a rich club of strongly interconnected members-was initially shown to exist in human structural networks, but recent evidence suggests a functional counterpart. This rich club typically includes key regions (or hubs) from multiple canonical networks, reducing the cost of inter-network communication. The posterior cingulate cortex (PCC), a hub node embedded within the default mode network, is known to facilitate communication between brain networks and is a key member of the "rich club." Here, we assessed how metabolic signatures of neuronal integrity and cortical thickness influence the global extent of a functional rich club as measured using the functional rich club coefficient (fRCC). Rich club estimation was performed on functional connectivity of resting state brain signals acquired at 3T in 48 healthy adult subjects. Magnetic resonance spectroscopy was measured in the same session using a point resolved spectroscopy sequence. We confirmed convergence of functional rich club with a previously established structural rich club. N-acetyl aspartate (NAA) in the PCC is significantly correlated with age ( p = 0.001), while the rich club coefficient showed no effect of age (p = 0.106). In addition, we found a significant quadratic relationship between fRCC and NAA concentration in PCC ( p = 0.009). Furthermore, cortical thinning in the PCC was correlated with a reduced rich club coefficient after accounting for age and NAA. In conclusion, we found that the fRCC is related to a marker of neuronal integrity in a key region of the cingulate cortex. Furthermore, cortical thinning in the same area was observed, suggesting that both cortical thinning and neuronal integrity in the hub regions influence functional integration of at a whole brain level.

The Relationship between Running Velocity and the Energy Cost of Turning during Running

PubMed Central

Hatamoto, Yoichi; Yamada, Yosuke; Sagayama, Hiroyuki; Higaki, Yasuki; Kiyonaga, Akira; Tanaka, Hiroaki

2014-01-01

Ball game players frequently perform changes of direction (CODs) while running; however, there has been little research on the physiological impact of CODs. In particular, the effect of running velocity on the physiological and energy demands of CODs while running has not been clearly determined. The purpose of this study was to examine the relationship between running velocity and the energy cost of a 180°COD and to quantify the energy cost of a 180°COD. Nine male university students (aged 18–22 years) participated in the study. Five shuttle trials were performed in which the subjects were required to run at different velocities (3, 4, 5, 6, 7, and 8 km/h). Each trial consisted of four stages with different turn frequencies (13, 18, 24 and 30 per minute), and each stage lasted 3 minutes. Oxygen consumption was measured during the trial. The energy cost of a COD significantly increased with running velocity (except between 7 and 8 km/h, p = 0.110). The relationship between running velocity and the energy cost of a 180°COD is best represented by a quadratic function (y = −0.012+0.066x +0.008x2, [r = 0.994, p = 0.001]), but is also well represented by a linear (y = −0.228+0.152x, [r = 0.991, p<0.001]). These data suggest that even low running velocities have relatively high physiological demands if the COD frequency increases, and that running velocities affect the physiological demands of CODs. These results also showed that the energy expenditure of COD can be evaluated using only two data points. These results may be useful for estimating the energy expenditure of players during a match and designing shuttle exercise training programs. PMID:24497913

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

PubMed Central

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

2016-01-01

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

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…

Optimal External Wrench Distribution During a Multi-Contact Sit-to-Stand Task.

PubMed

Bonnet, Vincent; Azevedo-Coste, Christine; Robert, Thomas; Fraisse, Philippe; Venture, Gentiane

2017-07-01

This paper aims at developing and evaluating a new practical method for the real-time estimate of joint torques and external wrenches during multi-contact sit-to-stand (STS) task using kinematics data only. The proposed method allows also identifying subject specific body inertial segment parameters that are required to perform inverse dynamics. The identification phase is performed using simple and repeatable motions. Thanks to an accurately identified model the estimate of the total external wrench can be used as an input to solve an under-determined multi-contact problem. It is solved using a constrained quadratic optimization process minimizing a hybrid human-like energetic criterion. The weights of this hybrid cost function are adjusted and a sensitivity analysis is performed in order to reproduce robustly human external wrench distribution. The results showed that the proposed method could successfully estimate the external wrenches under buttocks, feet, and hands during STS tasks (RMS error lower than 20 N and 6 N.m). The simplicity and generalization abilities of the proposed method allow paving the way of future diagnosis solutions and rehabilitation applications, including in-home use.

Polynomial-time quantum algorithm for the simulation of chemical dynamics

PubMed Central

Kassal, Ivan; Jordan, Stephen P.; Love, Peter J.; Mohseni, Masoud; Aspuru-Guzik, Alán

2008-01-01

The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can be applied only to small systems. By contrast, we demonstrate that quantum computers could exactly simulate chemical reactions in polynomial time. Our algorithm uses the split-operator approach and explicitly simulates all electron-nuclear and interelectronic interactions in quadratic time. Surprisingly, this treatment is not only more accurate than the Born–Oppenheimer approximation but faster and more efficient as well, for all reactions with more than about four atoms. This is the case even though the entire electronic wave function is propagated on a grid with appropriately short time steps. Although the preparation and measurement of arbitrary states on a quantum computer is inefficient, here we demonstrate how to prepare states of chemical interest efficiently. We also show how to efficiently obtain chemically relevant observables, such as state-to-state transition probabilities and thermal reaction rates. Quantum computers using these techniques could outperform current classical computers with 100 qubits. PMID:19033207

Global optimization methods for engineering design

NASA Technical Reports Server (NTRS)

Arora, Jasbir S.

1990-01-01

The problem is to find a global minimum for the Problem P. Necessary and sufficient conditions are available for local optimality. However, global solution can be assured only under the assumption of convexity of the problem. If the constraint set S is compact and the cost function is continuous on it, existence of a global minimum is guaranteed. However, in view of the fact that no global optimality conditions are available, a global solution can be found only by an exhaustive search to satisfy Inequality. The exhaustive search can be organized in such a way that the entire design space need not be searched for the solution. This way the computational burden is reduced somewhat. It is concluded that zooming algorithm for global optimizations appears to be a good alternative to stochastic methods. More testing is needed; a general, robust, and efficient local minimizer is required. IDESIGN was used in all numerical calculations which is based on a sequential quadratic programming algorithm, and since feasible set keeps on shrinking, a good algorithm to find an initial feasible point is required. Such algorithms need to be developed and evaluated.

Optimal Attack Strategies Subject to Detection Constraints Against Cyber-Physical Systems

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

Chen, Yuan; Kar, Soummya; Moura, Jose M. F.

This paper studies an attacker against a cyberphysical system (CPS) whose goal is to move the state of a CPS to a target state while ensuring that his or her probability of being detected does not exceed a given bound. The attacker’s probability of being detected is related to the nonnegative bias induced by his or her attack on the CPS’s detection statistic. We formulate a linear quadratic cost function that captures the attacker’s control goal and establish constraints on the induced bias that reflect the attacker’s detection-avoidance objectives. When the attacker is constrained to be detected at the false-alarmmore » rate of the detector, we show that the optimal attack strategy reduces to a linear feedback of the attacker’s state estimate. In the case that the attacker’s bias is upper bounded by a positive constant, we provide two algorithms – an optimal algorithm and a sub-optimal, less computationally intensive algorithm – to find suitable attack sequences. Lastly, we illustrate our attack strategies in numerical examples based on a remotely-controlled helicopter under attack.« less

A preliminary look at an optimal multivariable design for propulsion-only flight control of jet-transport aircraft

NASA Technical Reports Server (NTRS)

Azzano, Christopher P.

1992-01-01

Control of a large jet transport aircraft without the use of conventional control surfaces was studied. Engine commands were used to attempt to recreate the forces and moments typically provided by the elevator, ailerons, and rudder. Necessary conditions for aircraft controllability were developed pertaining to aircraft configuration such as the number of engines and engine placement. An optimal linear quadratic regulator controller was developed for the Boeing 707-720, in particular, for regulation of its natural dynamic modes. The design used a method of assigning relative weights to the natural modes, i.e., phugoid and dutch roll, for a more intuitive selection of the cost function. A prototype pilot command interface was then integrated into the loop based on pseudorate command of both pitch and roll. Closed loop dynamics were evaluated first with a batch linear simulation and then with a real time high fidelity piloted simulation. The NASA research pilots assisted in evaluation of closed loop handling qualities for typical cruise and landing tasks. Recommendations for improvement on this preliminary study of optimal propulsion only flight control are provided.

Utilization of rice husks modified by organomultiphosphonic acids as low-cost biosorbents for enhanced adsorption of heavy metal ions.

PubMed

Xu, Mingyu; Yin, Ping; Liu, Xiguang; Tang, Qinghua; Qu, Rongjun; Xu, Qiang

2013-12-01

Novel biosorbent materials (RH-2 and RH-3) obtained from agricultural waste materials rice husks (RH-1) were successfully developed through fast and facile esterification reactions with hydroxylethylidenediphosphonic acid and nitrilotrimethylenetriphosphonic acid, respectively. The present paper reported the feasibility of using RH-1, RH-2 and RH-3 for removal of heavy metals from simulated wastewater, the results revealed that the adsorption property of functionalized rice husks with organotriphosphonic acid RH-3 for Au(III) was very excellent, especially for gold ions. The combined effect of initial solution pH, RH-3 dosage and initial Au(III) concentration was investigated using response surface methodology (RSM), the results showed that initial Au(III) concentration exerted stronger influence on Au(III) uptake than initial pH and biomass dosage. The analysis of variance (ANOVA) of the quadratic model demonstrated that the model was highly significant, and under the optimum process conditions, the maximum adsorption capacity could reach 3.25 ± 0.07 mmol/g that is higher than other reported adsorbents. Copyright © 2013 Elsevier Ltd. All rights reserved.

Approximate N-Player Nonzero-Sum Game Solution for an Uncertain Continuous Nonlinear System.

PubMed

Johnson, Marcus; Kamalapurkar, Rushikesh; Bhasin, Shubhendu; Dixon, Warren E

2015-08-01

An approximate online equilibrium solution is developed for an N -player nonzero-sum game subject to continuous-time nonlinear unknown dynamics and an infinite horizon quadratic cost. A novel actor-critic-identifier structure is used, wherein a robust dynamic neural network is used to asymptotically identify the uncertain system with additive disturbances, and a set of critic and actor NNs are used to approximate the value functions and equilibrium policies, respectively. The weight update laws for the actor neural networks (NNs) are generated using a gradient-descent method, and the critic NNs are generated by least square regression, which are both based on the modified Bellman error that is independent of the system dynamics. A Lyapunov-based stability analysis shows that uniformly ultimately bounded tracking is achieved, and a convergence analysis demonstrates that the approximate control policies converge to a neighborhood of the optimal solutions. The actor, critic, and identifier structures are implemented in real time continuously and simultaneously. Simulations on two and three player games illustrate the performance of the developed method.

Optimal Attack Strategies Subject to Detection Constraints Against Cyber-Physical Systems

DOE PAGES

Chen, Yuan; Kar, Soummya; Moura, Jose M. F.

2017-03-31

This paper studies an attacker against a cyberphysical system (CPS) whose goal is to move the state of a CPS to a target state while ensuring that his or her probability of being detected does not exceed a given bound. The attacker’s probability of being detected is related to the nonnegative bias induced by his or her attack on the CPS’s detection statistic. We formulate a linear quadratic cost function that captures the attacker’s control goal and establish constraints on the induced bias that reflect the attacker’s detection-avoidance objectives. When the attacker is constrained to be detected at the false-alarmmore » rate of the detector, we show that the optimal attack strategy reduces to a linear feedback of the attacker’s state estimate. In the case that the attacker’s bias is upper bounded by a positive constant, we provide two algorithms – an optimal algorithm and a sub-optimal, less computationally intensive algorithm – to find suitable attack sequences. Lastly, we illustrate our attack strategies in numerical examples based on a remotely-controlled helicopter under attack.« less

Bias of cylinder diameter estimation from ground-based laser scanners with different beam widths: A simulation study

NASA Astrophysics Data System (ADS)

Forsman, Mona; Börlin, Niclas; Olofsson, Kenneth; Reese, Heather; Holmgren, Johan

2018-01-01

In this study we have investigated why diameters of tree stems, which are approximately cylindrical, are often overestimated by mobile laser scanning. This paper analyzes the physical processes when using ground-based laser scanning that may contribute to a bias when estimating cylinder diameters using circle-fit methods. A laser scanner simulator was implemented and used to evaluate various properties, such as distance, cylinder diameter, and beam width of a laser scanner-cylinder system to find critical conditions. The simulation results suggest that a positive bias of the diameter estimation is expected. Furthermore, the bias follows a quadratic function of one parameter - the relative footprint, i.e., the fraction of the cylinder width illuminated by the laser beam. The quadratic signature opens up a possibility to construct a compensation model for the bias.

Robust decentralised stabilisation of uncertain large-scale interconnected nonlinear descriptor systems via proportional plus derivative feedback

NASA Astrophysics Data System (ADS)

Li, Jian; Zhang, Qingling; Ren, Junchao; Zhang, Yanhao

2017-10-01

This paper studies the problem of robust stability and stabilisation for uncertain large-scale interconnected nonlinear descriptor systems via proportional plus derivative state feedback or proportional plus derivative output feedback. The basic idea of this work is to use the well-known differential mean value theorem to deal with the nonlinear model such that the considered nonlinear descriptor systems can be transformed into linear parameter varying systems. By using a parameter-dependent Lyapunov function, a decentralised proportional plus derivative state feedback controller and decentralised proportional plus derivative output feedback controller are designed, respectively such that the closed-loop system is quadratically normal and quadratically stable. Finally, a hypersonic vehicle practical simulation example and numerical example are given to illustrate the effectiveness of the results obtained in this paper.

Thermodynamics of charged Lifshitz black holes with quadratic corrections

NASA Astrophysics Data System (ADS)

Bravo-Gaete, Moisés; Hassaïne, Mokhtar

2015-03-01

In arbitrary dimension, we consider the Einstein-Maxwell Lagrangian supplemented by the more general quadratic-curvature corrections. For this model, we derive four classes of charged Lifshitz black hole solutions for which the metric function is shown to depend on a unique integration constant. The masses of these solutions are computed using the quasilocal formalism based on the relation established between the off-shell Abbott-Deser-Tekin and Noether potentials. Among these four solutions, three of them are interpreted as extremal in the sense that their masses vanish identically. For the last family of solutions, both the quasilocal mass and the electric charge are shown to depend on the integration constant. Finally, we verify that the first law of thermodynamics holds for each solution and a Smarr formula is also established for the four solutions.

Ambiguity resolution for satellite Doppler positioning systems

NASA Technical Reports Server (NTRS)

Argentiero, P. D.; Marini, J. W.

1977-01-01

A test for ambiguity resolution was derived which was the most powerful in the sense that it maximized the probability of a correct decision. When systematic error sources were properly included in the least squares reduction process to yield an optimal solution, the test reduced to choosing the solution which provided the smaller valuation of the least squares loss function. When systematic error sources were ignored in the least squares reduction, the most powerful test was a quadratic form comparison with the weighting matrix of the quadratic form obtained by computing the pseudo-inverse of a reduced rank square matrix. A formula is presented for computing the power of the most powerful test. A numerical example is included in which the power of the test is computed for a situation which may occur during an actual satellite aided search and rescue mission.

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

NASA Astrophysics Data System (ADS)

Zimina, S. V.

2015-06-01

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

Minimizing distortion and internal forces in truss structures by simulated annealing

NASA Technical Reports Server (NTRS)

Kincaid, Rex K.

1989-01-01

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

Accurate evaluation of exchange fields in finite element micromagnetic solvers

NASA Astrophysics Data System (ADS)

Chang, R.; Escobar, M. A.; Li, S.; Lubarda, M. V.; Lomakin, V.

2012-04-01

Quadratic basis functions (QBFs) are implemented for solving the Landau-Lifshitz-Gilbert equation via the finite element method. This involves the introduction of a set of special testing functions compatible with the QBFs for evaluating the Laplacian operator. The results by using QBFs are significantly more accurate than those via linear basis functions. QBF approach leads to significantly more accurate results than conventionally used approaches based on linear basis functions. Importantly QBFs allow reducing the error of computing the exchange field by increasing the mesh density for structured and unstructured meshes. Numerical examples demonstrate the feasibility of the method.

Some New Estimation Methods for Weighted Regression When There are Possible Outliers.

DTIC Science & Technology

1985-01-01

about influential points, and to add to our understanding of the structure of the data In Section 2 we show, by considering the influence function , why... influence function lampel; 1968, 1974) for the maximum likelihood esti- mator is proportional to (EP-l)h(x), where £= (y-x’B)exp[-h’(x)e], and is thus...unbounded. Since the influence function for the MLE is quadratic in the residual c, in theory a point with a sufficiently large residual can have an

Quadratic Damping

ERIC Educational Resources Information Center

Fay, Temple H.

2012-01-01

Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…

Visualising the Roots of Quadratic Equations with Complex Coefficients

ERIC Educational Resources Information Center

Bardell, Nicholas S.

2014-01-01

This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…

Simply Prairie Homepage

Science.gov Websites

Ed Home - Data Home PRAIRIE ADVOCATES Project - QUADRAT STUDY Project Answer research questions multi-state quadrat study. Bob Lootens, Fermilab Join us! Check out the Quadrat Study Project. Prairie study a prairie "expert" to facilitate your research student Internet access an e-mail address

Ground Juniperus pinchotii and urea in supplements fed to Rambouillet ewe lambs: I. Feedlot growth traits, blood serum parameters, and fecal characteristics.

PubMed

Whitney, T R

2017-08-01

Ground woody products and urea are low-cost roughage and N sources. Rambouillet ewe lambs ( = 48, 6 lambs/treatment; initial BW = 42 kg ± 3.8) were used to evaluate effects of using ground (juniper) and urea in supplements on feedlot lamb growth traits, blood serum parameters, and fecal characteristics. In a randomized complete block design (40 d), lambs were individually fed an ad libitum basal sorghum-Sudangrass hay diet, which was fed separate from 1 of 8 supplemental diets (6 lambs/diet; 533 g of supplement/d, as-fed basis). Treatment structure was a 4 × 2 factorial: 4 concentrations of ground juniper (JN: 15%, 30%, 45%, or 60% of DM) and 2 concentrations of urea (UR: 1 or 3% of DM). Lamb growth traits were evaluated on d 0, 5, 12, 19, 26, 33, and 40; blood serum was evaluated on d 6 to 8, 20 to 22, and 34 (at h 3 and 6), and feces was evaluated on d 35. Compared to lambs fed all of the other treatments, lambs fed JN60UR1 or JN60UR3 had reduced supplement DMI (negative quadratic, = 0.007). Hay and total DMI were variable across day (JN × UR × day, < 0.04), but no linear or quadratic trends were detected ( > 0.10). A JN × day interaction was detected ( < 0.001) for lamb BW and the JN × day negative quadratic trend ( = 0.02) for BW was influenced by reduced ADG (linear decrease, < 0.001) of lambs fed JN60. Lambs supplemented with UR3 vs. UR1 tended ( = 0.06) to have reduced BW but had similar ( > 0.17) ADG and G:F. Lamb G:F fluctuated across day (JN × day, = 0.007), but the JN × day quadratic trend ( < 0.001) was mainly due to reduced G:F in lambs fed JN45 or JN60 diets. As the percentage of JN increased in the supplement, serum IGF-1 linearly decreased ( = 0.04), and serum urea N quadratically increased ( < 0.001). The UR × hour interaction ( < 0.001) for serum urea N resulted from a greater decline from 3 to 6 h after feeding in lambs supplemented with UR1 vs. UR3. Increasing JN concentration tended to quadratically increase ( = 0.09) fecal DM and linearly decrease ( = 0.002) fecal N, but an effect due to dietary UR was not detected ( > 0.34). Results indicated that daily supplement DMI was restricted only by using JN60. However, a 60% JN-based supplement will not make an effective rangeland supplement for growing ewe lambs, and using 3% UR should not be considered, especially since daily UR intake was not restricted enough to be considered safe.

Role of orbital filling on nonlinear ionic Raman scattering in perovskite titanates

NASA Astrophysics Data System (ADS)

Gu, Mingqiang; Rondinelli, James M.

2017-01-01

The linear and nonlinear phononic interactions between an optically excited infrared (IR) or hyper-Raman mode and a driven Raman mode are computed for the d0 (CaTiO3) and d1 (LaTiO3) titanates within a first-principles density functional framework. We calculate the potential energy surface expanded in terms of the Ag or B1 g mode amplitudes coupled to the Au or the B3 u mode and determine the coupling coefficients for these multimode interactions. We find that the linear-quadratic coupling dominates the anharmonicities over the quadratic-quadratic interaction in the perovskite titanates. The IR and Raman modes both modify the electronic structure with the former being more significant but occurring on a different time scale; furthermore, the coupled-mode interactions lead to sizable perturbations to the valence bandwidth (˜100 meV ) and band gap (˜50 meV). By comparing the coupling coefficients of undoped CaTiO3 and LaTiO3 to those for electron-doped (CaTiO3) and hole-doped (LaTiO3) titanates, we isolate the role of orbital filling in the nonlinear coupling process. We find that with increasing occupancy of the d manifold, the linear-quadratic interaction decreases by approximately 30% with minor changes induced by the cation chemistry (that mainly affect the phonon mode frequencies) or by electron correlation. We identify the importance of the Ti-O bond stiffness, which depends on the orbital filling, in governing the lattice anharmonicitiy. This microscopic understanding can be used to increase the nonlinear coupling coefficient to facilitate more facile access of nonequilibrium structures and properties through ionic Raman scattering processes.

Kinematic parameters of internal waves of the second mode in the South China Sea

NASA Astrophysics Data System (ADS)

Kurkina, Oxana; Talipova, Tatyana; Soomere, Tarmo; Giniyatullin, Ayrat; Kurkin, Andrey

2017-10-01

Spatial distributions of the main properties of the mode function and kinematic and non-linear parameters of internal waves of the second mode are derived for the South China Sea for typical summer conditions in July. The calculations are based on the Generalized Digital Environmental Model (GDEM) climatology of hydrological variables, from which the local stratification is evaluated. The focus is on the phase speed of long internal waves and the coefficients at the dispersive, quadratic and cubic terms of the weakly non-linear Gardner model. Spatial distributions of these parameters, except for the coefficient at the cubic term, are qualitatively similar for waves of both modes. The dispersive term of Gardner's equation and phase speed for internal waves of the second mode are about a quarter and half, respectively, of those for waves of the first mode. Similarly to the waves of the first mode, the coefficients at the quadratic and cubic terms of Gardner's equation are practically independent of water depth. In contrast to the waves of the first mode, for waves of the second mode the quadratic term is mostly negative. The results can serve as a basis for expressing estimates of the expected parameters of internal waves for the South China Sea.

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

PubMed

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

2017-06-21

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

Formalism for the solution of quadratic Hamiltonians with large cosine terms

NASA Astrophysics Data System (ADS)

Ganeshan, Sriram; Levin, Michael

2016-02-01

We consider quantum Hamiltonians of the form H =H0-U ∑jcos(Cj) , where H0 is a quadratic function of position and momentum variables {x1,p1,x2,p2,⋯} and the Cj's are linear in these variables. We allow H0 and Cj to be completely general with only two restrictions: we require that (1) the Cj's are linearly independent and (2) [Cj,Ck] is an integer multiple of 2 π i for all j ,k so that the different cosine terms commute with one another. Our main result is a recipe for solving these Hamiltonians and obtaining their exact low-energy spectrum in the limit U →∞ . This recipe involves constructing creation and annihilation operators and is similar in spirit to the procedure for diagonalizing quadratic Hamiltonians. In addition to our exact solution in the infinite U limit, we also discuss how to analyze these systems when U is large but finite. Our results are relevant to a number of different physical systems, but one of the most natural applications is to understanding the effects of electron scattering on quantum Hall edge modes. To demonstrate this application, we use our formalism to solve a toy model for a fractional quantum spin Hall edge with different types of impurities.

Geometric quadratic stochastic operator on countable infinite set

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

Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

2015-02-03

In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.

Estimating factors influencing the detection probability of semiaquatic freshwater snails using quadrat survey methods

USGS Publications Warehouse

Roesler, Elizabeth L.; Grabowski, Timothy B.

2018-01-01

Developing effective monitoring methods for elusive, rare, or patchily distributed species requires extra considerations, such as imperfect detection. Although detection is frequently modeled, the opportunity to assess it empirically is rare, particularly for imperiled species. We used Pecos assiminea (Assiminea pecos), an endangered semiaquatic snail, as a case study to test detection and accuracy issues surrounding quadrat searches. Quadrats (9 × 20 cm; n = 12) were placed in suitable Pecos assiminea habitat and randomly assigned a treatment, defined as the number of empty snail shells (0, 3, 6, or 9). Ten observers rotated through each quadrat, conducting 5-min visual searches for shells. The probability of detecting a shell when present was 67.4 ± 3.0%, but it decreased with the increasing litter depth and fewer number of shells present. The mean (± SE) observer accuracy was 25.5 ± 4.3%. Accuracy was positively correlated to the number of shells in the quadrat and negatively correlated to the number of times a quadrat was searched. The results indicate quadrat surveys likely underrepresent true abundance, but accurately determine the presence or absence. Understanding detection and accuracy of elusive, rare, or imperiled species improves density estimates and aids in monitoring and conservation efforts.

Clarifying functional roles: algal removal by the surgeonfishes Ctenochaetus striatus and Acanthurus nigrofuscus

NASA Astrophysics Data System (ADS)

Tebbett, Sterling B.; Goatley, Christopher H. R.; Bellwood, David R.

2017-09-01

The lined bristletooth, Ctenochaetus striatus, and the brown surgeonfish, Acanthurus nigrofuscus, are among the most abundant surgeonfishes on Indo-Pacific coral reefs. Yet, the functional role of these species has been the focus of an ongoing debate lasting at least six decades. Specifically, to what extent are C. striatus herbivorous like the visually similar A. nigrofuscus? To address this question, we used natural feeding surfaces, covered with late successional stage reef-grown algal turfs, to examine turf algal removal by the two species. Surfaces exposed to C. striatus in laboratory experiments exhibited no significant reductions in turf length or area covered by turfing algae. In marked contrast, A. nigrofuscus reduced turf length by 51% and area covered by turfing algae by 15% in 1 h. The gut contents of specimens from the reef revealed that A. nigrofuscus predominantly ingests algae (the dominant item in 79.6-94.7% of gut content quadrats), while C. striatus ingests detritus and sediments (dominant in 99.6-100% of quadrats). Therefore, C. striatus ingests detritus and sediment, leaving mature algal turfs relatively intact, while A. nigrofuscus directly removes and ingests turf algae. The function of C. striatus differs from cropping herbivorous surgeonfishes such as A. nigrofuscus. On coral reefs, C. striatus brush detrital aggregates from algal turfs, removing microorganisms, organic detritus and inorganic sediment. Confusion over the functional role of C. striatus may stem from an inability to fit it into a single functional category.

Optimal perturbations for nonlinear systems using graph-based optimal transport

NASA Astrophysics Data System (ADS)

Grover, Piyush; Elamvazhuthi, Karthik

2018-06-01

We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on the phase space to a final measure in finite time. The measure is propagated under system dynamics in between the perturbations via the associated transfer operator. Each perturbation is described by a deterministic map in the measure space that implements a version of Monge-Kantorovich optimal transport with quadratic cost. Hence, the optimal solution minimizes a sum of quadratic costs on phase space transport due to the perturbations applied at specified times. The action of the transport map is approximated by a continuous pseudo-time flow on a graph, resulting in a tractable convex optimization problem. This problem is solved via state-of-the-art solvers to global optimality. We apply this algorithm to a problem of transport between measures supported on two disjoint almost-invariant sets in a chaotic fluid system, and to a finite-time optimal mixing problem by choosing the final measure to be uniform. In both cases, the optimal perturbations are found to exploit the phase space structures, such as lobe dynamics, leading to efficient global transport. As the time-horizon of the problem is increased, the optimal perturbations become increasingly localized. Hence, by combining the transfer operator approach with ideas from the theory of optimal mass transportation, we obtain a discrete-time graph-based algorithm for optimal transport and mixing in nonlinear systems.

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

PubMed

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

2012-01-01

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

Extremal entanglement witnesses

NASA Astrophysics Data System (ADS)

Hansen, Leif Ove; Hauge, Andreas; Myrheim, Jan; Sollid, Per Øyvind

2015-02-01

We present a study of extremal entanglement witnesses on a bipartite composite quantum system. We define the cone of witnesses as the dual of the set of separable density matrices, thus TrΩρ≥0 when Ω is a witness and ρ is a pure product state, ρ=ψψ† with ψ=ϕ⊗χ. The set of witnesses of unit trace is a compact convex set, uniquely defined by its extremal points. The expectation value f(ϕ,χ)=TrΩρ as a function of vectors ϕ and χ is a positive semidefinite biquadratic form. Every zero of f(ϕ,χ) imposes strong real-linear constraints on f and Ω. The real and symmetric Hessian matrix at the zero must be positive semidefinite. Its eigenvectors with zero eigenvalue, if such exist, we call Hessian zeros. A zero of f(ϕ,χ) is quadratic if it has no Hessian zeros, otherwise it is quartic. We call a witness quadratic if it has only quadratic zeros, and quartic if it has at least one quartic zero. A main result we prove is that a witness is extremal if and only if no other witness has the same, or a larger, set of zeros and Hessian zeros. A quadratic extremal witness has a minimum number of isolated zeros depending on dimensions. If a witness is not extremal, then the constraints defined by its zeros and Hessian zeros determine all directions in which we may search for witnesses having more zeros or Hessian zeros. A finite number of iterated searches in random directions, by numerical methods, leads to an extremal witness which is nearly always quadratic and has the minimum number of zeros. We discuss briefly some topics related to extremal witnesses, in particular the relation between the facial structures of the dual sets of witnesses and separable states. We discuss the relation between extremality and optimality of witnesses, and a conjecture of separability of the so-called structural physical approximation (SPA) of an optimal witness. Finally, we discuss how to treat the entanglement witnesses on a complex Hilbert space as a subset of the witnesses on a real Hilbert space.

Computing an upper bound on contact stress with surrogate duality

NASA Astrophysics Data System (ADS)

Xuan, Zhaocheng; Papadopoulos, Panayiotis

2016-07-01

We present a method for computing an upper bound on the contact stress of elastic bodies. The continuum model of elastic bodies with contact is first modeled as a constrained optimization problem by using finite elements. An explicit formulation of the total contact force, a fraction function with the numerator as a linear function and the denominator as a quadratic convex function, is derived with only the normalized nodal contact forces as the constrained variables in a standard simplex. Then two bounds are obtained for the sum of the nodal contact forces. The first is an explicit formulation of matrices of the finite element model, derived by maximizing the fraction function under the constraint that the sum of the normalized nodal contact forces is one. The second bound is solved by first maximizing the fraction function subject to the standard simplex and then using Dinkelbach's algorithm for fractional programming to find the maximum—since the fraction function is pseudo concave in a neighborhood of the solution. These two bounds are solved with the problem dimensions being only the number of contact nodes or node pairs, which are much smaller than the dimension for the original problem, namely, the number of degrees of freedom. Next, a scheme for constructing an upper bound on the contact stress is proposed that uses the bounds on the sum of the nodal contact forces obtained on a fine finite element mesh and the nodal contact forces obtained on a coarse finite element mesh, which are problems that can be solved at a lower computational cost. Finally, the proposed method is verified through some examples concerning both frictionless and frictional contact to demonstrate the method's feasibility, efficiency, and robustness.

Explicit asymmetric bounds for robust stability of continuous and discrete-time systems

NASA Technical Reports Server (NTRS)

Gao, Zhiqiang; Antsaklis, Panos J.

1993-01-01

The problem of robust stability in linear systems with parametric uncertainties is considered. Explicit stability bounds on uncertain parameters are derived and expressed in terms of linear inequalities for continuous systems, and inequalities with quadratic terms for discrete-times systems. Cases where system parameters are nonlinear functions of an uncertainty are also examined.

Orientations toward Mathematical Processes of Prospective Secondary Mathematics Teachers as Related to Work with Tasks

ERIC Educational Resources Information Center

Cannon, Tenille

2016-01-01

Mathematics can be conceptualized in different ways. Policy documents such as the National Council of Teachers of Mathematics (NCTM) (2000) and the Common Core State Standards Initiative (CCSSI) (2010), classify mathematics in terms of mathematical content (e.g., quadratic functions, Pythagorean theorem) and mathematical activity in the form of…

Compact Numerical Function Generators Based on Quadratic Approximation: Architecture and Synthesis Method

DTIC Science & Technology

2006-12-01

Specifi- cation described by Scilab [19], a MATLAB-like software, into HDL code. The Design Specification consists of a func- tion f (x), a domain over x...In- ter. Conf. on Field Programmable Logic and Applications (FPL’05), pp.118–123, Tampere, Finland, Aug. 2005. [19] Scilab 3.0, INRIA-ENPC, France

Programmable Numerical Function Generators Based on Quadratic Approximation: Architecture and Synthesis Method

DTIC Science & Technology

2006-01-01

experts. Fig. 1 shows the synthesis flow for the NFG. It converts the Design Specification described by Scilab [18], a MATLAB-like software, into HDL...Tam- pare, Finland, pp. 118–123, Aug. 2005. [18] Scilab 3.0, INRIA-ENPC, France, http://scilabsoft.inria.fr/ [19] M. J. Schulte and J. E. Stine

An Application of Quadratic Functions to Australian Government Policy on Funding Schools

ERIC Educational Resources Information Center

Nillsen, Rodney

2007-01-01

In the "Sydney Morning Herald" of 23 March 2005, Ross Gittins argued that the funding arrangements for private schools positively encourage parents to move their children from the state system. The then Federal Minister for Education, Dr Brendan Nelson, in a letter to the "Herald" of 25-27 March, responded by saying that 68% of…

Analytical Description of Ascending Motion of Rockets in the Atmosphere

ERIC Educational Resources Information Center

Rodrigues, H.; de Pinho, M. O.; Portes, D., Jr.; Santiago, A.

2009-01-01

In continuation of a previous work, we present an analytic study of ascending vertical motion of a rocket subjected to a quadratic drag for the case where the mass-variation law is a linear function of time. We discuss the detailed analytical solution of the model differential equations in closed form. Examples of application are presented and…

Effects of gypsy moth infestation on near-view aesthetic preferences and recreation behavior intentions

Treesearch

S.J. Hollenhorst; S.M. Brock; W.A. Freimund; M.J. Twery

1991-01-01

Using the Scenic Beauty Estimator (SBE) approach, near-view color photographs were taken of 25 forested sites exhibiting gypsy moth induced tree mortality from 6% - 97%. A quadratic function of tree mortality by preference rating best described the variability in ratings ( R2 = .60). The effect of flowering mountain laurel flowers was also...

Modelling Transformations of Quadratic Functions: A Proposal of Inductive Inquiry

ERIC Educational Resources Information Center

Sokolowski, Andrzej

2013-01-01

This paper presents a study about using scientific simulations to enhance the process of mathematical modelling. The main component of the study is a lesson whose major objective is to have students mathematise a trajectory of a projected object and then apply the model to formulate other trajectories by using the properties of function…

Optimal partial mass transportation and obstacle Monge-Kantorovich equation

NASA Astrophysics Data System (ADS)

Igbida, Noureddine; Nguyen, Van Thanh

2018-05-01

Optimal partial mass transport, which is a variant of the optimal transport problem, consists in transporting effectively a prescribed amount of mass from a source to a target. The problem was first studied by Caffarelli and McCann (2010) [6] and Figalli (2010) [12] with a particular attention to the quadratic cost. Our aim here is to study the optimal partial mass transport problem with Finsler distance costs including the Monge cost given by the Euclidian distance. Our approach is different and our results do not follow from previous works. Among our results, we introduce a PDE of Monge-Kantorovich type with a double obstacle to characterize active submeasures, Kantorovich potential and optimal flow for the optimal partial transport problem. This new PDE enables us to study the uniqueness and monotonicity results for the active submeasures. Another interesting issue of our approach is its convenience for numerical analysis and computations that we develop in a separate paper [14] (Igbida and Nguyen, 2018).

Cost-Sharing of Ecological Construction Based on Trapezoidal Intuitionistic Fuzzy Cooperative Games

PubMed Central

Liu, Jiacai; Zhao, Wenjian

2016-01-01

There exist some fuzziness and uncertainty in the process of ecological construction. The aim of this paper is to develop a direct and an effective simplified method for obtaining the cost-sharing scheme when some interested parties form a cooperative coalition to improve the ecological environment of Min River together. Firstly, we propose the solution concept of the least square prenucleolus of cooperative games with coalition values expressed by trapezoidal intuitionistic fuzzy numbers. Then, based on the square of the distance in the numerical value between two trapezoidal intuitionistic fuzzy numbers, we establish a corresponding quadratic programming model to obtain the least square prenucleolus, which can effectively avoid the information distortion and uncertainty enlargement brought about by the subtraction of trapezoidal intuitionistic fuzzy numbers. Finally, we give a numerical example about the cost-sharing of ecological construction in Fujian Province in China to show the validity, applicability, and advantages of the proposed model and method. PMID:27834830

Relationship between oxygen cost of walking and level of walking disability after stroke: An experimental study.

PubMed

Polese, Janaine C; Ada, Louise; Teixeira-Salmela, Luci F

2018-01-01

Since physical inactivity is the major risk factor for recurrent stroke, it is important to understand how level of disability impacts oxygen uptake by people after stroke. This study investigated the nature of the relationship between level of disability and oxygen cost in people with chronic stroke. Level of walking disability was measured as comfortable walking speed using the 10-m Walk Test reported in m/s with 55 ambulatory people 2 years after stroke. Oxygen cost was measured during 3 walking tasks: overground walking at comfortable speed, overground walking at fast speed, and stair walking at comfortable speed. Oxygen cost was calculated from oxygen uptake divided by distance covered during walking and reported in ml∙kg -1 ∙m -1 . The relationship between level of walking disability and oxygen cost was curvilinear for all 3 walking tasks. One quadratic model accounted for 81% (95% CI [74, 88]) of the variance in oxygen cost during the 3 walking tasks: [Formula: see text] DISCUSSION: The oxygen cost of walking was related the level of walking disability in people with chronic stroke, such that the more disabled the individual, the higher the oxygen cost of walking; with oxygen cost rising sharply as disability became severe. An equation that relates oxygen cost during different walking tasks according to the level of walking disability allows clinicians to determine oxygen cost indirectly without the difficulty of measuring oxygen uptake directly. Copyright © 2017 John Wiley & Sons, Ltd.

Some Paradoxical Results for the Quadratically Weighted Kappa

ERIC Educational Resources Information Center

Warrens, Matthijs J.

2012-01-01

The quadratically weighted kappa is the most commonly used weighted kappa statistic for summarizing interrater agreement on an ordinal scale. The paper presents several properties of the quadratically weighted kappa that are paradoxical. For agreement tables with an odd number of categories "n" it is shown that if one of the raters uses the same…

Quadratic elongation: A quantitative measure of distortion in coordination polyhedra

USGS Publications Warehouse

Robinson, Kelly F.; Gibbs, G.V.; Ribbe, P.H.

1971-01-01

Quadratic elongation and the variance of bond angles are linearly correlated for distorted octahedral and tetrahedral coordination complexes, both of which show variations in bond length and bond angle. The quadratic elonga tion is dimensionless, giving a quantitative measure of polyhedral distortion which is independent of the effective size of the polyhedron.

Analysis of Students' Error in Learning of Quadratic Equations

ERIC Educational Resources Information Center

Zakaria, Effandi; Ibrahim; Maat, Siti Mistima

2010-01-01

The purpose of the study was to determine the students' error in learning quadratic equation. The samples were 30 form three students from a secondary school in Jambi, Indonesia. Diagnostic test was used as the instrument of this study that included three components: factorization, completing the square and quadratic formula. Diagnostic interview…

No Evidence of Causal Effects of Blood Pressure on Cognition in the Population at Large.

PubMed

Swagerman, Suzanne C; van Bergen, Elsje; Kan, Kees-Jan; Koenis, Marinka M G; Hulshoff Pol, Hilleke E; Boomsma, Dorret I; de Geus, Eco J C

2016-02-01

The large body of literature on the association between blood pressure (BP) and cognitive functioning has yielded mixed results, possibly due to the presence of non-linear effects across age, or because BP affects specific brain areas differently, impacting more on some cognitive skills than on others. If a robust association was detected among BP and specific cognitive tasks, the causal nature of reported associations between BP and cognition could be investigated in twin data, which allow a test of alternative explanations, including genetic pleiotropy. The present study first examines the association between BP and cognition in a sample of 1,140 participants with an age range between 10 and 86 years. Linear and quadratic effects of systolic BP (SBP) and diastolic BP (DBP) on cognitive functioning were examined for 17 tests across five functions. Associations were corrected for effects of sex and linear and quadratic effects of age. Second, to test a causal model, data from 123 monozygotic (MZ) twin pairs were analyzed to test whether cognitive functioning of the twins with the higher BP was different from that of the co-twins with lower BP. Associations between BP and cognitive functioning were absent for the majority of the cognitive tests, with the exception of a lower speed of emotion identification and verbal reasoning in subjects with high diastolic BP. In the MZ twin pair analyses, no effects of BP on cognition were found. We conclude that in the population at large, BP level is not associated with cognitive functioning in a clinically meaningful way.

A robust momentum management and attitude control system for the space station

NASA Technical Reports Server (NTRS)

Speyer, J. L.; Rhee, Ihnseok

1991-01-01

A game theoretic controller is synthesized for momentum management and attitude control of the Space Station in the presence of uncertainties in the moments of inertia. Full state information is assumed since attitude rates are assumed to be very assurately measured. By an input-output decomposition of the uncertainty in the system matrices, the parameter uncertainties in the dynamic system are represented as an unknown gain associated with an internal feedback loop (IFL). The input and output matrices associated with the IFL form directions through which the uncertain parameters affect system response. If the quadratic form of the IFL output augments the cost criterion, then enhanced parameter robustness is anticipated. By considering the input and the input disturbance from the IFL as two noncooperative players, a linear-quadratic differential game is constructed. The solution in the form of a linear controller is used for synthesis. Inclusion of the external disturbance torques results in a dynamic feedback controller which consists of conventional PID (proportional integral derivative) control and cyclic disturbance rejection filters. It is shown that the game theoretic design allows large variations in the inertias in directions of importance.

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

PubMed

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

2017-04-01

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

Robust momentum management and attitude control system for the Space Station

NASA Technical Reports Server (NTRS)

Rhee, Ihnseok; Speyer, Jason L.

1992-01-01

A game theoretic controller is synthesized for momentum management and attitude control of the Space Station in the presence of uncertainties in the moments of inertia. Full state information is assumed since attitude rates are assumed to be very accurately measured. By an input-output decomposition of the uncertainty in the system matrices, the parameter uncertainties in the dynamic system are represented as an unknown gain associated with an internal feedback loop (IFL). The input and output matrices associated with the IFL form directions through which the uncertain parameters affect system response. If the quadratic form of the IFL output augments the cost criterion, then enhanced parameter robustness is anticipated. By considering the input and the input disturbance from the IFL as two noncooperative players, a linear-quadratic differential game is constructed. The solution in the form of a linear controller is used for synthesis. Inclusion of the external disturbance torques results in a dynamic feedback controller which consists of conventional PID (proportional integral derivative) control and cyclic disturbance rejection filters. It is shown that the game theoretic design allows large variations in the inertias in directions of importance.

Steepest descent with momentum for quadratic functions is a version of the conjugate gradient method.

PubMed

Bhaya, Amit; Kaszkurewicz, Eugenius

2004-01-01

It is pointed out that the so called momentum method, much used in the neural network literature as an acceleration of the backpropagation method, is a stationary version of the conjugate gradient method. Connections with the continuous optimization method known as heavy ball with friction are also made. In both cases, adaptive (dynamic) choices of the so called learning rate and momentum parameters are obtained using a control Liapunov function analysis of the system.

Graded-index fibers, Wigner-distribution functions, and the fractional Fourier transform.

PubMed

Mendlovic, D; Ozaktas, H M; Lohmann, A W

1994-09-10

Two definitions of a fractional Fourier transform have been proposed previously. One is based on the propagation of a wave field through a graded-index medium, and the other is based on rotating a function's Wigner distribution. It is shown that both definitions are equivalent. An important result of this equivalency is that the Wigner distribution of a wave field rotates as the wave field propagates through a quadratic graded-index medium. The relation with ray-optics phase space is discussed.

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

PubMed

Alessandri, Angelo; Cervellera, Cristiano; Sanguineti, Marcello

2007-01-01

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

Number Theoretic Background

NASA Astrophysics Data System (ADS)

Rudnick, Z.

Contents: 1. Introduction 2. Divisibility 2.1. Basics on Divisibility 2.2. The Greatest Common Divisor 2.3. The Euclidean Algorithm 2.4. The Diophantine Equation ax+by=c 3. Prime Numbers 3.1. The Fundamental Theorem of Arithmetic 3.2. There Are Infinitely Many Primes 3.3. The Density of Primes 3.4. Primes in Arithmetic Progressions 4. Continued Fractions 5. Modular Arithmetic 5.1. Congruences 5.2. Modular Inverses 5.3. The Chinese Remainder Theorem 5.4. The Structure of the Multiplicative Group (Z/NZ)^* 5.5. Primitive Roots 6. Quadratic Congruences 6.1. Euler's Criterion 6.2. The Legendre Symbol and Quadratic Reciprocity 7. Pell's Equation 7.1. The Group Law 7.2. Integer Solutions 7.3. Finding the Fundamental Solution 8. The Riemann Zeta Function 8.1 Analytic Continuation and Functinal Equation of ζ(s) 8.2 Connecting the Primes and the Zeros of ζ(s) 8.3 The Riemann Hypothesis References

Limit Cycle Bifurcations Near a Piecewise Smooth Generalized Homoclinic Loop with a Saddle-Fold Point

NASA Astrophysics Data System (ADS)

Liang, Feng; Wang, Dechang

In this paper, we suppose that a planar piecewise Hamiltonian system, with a straight line of separation, has a piecewise generalized homoclinic loop passing through a Saddle-Fold point, and assume that there exists a family of piecewise smooth periodic orbits near the loop. By studying the asymptotic expansion of the first order Melnikov function corresponding to the period annulus, we obtain the formulas of the first six coefficients in the expansion, based on which, we provide a lower bound for the maximal number of limit cycles bifurcated from the period annulus. As applications, two concrete systems are considered. Especially, the first one reveals that a quadratic piecewise Hamiltonian system can have five limit cycles near a generalized homoclinic loop under a quadratic piecewise smooth perturbation. Compared with the smooth case [Horozov & Iliev, 1994; Han et al., 1999], three more limit cycles are found.

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

NASA Astrophysics Data System (ADS)

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

1992-01-01

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

Stochastic Multiresonance for a Fractional Linear Oscillator with Quadratic Trichotomous Noise

NASA Astrophysics Data System (ADS)

Zhu, Jian-Qu; Jin, Wei-Dong; Zheng, Gao; Guo, Feng

2017-11-01

The stochastic multiresonance behavior for a fractional linear oscillator with random system frequency is investigated. The fluctuation of the system frequency is a quadratic trichotomous noise, the memory kernel of the fractional oscillator is modeled as a Mittag-Leffler function. Based on linear system theory, applying Laplace transform and the definition of fractional derivative, the expression of the system output amplitude (SPA) is obtained. Stochastic multiresonance phenomenon is found on the curves of SPA versus the memory time and the memory exponent of the fractional oscillator, as well as versus the trichotomous noise amplitude. The SPA depends non-monotonically on the stationary probability of the trichotomous noise, on the viscous damping coefficient and system characteristic frequency of the oscillator, as well as on the driving frequency of external force. Supported by National Natural Science Foundation of China under Grant No. 61134002