The quadratic speedup in Grover's search algorithm from the entanglement perspective

International Nuclear Information System (INIS)

Rungta, Pranaw

2009-01-01

We show that Grover's algorithm can be described as an iterative change of the bipartite entanglement, which leads to a necessary and sufficient condition for quadratic speedup. This allows us to reestablish, from the entanglement perspective, that Grover's search algorithm is the only optimal pure state search algorithm.

A New GCD Algorithm for Quadratic Number Rings with Unique Factorization

DEFF Research Database (Denmark)

Agarwal, Saurabh; Frandsen, Gudmund Skovbjerg

2006-01-01

We present an algorithm to compute a greatest common divisor of two integers in a quadratic number ring that is a unique factorization domain. The algorithm uses bit operations in a ring of discriminant Δ. This appears to be the first gcd algorithm of complexity o(n 2) for any fixed non-Euclidean...

An algorithm for the solution of dynamic linear programs

Science.gov (United States)

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

MM Algorithms for Geometric and Signomial Programming.

Science.gov (United States)

Lange, Kenneth; Zhou, Hua

2014-02-01

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

On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity

Directory of Open Access Journals (Sweden)

Koh Kim Jie

2017-01-01

Full Text Available Quadratic damping nonlinearity is challenging for displacement based structural dynamics problem as the problem is nonlinear in time derivative of the primitive variable. For such nonlinearity, the formulation of tangent stiffness matrix is not lucid in the literature. Consequently, ambiguity related to kinematics update arises when implementing the time integration-iterative algorithm. In present work, an Euler-Bernoulli beam vibration problem with quadratic damping nonlinearity is addressed as the main source of quadratic damping nonlinearity arises from drag force estimation, which is generally valid only for slender structures. Employing Newton-Raphson formulation, tangent stiffness components associated with quadratic damping nonlinearity requires velocity input for evaluation purpose. For this reason, two mathematically equivalent algorithm structures with different kinematics arrangement are tested. Both algorithm structures result in the same accuracy and convergence characteristic of solution.

Quadratic third-order tensor optimization problem with quadratic constraints

Directory of Open Access Journals (Sweden)

Lixing Yang

2014-05-01

Full Text Available Quadratically constrained quadratic programs (QQPs problems play an important modeling role for many diverse problems. These problems are in general NP hard and numerically intractable. Semidenite programming (SDP relaxations often provide good approximate solutions to these hard problems. For several special cases of QQP, e.g., convex programs and trust region subproblems, SDP relaxation provides the exact optimal value, i.e., there is a zero duality gap. However, this is not true for the general QQP, or even the QQP with two convex constraints, but a nonconvex objective.In this paper, we consider a certain QQP where the variable is neither vector nor matrix but a third-order tensor. This problem can be viewed as a generalization of the ordinary QQP with vector or matrix as it's variant. Under some mild conditions, we rst show that SDP relaxation provides exact optimal solutions for the original problem. Then we focus on two classes of homogeneous quadratic tensor programming problems which have no requirements on the constraints number. For one, we provide an easily implemental polynomial time algorithm to approximately solve the problem and discuss the approximation ratio. For the other, we show there is no gap between the SDP relaxation and itself.

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

Science.gov (United States)

Chang, Weng-Long

2012-03-01

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

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

Science.gov (United States)

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.

Lambda-Lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, Olivier; Schultz, Ulrik Pagh

2002-01-01

Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

Lambda-Lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, Olivier; Schultz, Ulrik Pagh

2003-01-01

Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

Lambda-Lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, Olivier; Schultz, Ulrik Pagh

2004-01-01

Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

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

Science.gov (United States)

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 iterative method for tri-level quadratic fractional programming problems using fuzzy goal programming approach

Science.gov (United States)

Kassa, Semu Mitiku; Tsegay, Teklay Hailay

2017-08-01

Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fractional objective functions at each of the three levels. A solution algorithm has been proposed by applying fuzzy goal programming approach and by reformulating the fractional constraints to equivalent but non-fractional non-linear constraints. Based on the transformed formulation, an iterative procedure is developed that can yield a satisfactory solution to the tri-level problem. The numerical results on various illustrative examples demonstrated that the proposed algorithm is very much promising and it can also be used to solve larger-sized as well as n-level problems of similar structure.

Identify Beta-Hairpin Motifs with Quadratic Discriminant Algorithm Based on the Chemical Shifts.

Directory of Open Access Journals (Sweden)

Feng YongE

Full Text Available Successful prediction of the beta-hairpin motif will be helpful for understanding the of the fold recognition. Some algorithms have been proposed for the prediction of beta-hairpin motifs. However, the parameters used by these methods were primarily based on the amino acid sequences. Here, we proposed a novel model for predicting beta-hairpin structure based on the chemical shift. Firstly, we analyzed the statistical distribution of chemical shifts of six nuclei in not beta-hairpin and beta-hairpin motifs. Secondly, we used these chemical shifts as features combined with three algorithms to predict beta-hairpin structure. Finally, we achieved the best prediction, namely sensitivity of 92%, the specificity of 94% with 0.85 of Mathew's correlation coefficient using quadratic discriminant analysis algorithm, which is clearly superior to the same method for the prediction of beta-hairpin structure from 20 amino acid compositions in the three-fold cross-validation. Our finding showed that the chemical shift is an effective parameter for beta-hairpin prediction, suggesting the quadratic discriminant analysis is a powerful algorithm for the prediction of beta-hairpin.

Optimization Models for Reaction Networks: Information Divergence, Quadratic Programming and Kirchhoff’s Laws

Directory of Open Access Journals (Sweden)

Julio Michael Stern

2014-03-01

Full Text Available This article presents a simple derivation of optimization models for reaction networks leading to a generalized form of the mass-action law, and compares the formal structure of Minimum Information Divergence, Quadratic Programming and Kirchhoff type network models. These optimization models are used in related articles to develop and illustrate the operation of ontology alignment algorithms and to discuss closely connected issues concerning the epistemological and statistical significance of sharp or precise hypotheses in empirical science.

Primal-dual predictor-corrector interior point algorithm for quadratic semidefinite programming%二次半定规划的原始对偶预估校正内点算法

Institute of Scientific and Technical Information of China (English)

黄静静; 商朋见; 王爱文

2011-01-01

将半定规划(Semidefinite Programming,SDP)的内点算法推广到二次半定规划(QuadraticSemidefinite Programming,QSDP),重点讨论了AHO搜索方向的产生方法.首先利用Wolfe对偶理论推导得到了求解二次半定规划的非线性方程组,利用牛顿法求解该方程组,得到了求解QSDP的内点算法的AHO搜索方向,证明了该搜索方向的存在唯一性,最后给出了求解二次半定规划的预估校正内点算法的具体步骤,并对基于不同搜索方向的内点算法进行了数值实验,结果表明基于NT方向的内点算法最为稳健.%This paper extends the interior point algorithm for solving Semidefinite Programming (SDP) to Quadratic Semidefinite Programming(QSDP) and especially discusses the generation of AHO search direction. Firstly, we derive the nonlinear equations for solving QSDP using Wolfe's dual theorem.The AHO search direction is got by applying Newton' s method to the equations. Then we prove the existence and uniqueness of the search direction, and give the detaied steps of predictor-corrector interior-point algorithm. At last, this paper provides a numerical comparison of the algoritms using three different search directions and suggests the algorithm using NT direction is the most robust.

PSQP: Puzzle Solving by Quadratic Programming.

Science.gov (United States)

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.

Designing Camera Networks by Convex Quadratic Programming

KAUST Repository

Ghanem, Bernard; Wonka, Peter; Cao, Yuanhao

2015-01-01

be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution

Comparison of optimization algorithms in intensity-modulated radiation therapy planning

Science.gov (United States)

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.

Obstacle Avoidance for Redundant Manipulators Utilizing a Backward Quadratic Search Algorithm

Directory of Open Access Journals (Sweden)

Tianjian Hu

2016-06-01

Full Text Available Obstacle avoidance can be achieved as a secondary task by appropriate inverse kinematics (IK resolution of redundant manipulators. Most prior literature requires the time-consuming determination of the closest point to the obstacle for every calculation step. Aiming at the relief of computational burden, this paper develops what is termed a backward quadratic search algorithm (BQSA as another option for solving IK problems in obstacle avoidance. The BQSA detects possible collisions based on the root property of a category of quadratic functions, which are derived from ellipse-enveloped obstacles and the positions of each link's end-points. The algorithm executes a backward search for possible obstacle collisions, from the end-effector to the base, and avoids obstacles by utilizing a hybrid IK scheme, incorporating the damped least-squares method, the weighted least-norm method and the gradient projection method. Some details of the hybrid IK scheme, such as values of the damped factor, weights and the clamping velocity, are discussed, along with a comparison of computational load between previous methods and BQSA. Simulations of a planar seven-link manipulator and a PUMA 560 robot verify the effectiveness of BQSA.

A quadratic approximation-based algorithm for the solution of multiparametric mixed-integer nonlinear programming problems

KAUST Repository

Domí nguez, Luis F.; Pistikopoulos, Efstratios N.

2012-01-01

An algorithm for the solution of convex multiparametric mixed-integer nonlinear programming problems arising in process engineering problems under uncertainty is introduced. The proposed algorithm iterates between a multiparametric nonlinear

Quadratic Stabilization of LPV System by an LTI Controller Based on ILMI Algorithm

Directory of Open Access Journals (Sweden)

Wei Xie

2007-01-01

Full Text Available A linear time-invariant (LTI output feedback controller is designed for a linear parameter-varying (LPV control system to achieve quadratic stability. The LPV system includes immeasurable dependent parameters that are assumed to vary in a polytopic space. To solve this control problem, a heuristic algorithm is proposed in the form of an iterative linear matrix inequality (ILMI formulation. Furthermore, an effective method of setting an initial value of the ILMI algorithm is also proposed to increase the probability of getting an admissible solution for the controller design problem.

A Collision-Free G2 Continuous Path-Smoothing Algorithm Using Quadratic Polynomial Interpolation

Directory of Open Access Journals (Sweden)

Seong-Ryong Chang

2014-12-01

Full Text Available Most path-planning algorithms are used to obtain a collision-free path without considering continuity. On the other hand, a continuous path is needed for stable movement. In this paper, the searched path was converted into a G2 continuous path using the modified quadratic polynomial and membership function interpolation algorithm. It is simple, unique and provides a good geometric interpretation. In addition, a collision-checking and improvement algorithm is proposed. The collision-checking algorithm can check the collisions of a smoothed path. If collisions are detected, the collision improvement algorithm modifies the collision path to a collision-free path. The collision improvement algorithm uses a geometric method. This method uses the perpendicular line between a collision position and the collision piecewise linear path. The sub-waypoint is added, and the QPMI algorithm is applied again. As a result, the collision-smoothed path is converted into a collision-free smooth path without changing the continuity.

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

Directory of Open Access Journals (Sweden)

Xiangrong Li

Full Text Available 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.

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

Science.gov (United States)

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.

Application of a quadratic method of programming to a particular problem of a rational development of a waterflooded field

Energy Technology Data Exchange (ETDEWEB)

Korotkov, S F; Khalitov, N T

1965-01-01

he quadratic method of programming is used to solve the following type of problem. A circular reservoir is subjected to a peripheral waterflood. The reservoir is drained by wells arranged in 3 concentric circles. The objective is to control the operation of producing wells, that a maximum quantity of water-free oil will be produced. The wells are flowed so that bottomhole pressure is above the bubble point. A quadratic equation is used to express the essential features of the problem; a system of linear equations is used to express the boundary conditions. The problem is solved by means of the Wolf algorithm method. The method is demonstrated by an illustrative example.

Exploiting Group Symmetry in Semidefinite Programming Relaxations of the Quadratic Assignment Problem

NARCIS (Netherlands)

de Klerk, E.; Sotirov, R.

2007-01-01

We consider semidefinite programming relaxations of the quadratic assignment problem, and show how to exploit group symmetry in the problem data. Thus we are able to compute the best known lower bounds for several instances of quadratic assignment problems from the problem library: [R.E. Burkard,

Evaluation of a photovoltaic energy mechatronics system with a built-in quadratic maximum power point tracking algorithm

Energy Technology Data Exchange (ETDEWEB)

Chao, R.M.; Ko, S.H.; Lin, I.H. [Department of Systems and Naval Mechatronics Engineering, National Cheng Kung University, Tainan, Taiwan 701 (China); Pai, F.S. [Department of Electronic Engineering, National University of Tainan (China); Chang, C.C. [Department of Environment and Energy, National University of Tainan (China)

2009-12-15

The historically high cost of crude oil price is stimulating research into solar (green) energy as an alternative energy source. In general, applications with large solar energy output require a maximum power point tracking (MPPT) algorithm to optimize the power generated by the photovoltaic effect. This work aims to provide a stand-alone solution for solar energy applications by integrating a DC/DC buck converter to a newly developed quadratic MPPT algorithm along with its appropriate software and hardware. The quadratic MPPT method utilizes three previously used duty cycles with their corresponding power outputs. It approaches the maximum value by using a second order polynomial formula, which converges faster than the existing MPPT algorithm. The hardware implementation takes advantage of the real-time controller system from National Instruments, USA. Experimental results have shown that the proposed solar mechatronics system can correctly and effectively track the maximum power point without any difficulties. (author)

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

Science.gov (United States)

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

A Quadratically Convergent O(square root of nL-Iteration Algorithm for Linear Programming

National Research Council Canada - National Science Library

Ye, Y; Gueler, O; Tapia, Richard A; Zhang, Y

1991-01-01

...)-iteration complexity while exhibiting superlinear convergence of the duality gap to zero under the assumption that the iteration sequence converges, and quadratic convergence of the duality gap...

An Alternating Direction Method for Convex Quadratic Second-Order Cone Programming with Bounded Constraints

Directory of Open Access Journals (Sweden)

Xuewen Mu

2015-01-01

quadratic programming over second-order cones and a bounded set. At each iteration, we only need to compute the metric projection onto the second-order cones and the projection onto the bound set. The result of convergence is given. Numerical results demonstrate that our method is efficient for the convex quadratic second-order cone programming problems with bounded constraints.

On Characterization of Quadratic Splines

DEFF Research Database (Denmark)

Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong

2005-01-01

that the representation can be refined in a neighborhood of a non-degenerate point and a set of non-degenerate minimizers. Based on these characterizations, many existing algorithms for specific convex quadratic splines are also finite convergent for a general convex quadratic spline. Finally, we study the relationship...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general....

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

Science.gov (United States)

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

2018-06-01

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

Algorithms for sparse, symmetric, definite quadratic lambda-matrix eigenproblems

International Nuclear Information System (INIS)

Scott, D.S.; Ward, R.C.

1981-01-01

Methods are presented for computing eigenpairs of the quadratic lambda-matrix, M lambda 2 + C lambda + K, where M, C, and K are large and sparse, and have special symmetry-type properties. These properties are sufficient to insure that all the eigenvalues are real and that theory analogous to the standard symmetric eigenproblem exists. The methods employ some standard techniques such as partial tri-diagonalization via the Lanczos Method and subsequent eigenpair calculation, shift-and- invert strategy and subspace iteration. The methods also employ some new techniques such as Rayleigh-Ritz quadratic roots and the inertia of symmetric, definite, quadratic lambda-matrices

FGP Approach for Solving Multi-level Multi-objective Quadratic Fractional Programming Problem with Fuzzy parameters

Directory of Open Access Journals (Sweden)

m. s. osman

2017-09-01

Full Text Available In this paper, we consider fuzzy goal programming (FGP approach for solving multi-level multi-objective quadratic fractional programming (ML-MOQFP problem with fuzzy parameters in the constraints. Firstly, the concept of the ?-cut approach is applied to transform the set of fuzzy constraints into a common deterministic one. Then, the quadratic fractional objective functions in each level are transformed into quadratic objective functions based on a proposed transformation. Secondly, the FGP approach is utilized to obtain a compromise solution for the ML-MOQFP problem by minimizing the sum of the negative deviational variables. Finally, an illustrative numerical example is given to demonstrate the applicability and performance of the proposed approach.

An online re-linearization scheme suited for Model Predictive and Linear Quadratic Control

DEFF Research Database (Denmark)

Henriksen, Lars Christian; Poulsen, Niels Kjølstad

This technical note documents the equations for primal-dual interior-point quadratic programming problem solver used for MPC. The algorithm exploits the special structure of the MPC problem and is able to reduce the computational burden such that the computational burden scales with prediction...... horizon length in a linear way rather than cubic, which would be the case if the structure was not exploited. It is also shown how models used for design of model-based controllers, e.g. linear quadratic and model predictive, can be linearized both at equilibrium and non-equilibrium points, making...

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

Science.gov (United States)

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

2016-01-01

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

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

Science.gov (United States)

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

2016-01-01

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

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

Science.gov (United States)

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

2015-04-01

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

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

Science.gov (United States)

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

2012-01-01

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

DE and NLP Based QPLS Algorithm

Science.gov (United States)

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

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

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

Energy Technology Data Exchange (ETDEWEB)

Liu, X; Belcher, AH; Wiersma, R [The University of Chicago, Chicago, IL (United States)

2016-06-15

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

Portfolio selection using genetic algorithms | Yahaya | International ...

African Journals Online (AJOL)

In this paper, one of the nature-inspired evolutionary algorithms – a Genetic Algorithms (GA) was used in solving the portfolio selection problem (PSP). Based on a real dataset from a popular stock market, the performance of the algorithm in relation to those obtained from one of the popular quadratic programming (QP) ...

Development of C++ Application Program for Solving Quadratic Equation in Elementary School in Nigeria

Science.gov (United States)

Bandele, Samuel Oye; Adekunle, Adeyemi Suraju

2015-01-01

The study was conducted to design, develop and test a c++ application program CAP-QUAD for solving quadratic equation in elementary school in Nigeria. The package was developed in c++ using object-oriented programming language, other computer program that were also utilized during the development process is DevC++ compiler, it was used for…

Solving symmetric-definite quadratic lambda-matrix problems without factorization

International Nuclear Information System (INIS)

Scott, D.S.; Ward, R.C.

1982-01-01

Algorithms are presented for computing some of the eigenvalues and their associated eigenvectors of the quadratic lambda-matrix M lambda 2 C lambda + K. M, C, and K are assumed to have special symmetry-type properties which insure that theory analogous to the standard symmetric eigenproblem exists. The algorithms are based on a generalization of the Rayleigh quotient and the Lanczos method for computing eigenpairs of standard symmetric eigenproblems. Monotone quadratic convergence of the basic method is proved. Test examples are presented

Quadratic Frequency Modulation Signals Parameter Estimation Based on Two-Dimensional Product Modified Parameterized Chirp Rate-Quadratic Chirp Rate Distribution.

Science.gov (United States)

Qu, Zhiyu; Qu, Fuxin; Hou, Changbo; Jing, Fulong

2018-05-19

In an inverse synthetic aperture radar (ISAR) imaging system for targets with complex motion, the azimuth echo signals of the target are always modeled as multicomponent quadratic frequency modulation (QFM) signals. The chirp rate (CR) and quadratic chirp rate (QCR) estimation of QFM signals is very important to solve the ISAR image defocus problem. For multicomponent QFM (multi-QFM) signals, the conventional QR and QCR estimation algorithms suffer from the cross-term and poor anti-noise ability. This paper proposes a novel estimation algorithm called a two-dimensional product modified parameterized chirp rate-quadratic chirp rate distribution (2D-PMPCRD) for QFM signals parameter estimation. The 2D-PMPCRD employs a multi-scale parametric symmetric self-correlation function and modified nonuniform fast Fourier transform-Fast Fourier transform to transform the signals into the chirp rate-quadratic chirp rate (CR-QCR) domains. It can greatly suppress the cross-terms while strengthening the auto-terms by multiplying different CR-QCR domains with different scale factors. Compared with high order ambiguity function-integrated cubic phase function and modified Lv's distribution, the simulation results verify that the 2D-PMPCRD acquires higher anti-noise performance and obtains better cross-terms suppression performance for multi-QFM signals with reasonable computation cost.

Incorporating a modified uniform crossover and 2-exchange neighborhood mechanism in a discrete bat algorithm to solve the quadratic assignment problem

Directory of Open Access Journals (Sweden)

Mohammed Essaid Riffi

2017-11-01

Full Text Available The bat algorithm is one of the recent nature-inspired algorithms, which has been emerged as a powerful search method for solving continuous as well as discrete problems. The quadratic assignment problem is a well-known NP-hard problem in combinatorial optimization. The goal of this problem is to assign n facilities to n locations in such a way as to minimize the assignment cost. For that purpose, this paper introduces a novel discrete variant of bat algorithm to deal with this combinatorial optimization problem. The proposed algorithm was evaluated on a set of benchmark instances from the QAPLIB library and the performance was compared to other algorithms. The empirical results of exhaustive experiments were promising and illustrated the efficacy of the suggested approach.

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

Science.gov (United States)

Gupta, K. K.

1973-01-01

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

Beams configuration design in target area with successive quadratic programming method

International Nuclear Information System (INIS)

Shi Zhiquan; Tan Jichun; Wei Xiaofeng; Man Jongzai; Zhang Xiaomin; Yuan Jing; Yuan Xiaodong

1998-01-01

The author describes the application of successive quadratic programming method (SQP) to design laser beam configuration in target area. Based on the requirement of ICF experiment physics, a math model of indirect-driver beam geometry is given. A 3D wire-frame is plotted, in which support lines represent 60 laser entireties and 240 turning points of support lines' segments stand for the spatial positions of reflectors

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

Science.gov (United States)

Banks, H. T.; Ito, K.

1991-01-01

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

Optimization algorithms and applications

CERN Document Server

Arora, Rajesh Kumar

2015-01-01

Choose the Correct Solution Method for Your Optimization ProblemOptimization: Algorithms and Applications presents a variety of solution techniques for optimization problems, emphasizing concepts rather than rigorous mathematical details and proofs. The book covers both gradient and stochastic methods as solution techniques for unconstrained and constrained optimization problems. It discusses the conjugate gradient method, Broyden-Fletcher-Goldfarb-Shanno algorithm, Powell method, penalty function, augmented Lagrange multiplier method, sequential quadratic programming, method of feasible direc

Separation and Extension of Cover Inequalities for Conic Quadratic Knapsack Constraints with Generalized Upper Bounds

DEFF Research Database (Denmark)

Atamtürk, Alper; Muller, Laurent Flindt; Pisinger, David

2013-01-01

Motivated by addressing probabilistic 0-1 programs we study the conic quadratic knapsack polytope with generalized upper bound (GUB) constraints. In particular, we investigate separating and extending GUB cover inequalities. We show that, unlike in the linear case, determining whether a cover can...... be extended with a single variable is NP-hard. We describe and compare a number of exact and heuristic separation and extension algorithms which make use of the structure of the constraints. Computational experiments are performed for comparing the proposed separation and extension algorithms...

Fitting timeseries by continuous-time Markov chains: A quadratic programming approach

International Nuclear Information System (INIS)

Crommelin, D.T.; Vanden-Eijnden, E.

2006-01-01

Construction of stochastic models that describe the effective dynamics of observables of interest is an useful instrument in various fields of application, such as physics, climate science, and finance. We present a new technique for the construction of such models. From the timeseries of an observable, we construct a discrete-in-time Markov chain and calculate the eigenspectrum of its transition probability (or stochastic) matrix. As a next step we aim to find the generator of a continuous-time Markov chain whose eigenspectrum resembles the observed eigenspectrum as closely as possible, using an appropriate norm. The generator is found by solving a minimization problem: the norm is chosen such that the object function is quadratic and convex, so that the minimization problem can be solved using quadratic programming techniques. The technique is illustrated on various toy problems as well as on datasets stemming from simulations of molecular dynamics and of atmospheric flows

New generalized conjugate gradient methods for the non-quadratic model in unconstrained optimization

International Nuclear Information System (INIS)

Al-Bayati, A.

2001-01-01

This paper present two new conjugate gradient algorithms which use the non-quadratic model in unconstrained optimization. The first is a new generalized self-scaling variable metric algorithm based on the sloboda generalized conjugate gradient method which is invariant to a nonlinear scaling of a stricity convex quadratic function; the second is an interleaving between the generalized sloboda method and the first algorithm; all these algorithm use exact line searches. Numerical comparisons over twenty test functions show that the interleaving algorithm is best overall and requires only about half the function evaluations of the Sloboda method: interleaving algorithms are likely to be preferred when the dimensionality of the problem is increased. (author). 29 refs., 1 tab

Sub-quadratic decoding of one-point hermitian codes

DEFF Research Database (Denmark)

Nielsen, Johan Sebastian Rosenkilde; Beelen, Peter

2015-01-01

We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realization of the Guruswami-Sudan algorithm using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimization. The second is a power...... decoding algorithm: an extension of classical key equation decoding which gives a probabilistic decoding algorithm up to the Sudan radius. We show how the resulting key equations can be solved by the matrix minimization algorithms from computer algebra, yielding similar asymptotic complexities....

A Strongly and Superlinearly Convergent SQP Algorithm for Optimization Problems with Linear Complementarity Constraints

International Nuclear Information System (INIS)

Jian Jinbao; Li Jianling; Mo Xingde

2006-01-01

This paper discusses a kind of optimization problem with linear complementarity constraints, and presents a sequential quadratic programming (SQP) algorithm for solving a stationary point of the problem. The algorithm is a modification of the SQP algorithm proposed by Fukushima et al. [Computational Optimization and Applications, 10 (1998),5-34], and is based on a reformulation of complementarity condition as a system of linear equations. At each iteration, one quadratic programming and one system of equations needs to be solved, and a curve search is used to yield the step size. Under some appropriate assumptions, including the lower-level strict complementarity, but without the upper-level strict complementarity for the inequality constraints, the algorithm is proved to possess strong convergence and superlinear convergence. Some preliminary numerical results are reported

On a quadratic inverse eigenvalue problem

International Nuclear Information System (INIS)

Cai, Yunfeng; Xu, Shufang

2009-01-01

This paper concerns the quadratic inverse eigenvalue problem (QIEP) of constructing real symmetric matrices M, C and K of size n × n, with M nonsingular, so that the quadratic matrix polynomial Q(λ) ≡ λ 2 M + λC + K has a completely prescribed set of eigenvalues and eigenvectors. It is shown via construction that the QIEP has a solution if and only if r 0, where r and δ are computable from the prescribed spectral data. A necessary and sufficient condition for the existence of a solution to the QIEP with M being positive definite is also established in a constructive way. Furthermore, two algorithms are developed: one is to solve the QIEP; another is to find a particular solution to the QIEP with the leading coefficient matrix being positive definite, which also provides us an approach to a simultaneous reduction of real symmetric matrix triple (M, C, K) by real congruence. Numerical results show that the two algorithms are feasible and numerically reliable

Lambda-lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, O.; Schultz, U.P.

2004-01-01

-lifting transforms a block-structured program into a set of recursive equations, one for each local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters......Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...

A new separation algorithm for the Boolean quadric and cut polytopes

DEFF Research Database (Denmark)

Sørensen, Michael Malmros; Letchford, Adam N.

2014-01-01

A separation algorithm is a procedure for generating cutting planes. Up to now, only a few polynomial-time separation algorithms were known for the Boolean quadric and cut polytopes. These polytopes arise in connection with zero–one quadratic programming and the max-cut problem, respectively. We...

Computational Recognition of RNA Splice Sites by Exact Algorithms for the Quadratic Traveling Salesman Problem

Directory of Open Access Journals (Sweden)

Anja Fischer

2015-06-01

Full Text Available One fundamental problem of bioinformatics is the computational recognition of DNA and RNA binding sites. Given a set of short DNA or RNA sequences of equal length such as transcription factor binding sites or RNA splice sites, the task is to learn a pattern from this set that allows the recognition of similar sites in another set of DNA or RNA sequences. Permuted Markov (PM models and permuted variable length Markov (PVLM models are two powerful models for this task, but the problem of finding an optimal PM model or PVLM model is NP-hard. While the problem of finding an optimal PM model or PVLM model of order one is equivalent to the traveling salesman problem (TSP, the problem of finding an optimal PM model or PVLM model of order two is equivalent to the quadratic TSP (QTSP. Several exact algorithms exist for solving the QTSP, but it is unclear if these algorithms are capable of solving QTSP instances resulting from RNA splice sites of at least 150 base pairs in a reasonable time frame. Here, we investigate the performance of three exact algorithms for solving the QTSP for ten datasets of splice acceptor sites and splice donor sites of five different species and find that one of these algorithms is capable of solving QTSP instances of up to 200 base pairs with a running time of less than two days.

Neural network for solving convex quadratic bilevel programming problems.

Science.gov (United States)

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

2014-03-01

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

Semi-Supervised Half-Quadratic Nonnegative Matrix Factorization for Face Recognition

KAUST Repository

Alghamdi, Masheal M.

2014-05-01

Face recognition is a challenging problem in computer vision. Difficulties such as slight differences between similar faces of different people, changes in facial expressions, light and illumination condition, and pose variations add extra complications to the face recognition research. Many algorithms are devoted to solving the face recognition problem, among which the family of nonnegative matrix factorization (NMF) algorithms has been widely used as a compact data representation method. Different versions of NMF have been proposed. Wang et al. proposed the graph-based semi-supervised nonnegative learning (S2N2L) algorithm that uses labeled data in constructing intrinsic and penalty graph to enforce separability of labeled data, which leads to a greater discriminating power. Moreover the geometrical structure of labeled and unlabeled data is preserved through using the smoothness assumption by creating a similarity graph that conserves the neighboring information for all labeled and unlabeled data. However, S2N2L is sensitive to light changes, illumination, and partial occlusion. In this thesis, we propose a Semi-Supervised Half-Quadratic NMF (SSHQNMF) algorithm that combines the benefits of S2N2L and the robust NMF by the half- quadratic minimization (HQNMF) algorithm.Our algorithm improves upon the S2N2L algorithm by replacing the Frobenius norm with a robust M-Estimator loss function. A multiplicative update solution for our SSHQNMF algorithmis driven using the half- 4 quadratic (HQ) theory. Extensive experiments on ORL, Yale-A and a subset of the PIE data sets for nine M-estimator loss functions for both SSHQNMF and HQNMF algorithms are investigated, and compared with several state-of-the-art supervised and unsupervised algorithms, along with the original S2N2L algorithm in the context of classification, clustering, and robustness against partial occlusion. The proposed algorithm outperformed the other algorithms. Furthermore, SSHQNMF with Maximum Correntropy

Distribution Locational Marginal Pricing through Quadratic Programming for Congestion Management in Distribution Networks

DEFF Research Database (Denmark)

Huang, Shaojun; Wu, Qiuwei; Oren, Shmuel S.

2015-01-01

) calculates dynamic tariffs and publishes them to the aggregators, who make the optimal energy plans for the flexible demands. The DLMP through QP instead of linear programing as studied in previous literatures solves the multiple solution issue of the ag- gregator optimization which may cause......This paper presents the distribution locational mar- ginal pricing (DLMP) method through quadratic programming (QP) designed to alleviate the congestion that might occur in a distribution network with high penetration of flexible demands. In the DLMP method, the distribution system operator (DSO...

A Linear Programming Reformulation of the Standard Quadratic Optimization Problem

NARCIS (Netherlands)

de Klerk, E.; Pasechnik, D.V.

2005-01-01

The problem of minimizing a quadratic form over the standard simplex is known as the standard quadratic optimization problem (SQO).It is NPhard, and contains the maximum stable set problem in graphs as a special case.In this note we show that the SQO problem may be reformulated as an (exponentially

A high-performance Riccati based solver for tree-structured quadratic programs

DEFF Research Database (Denmark)

Frison, Gianluca; Kouzoupis, Dimitris; Diehl, Moritz

2017-01-01

the online solution of such problems challenging and the development of tailored solvers crucial. In this paper, an interior point method is presented that can solve Quadratic Programs (QPs) arising in multi-stage MPC efficiently by means of a tree-structured Riccati recursion and a high-performance linear...... algebra library. A performance comparison with code-generated and general purpose sparse QP solvers shows that the computation times can be significantly reduced for all problem sizes that are practically relevant in embedded MPC applications. The presented implementation is freely available as part...

Scheduling of head-dependent cascaded hydro systems: Mixed-integer quadratic programming approach

International Nuclear Information System (INIS)

Catalao, J.P.S.; Pousinho, H.M.I.; Mendes, V.M.F.

2010-01-01

This paper is on the problem of short-term hydro scheduling, particularly concerning head-dependent cascaded hydro systems. We propose a novel mixed-integer quadratic programming approach, considering not only head-dependency, but also discontinuous operating regions and discharge ramping constraints. Thus, an enhanced short-term hydro scheduling is provided due to the more realistic modeling presented in this paper. Numerical results from two case studies, based on Portuguese cascaded hydro systems, illustrate the proficiency of the proposed approach.

An Augmented Lagrangian Method for a Class of Inverse Quadratic Programming Problems

International Nuclear Information System (INIS)

Zhang Jianzhong; Zhang Liwei

2010-01-01

We consider an inverse quadratic programming (QP) problem in which the parameters in the objective function of a given QP problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a minimization problem with a positive semidefinite cone constraint and its dual is a linearly constrained semismoothly differentiable (SC 1 ) convex programming problem with fewer variables than the original one. We demonstrate the global convergence of the augmented Lagrangian method for the dual problem and prove that the convergence rate of primal iterates, generated by the augmented Lagrange method, is proportional to 1/r, and the rate of multiplier iterates is proportional to 1/√r, where r is the penalty parameter in the augmented Lagrangian. As the objective function of the dual problem is a SC 1 function involving the projection operator onto the cone of symmetrically semi-definite matrices, the analysis requires extensive tools such as the singular value decomposition of matrices, an implicit function theorem for semismooth functions, and properties of the projection operator in the symmetric-matrix space. Furthermore, the semismooth Newton method with Armijo line search is applied to solve the subproblems in the augmented Lagrange approach, which is proven to have global convergence and local quadratic rate. Finally numerical results, implemented by the augmented Lagrangian method, are reported.

Binary classification posed as a quadratically constrained quadratic ...

Indian Academy of Sciences (India)

Binary classification is posed as a quadratically constrained quadratic problem and solved using the proposed method. Each class in the binary classification problem is modeled as a multidimensional ellipsoid to forma quadratic constraint in the problem. Particle swarms help in determining the optimal hyperplane or ...

A Superlinearly Convergent O(square root of nL)-Iteration Algorithm for Linear Programming

National Research Council Canada - National Science Library

Ye, Y; Tapia, Richard A; Zhang, Y

1991-01-01

.... We demonstrate that the modified algorithm maintains its O(square root of nL)-iteration complexity, while exhibiting superlinear convergence for general problems and quadratic convergence for nondegenerate problems...

Scheduling of head-dependent cascaded hydro systems: Mixed-integer quadratic programming approach

Energy Technology Data Exchange (ETDEWEB)

Catalao, J.P.S.; Pousinho, H.M.I. [Department of Electromechanical Engineering, University of Beira Interior, R. Fonte do Lameiro, 6201-001 Covilha (Portugal); Mendes, V.M.F. [Department of Electrical Engineering and Automation, Instituto Superior de Engenharia de Lisboa, R. Conselheiro Emidio Navarro, 1950-062 Lisbon (Portugal)

2010-03-15

This paper is on the problem of short-term hydro scheduling, particularly concerning head-dependent cascaded hydro systems. We propose a novel mixed-integer quadratic programming approach, considering not only head-dependency, but also discontinuous operating regions and discharge ramping constraints. Thus, an enhanced short-term hydro scheduling is provided due to the more realistic modeling presented in this paper. Numerical results from two case studies, based on Portuguese cascaded hydro systems, illustrate the proficiency of the proposed approach. (author)

Zhang neural network for online solution of time-varying convex quadratic program subject to time-varying linear-equality constraints

International Nuclear Information System (INIS)

Zhang Yunong; Li Zhan

2009-01-01

In this Letter, by following Zhang et al.'s method, a recurrent neural network (termed as Zhang neural network, ZNN) is developed and analyzed for solving online the time-varying convex quadratic-programming problem subject to time-varying linear-equality constraints. Different from conventional gradient-based neural networks (GNN), such a ZNN model makes full use of the time-derivative information of time-varying coefficient. The resultant ZNN model is theoretically proved to have global exponential convergence to the time-varying theoretical optimal solution of the investigated time-varying convex quadratic program. Computer-simulation results further substantiate the effectiveness, efficiency and novelty of such ZNN model and method.

AUTOJOM, Quadratic Equation Coefficient for Conic Volume, Parallelepipeds, Wedges, Pyramids. JOMREAD, Check of 3-D Geometry Structure from Quadratic Surfaces

International Nuclear Information System (INIS)

2005-01-01

Nature of physical problem solved: AUTOJOM is a computer program that will generate the coefficients of any quadratic equation used to define conic volumes and also the coefficients of the planes needed to define parallelepipeds, wedges, and pyramids. JOMREAD is a computer code to check any 3D geometry composed of and constructed with quadratic surfaces

Designing Camera Networks by Convex Quadratic Programming

KAUST Repository

Ghanem, Bernard

2015-05-04

​In this paper, we study the problem of automatic camera placement for computer graphics and computer vision applications. We extend the problem formulations of previous work by proposing a novel way to incorporate visibility constraints and camera-to-camera relationships. For example, the placement solution can be encouraged to have cameras that image the same important locations from different viewing directions, which can enable reconstruction and surveillance tasks to perform better. We show that the general camera placement problem can be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution is almost as fast as a greedy treatment of the problem, but the quality is significantly higher, so much so that it is comparable to exact solutions that take orders of magnitude more computation time. Because it is computationally attractive, our method also allows users to explore the space of solutions for variations in input parameters. To evaluate its effectiveness, we show a range of 3D results on real-world floorplans (garage, hotel, mall, and airport). ​

orthogonal and scaling transformations of quadratic functions

African Journals Online (AJOL)

Preferred Customer

functions of sub-problems of various nonlinear programming problems that employ methods such as sequential quadratic programming and trust-region methods (Sorensen, 1982; Eldersveld,. 1991; Nocedal and Wright, 1999). Various problems in Algebra, Functional Analysis,. Analytic Geometry and Computational Mathe-.

Smoothing optimization of supporting quadratic surfaces with Zernike polynomials

Science.gov (United States)

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

2018-03-01

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

Numerical Methods for Solution of the Extended Linear Quadratic Control Problem

DEFF Research Database (Denmark)

Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog

2012-01-01

In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....

Quadratic-linear pattern in cancer fractional radiotherapy. Equations for a computering program

International Nuclear Information System (INIS)

Burgos, D.; Bullejos, J.; Garcia Puche, J.L.; Pedraza, V.

1990-01-01

Knowledge of equivalence between different tratment schemes with the same iso-effect is the essential thing in clinical cancer radiotherapy. For this purpose it is very useful the group of ideas derived from quadratic-linear pattern (Q-L) proposed in order to analyze cell survival curve to radiation. Iso-effect definition caused by several irradiation rules is done by extrapolated tolerance dose (ETD). Because equations for ETD are complex, a computering program have been carried out. In this paper, iso-effect equations for well defined therapeutic situations and flow diagram proposed for resolution, have been studied. (Author)

Hidden conic quadratic representation of some nonconvex quadratic optimization problems

NARCIS (Netherlands)

Ben-Tal, A.; den Hertog, D.

The problem of minimizing a quadratic objective function subject to one or two quadratic constraints is known to have a hidden convexity property, even when the quadratic forms are indefinite. The equivalent convex problem is a semidefinite one, and the equivalence is based on the celebrated

Further Developments on Optimum Structural Design Using MSC/Nastran and Sequential Quadratic Programming

DEFF Research Database (Denmark)

Holzleitner, Ludwig

1996-01-01

, here the shape of two dimensional parts with different thickness areas will be optimized. As in the previos paper, a methodology for structural optimization using the commercial finite element package MSC/NASTRAN for structural analysis is described. Three different methods for design sensitivity......This work is closely connected to the paper: K.G. MAHMOUD, H.W. ENGL and HOLZLEITNER: "OPTIMUM STRUCTURAL DESIGN USING MSC/NASTRAN AND SEQUENTIAL QUADRATIC PROGRAMMING", Computers & Structures, Vol. 52, No. 3, pp. 437-447, (1994). In contrast to that paper, where thickness optimization is described...

Algorithmic Principles of Mathematical Programming

NARCIS (Netherlands)

Faigle, Ulrich; Kern, Walter; Still, Georg

2002-01-01

Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear

Dhage Iteration Method for Generalized Quadratic Functional Integral Equations

Directory of Open Access Journals (Sweden)

Bapurao C. Dhage

2015-01-01

Full Text Available In this paper we prove the existence as well as approximations of the solutions for a certain nonlinear generalized quadratic functional integral equation. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting at a lower or upper solution converges monotonically to the solutions of related quadratic functional integral equation under some suitable mixed hybrid conditions. We rely our main result on Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.

Unified solution of a non-convex SCUC problem using combination of modified Branch-and-Bound method with Quadratic Programming

International Nuclear Information System (INIS)

Shafie-khah, M.; Parsa Moghaddam, M.; Sheikh-El-Eslami, M.K.

2011-01-01

Highlights: → A hybrid SCUC solution is developed to deal with large-scale, real-time and long-term problems. → New formulations are proposed for considering valve point effect and warmth-dependent start-up cost. → A new algorithm is developed for modeling the AC power flow in SCUC problems. → Using the power flow algorithm both steps in traditional SCUC is done simultaneously. → The proposed method provides better solutions than previous ones with a fast speed. - Abstract: In this paper, a new practical method is presented for solving the non-convex security constraint unit commitment (SCUC) problem in power systems. The accuracy of the proposed method is desirable while the shorter computation time makes it useful for SCUC solution of large-scale power systems, real-time market operation and long-term SCUC problems. The proposed framework allows inclusion of the valve point effects, warmth-dependent start-up costs, ramp rates, minimum up/down time constraints, multiple fuels costs, emission costs, prohibited operating zones and AC power flow limits in normal and contingency conditions. To solve the non-convex problem, combination of a modified Branch-and-Bound method with the Quadratic Programming is used as an optimization tool and a developed AC power flow algorithm is applied for considering the security and contingency concerns using the nonlinear/linear AC model. These modifications improve the convergence speed and solution precision of SCUC problem. In the proposed method, in contrast with traditional SCUC algorithms, unit commitment solution, checking and satisfying the security constraints are managed simultaneously. The obtained results are compared with other reported methods for investigating the effectiveness of the proposed method. Also, the proposed method is applied to an Iranian power system including 493 thermal units.

Bôcher and Abstract Contractions of 2nd Order Quadratic Algebras

Science.gov (United States)

Escobar-Ruiz, Mauricio A.; Kalnins, Ernest G.; Miller, Willar, Jr.; Subag, Eyal

2017-03-01

Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. Distinct superintegrable systems and their quadratic algebras can be related by geometric contractions, induced by Bôcher contractions of the conformal Lie algebra {so}(4,C) to itself. In this paper we give a precise definition of Bôcher contractions and show how they can be classified. They subsume well known contractions of {e}(2,C) and {so}(3,C) and have important physical and geometric meanings, such as the derivation of the Askey scheme for obtaining all hypergeometric orthogonal polynomials as limits of Racah/Wilson polynomials. We also classify abstract nondegenerate quadratic algebras in terms of an invariant that we call a canonical form. We describe an algorithm for finding the canonical form of such algebras. We calculate explicitly all canonical forms arising from quadratic algebras of 2D nondegenerate superintegrable systems on constant curvature spaces and Darboux spaces. We further discuss contraction of quadratic algebras, focusing on those coming from superintegrable systems.

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

Science.gov (United States)

Altin, Necmi

2018-05-01

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

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

Science.gov (United States)

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

2018-01-01

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

Self-Replicating Quadratics

Science.gov (United States)

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…

Low-rank quadratic semidefinite programming

KAUST Repository

Yuan, Ganzhao

2013-04-01

Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.

Low-rank quadratic semidefinite programming

KAUST Repository

Yuan, Ganzhao; Zhang, Zhenjie; Ghanem, Bernard; Hao, Zhifeng

2013-01-01

Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.

A Note on 5-bit Quadratic Permutations’ Classification

OpenAIRE

Božilov, Dušan; Bilgin, Begül; Sahin, Hacı Ali

2017-01-01

Classification of vectorial Boolean functions up to affine equivalence is used widely to analyze various cryptographic and implementation properties of symmetric-key algorithms. We show that there exist 75 affine equivalence classes of 5-bit quadratic permutations. Furthermore, we explore important cryptographic properties of these classes, such as linear and differential properties and degrees of their inverses, together with multiplicative complexity and existence of uniform threshold reali...

Quaternion orders, quadratic forms, and Shimura curves

CERN Document Server

Alsina, Montserrat

2004-01-01

Shimura curves are a far-reaching generalization of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. The text provides an introduction to the subject from a theoretic and algorithmic perspective. The main topics covered in it are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplication points. The study of complex multiplication points in Shimura curves leads to the study of families of binary quadratic forms with algebraic coefficients and to their classification by arithmetic Fuchsian groups. In this regard, the authors develop a theory full of new possibilities which parallels Gauss' theory on the classification of binary quadratic forms with integral coefficients by the action of the modular group. Each topic covered in the book begins with a theoretical discussion followed by carefully worked...

Quadratic Damping

Science.gov (United States)

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…

Fast, multiple optimizations of quadratic dose objective functions in IMRT

International Nuclear Information System (INIS)

Breedveld, Sebastiaan; Storchi, Pascal R M; Keijzer, Marleen; Heijmen, Ben J M

2006-01-01

Inverse treatment planning for intensity-modulated radiotherapy may include time consuming, multiple minimizations of an objective function. In this paper, methods are presented to speed up the process of (repeated) minimization of the well-known quadratic dose objective function, extended with a smoothing term that ensures generation of clinically acceptable beam profiles. In between two subsequent optimizations, the voxel-dependent importance factors of the quadratic terms will generally be adjusted, based on an intermediate plan evaluation. The objective function has been written in matrix-vector format, facilitating the use of a recently published, fast quadratic minimization algorithm, instead of commonly applied gradient-based methods. This format also reduces the calculation time in between subsequent minimizations, related to adjustment of the voxel-dependent importance factors. Sparse matrices are used to limit the required amount of computer memory. For three patients, comparisons have been made with a gradient method. Mean speed improvements of up to a factor of 37 have been achieved

Penerapan Batas Ramp-Rate dengan Menggunakan Kombinasi Metode FDP (Forward Dynamic Programming dan QP (Quadratic Programming Pada Unit Commitment-Economic Dispatch

Directory of Open Access Journals (Sweden)

Riza Fahmi Andriyanto

2017-01-01

Full Text Available Kebutuhan akan energi listrik terus menigkat seiring dengan perkembangan teknologi. meningkatnya beban listrik ini harus diimbangi dengan penambahan daya yang dibangkitkan. Hal ini sangat berpengaruh pada penjadwalan unit pembangkit yang harus ditentukan dengan baik agar didapatkan pembangkitan yang optimal. Pada Tugas Akhir ini mengambil topik mengenai unit commitment dan economic dispatch dengan mempertimbangkan nilai dari batasan generator (ramp-rate. Metode yang digunakan adalah complete enumeration dengan forward dynamic programming pada unit commitment dan quadratic programming pada economic dispatch. Metode - metode tersebut diterapkan dalam pemrograman matlab sehingga dapat dijadikan suatu program perhitungan unit commitment dan economic dispatch dengan mempertimbangkan nilai batasan ramp-rate. Dengan metode tersebut, diharapkan permasalahan penjadwalan unit pembangkit dapat terselesaikan dengan baik dan optimal sehingga memperoleh total biaya pembangkitan yang ekonomis.

Quadratic soliton self-reflection at a quadratically nonlinear interface

Science.gov (United States)

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.

Multiobjective Optimization Involving Quadratic Functions

Directory of Open Access Journals (Sweden)

Oscar Brito Augusto

2014-01-01

Full Text Available Multiobjective optimization is nowadays a word of order in engineering projects. Although the idea involved is simple, the implementation of any procedure to solve a general problem is not an easy task. Evolutionary algorithms are widespread as a satisfactory technique to find a candidate set for the solution. Usually they supply a discrete picture of the Pareto front even if this front is continuous. In this paper we propose three methods for solving unconstrained multiobjective optimization problems involving quadratic functions. In the first, for biobjective optimization defined in the bidimensional space, a continuous Pareto set is found analytically. In the second, applicable to multiobjective optimization, a condition test is proposed to check if a point in the decision space is Pareto optimum or not and, in the third, with functions defined in n-dimensional space, a direct noniterative algorithm is proposed to find the Pareto set. Simple problems highlight the suitability of the proposed methods.

Multiparametric programming based algorithms for pure integer and mixed-integer bilevel programming problems

KAUST Repository

Domínguez, Luis F.

2010-12-01

This work introduces two algorithms for the solution of pure integer and mixed-integer bilevel programming problems by multiparametric programming techniques. The first algorithm addresses the integer case of the bilevel programming problem where integer variables of the outer optimization problem appear in linear or polynomial form in the inner problem. The algorithm employs global optimization techniques to convexify nonlinear terms generated by a reformulation linearization technique (RLT). A continuous multiparametric programming algorithm is then used to solve the reformulated convex inner problem. The second algorithm addresses the mixed-integer case of the bilevel programming problem where integer and continuous variables of the outer problem appear in linear or polynomial forms in the inner problem. The algorithm relies on the use of global multiparametric mixed-integer programming techniques at the inner optimization level. In both algorithms, the multiparametric solutions obtained are embedded in the outer problem to form a set of single-level (M)(I)(N)LP problems - which are then solved to global optimality using standard fixed-point (global) optimization methods. Numerical examples drawn from the open literature are presented to illustrate the proposed algorithms. © 2010 Elsevier Ltd.

Social Welfare Improvement by TCSC using Real Code Based Genetic Algorithm in Double-Sided Auction Market

Directory of Open Access Journals (Sweden)

MASOUM, M. A. S.

2011-05-01

Full Text Available This paper presents a genetic algorithm (GA to maximize total system social welfare and alleviate congestion by best placement and sizing of TCSC device, in a double-sided auction market. To introduce more accurate modeling, the valve loading effects is incorporated to the conventional quadratic smooth generator cost curves. By adding the valve point effect, the model presents nondifferentiable and nonconvex regions that challenge most gradient-based optimization algorithms. In addition, quadratic consumer benefit functions integrated in the objective function to guarantee that locational marginal prices charged at the demand buses is less than or equal to DisCos benefit, earned by selling that power to retail customers. The proposed approach makes use of the genetic algorithm to optimal schedule GenCos, DisCos and TCSC location and size, while the Newton-Raphson algorithm minimizes the mismatch of the power flow equations. Simulation results on the modified IEEE 14-bus and 30-bus test systems (with/without line flow constraints, before and after the compensation are used to examine the impact of TCSC on the total system social welfare improvement. Several cases are considered to test and validate the consistency of detecting best solutions. Simulation results are compared to solutions obtained by sequential quadratic programming (SQP approaches.

Linear-quadratic control and quadratic differential forms for multidimensional behaviors

NARCIS (Netherlands)

Napp, D.; Trentelman, H.L.

2011-01-01

This paper deals with systems described by constant coefficient linear partial differential equations (nD-systems) from a behavioral point of view. In this context we treat the linear-quadratic control problem where the performance functional is the integral of a quadratic differential form. We look

Binary GCD like Algorithms for Some Complex Quadratic Rings

DEFF Research Database (Denmark)

Agarwal, Saurabh; Frandsen, Gudmund Skovbjerg

2004-01-01

On the lines of the binary gcd algorithm for rational integers, algorithms for computing the gcd are presented for the ring of integers in where . Thus a binary gcd like algorithm is presented for a unique factorization domain which is not Euclidean (case d=-19). Together with the earlier known b...

Rescuing Quadratic Inflation

CERN Document Server

Ellis, John; Sueiro, Maria

2014-01-01

Inflationary models based on a single scalar field $\\phi$ with a quadratic potential $V = \\frac{1}{2} m^2 \\phi^2$ are disfavoured by the recent Planck constraints on the scalar index, $n_s$, and the tensor-to-scalar ratio for cosmological density perturbations, $r_T$. In this paper we study how such a quadratic inflationary model can be rescued by postulating additional fields with quadratic potentials, such as might occur in sneutrino models, which might serve as either curvatons or supplementary inflatons. Introducing a second scalar field reduces but does not remove the pressure on quadratic inflation, but we find a sample of three-field models that are highly compatible with the Planck data on $n_s$ and $r_T$. We exhibit a specific three-sneutrino example that is also compatible with the data on neutrino mass difference and mixing angles.

On the solution of nonconvex cardinality Boolean quadratic programming problems: a computational study

KAUST Repository

Lima, Ricardo

2016-06-16

This paper addresses the solution of a cardinality Boolean quadratic programming problem using three different approaches. The first transforms the original problem into six mixed-integer linear programming (MILP) formulations. The second approach takes one of the MILP formulations and relies on the specific features of an MILP solver, namely using starting incumbents, polishing, and callbacks. The last involves the direct solution of the original problem by solvers that can accomodate the nonlinear combinatorial problem. Particular emphasis is placed on the definition of the MILP reformulations and their comparison with the other approaches. The results indicate that the data of the problem has a strong influence on the performance of the different approaches, and that there are clear-cut approaches that are better for some instances of the data. A detailed analysis of the results is made to identify the most effective approaches for specific instances of the data. © 2016 Springer Science+Business Media New York

On the solution of nonconvex cardinality Boolean quadratic programming problems: a computational study

KAUST Repository

Lima, Ricardo; Grossmann, Ignacio E.

2016-01-01

This paper addresses the solution of a cardinality Boolean quadratic programming problem using three different approaches. The first transforms the original problem into six mixed-integer linear programming (MILP) formulations. The second approach takes one of the MILP formulations and relies on the specific features of an MILP solver, namely using starting incumbents, polishing, and callbacks. The last involves the direct solution of the original problem by solvers that can accomodate the nonlinear combinatorial problem. Particular emphasis is placed on the definition of the MILP reformulations and their comparison with the other approaches. The results indicate that the data of the problem has a strong influence on the performance of the different approaches, and that there are clear-cut approaches that are better for some instances of the data. A detailed analysis of the results is made to identify the most effective approaches for specific instances of the data. © 2016 Springer Science+Business Media New York

Quadratic algebras

CERN Document Server

Polishchuk, Alexander

2005-01-01

Quadratic algebras, i.e., algebras defined by quadratic relations, often occur in various areas of mathematics. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, noncommutative geometry, K-theory, number theory, and noncommutative linear algebra. The book offers a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincar�-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes.

Faithfully quadratic rings

CERN Document Server

Dickmann, M

2015-01-01

In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where -1 is not a sum of squares and 2 is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of T-isometry, where T is a preorder of the given ring, A, or T = A^2. (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in

Genetic algorithm–based varying parameter linear quadratic regulator control for four-wheel independent steering vehicle

Directory of Open Access Journals (Sweden)

Linlin Gao

2015-11-01

Full Text Available From the perspective of vehicle dynamics, the four-wheel independent steering vehicle dynamics stability control method is studied, and a four-wheel independent steering varying parameter linear quadratic regulator control system is proposed with the help of expert control method. In the article, a four-wheel independent steering linear quadratic regulator controller for model following purpose is designed first. Then, by analyzing the four-wheel independent steering vehicle dynamic characteristics and the influence of linear quadratic regulator control parameters on control performance, a linear quadratic regulator control parameter adjustment strategy based on vehicle steering state is proposed to achieve the adaptive adjustment of linear quadratic regulator control parameters. In addition, to further improve the control performance, the proposed varying parameter linear quadratic regulator control system is optimized by genetic algorithm. Finally, simulation studies have been conducted by applying the proposed control system to the 8-degree-of-freedom four-wheel independent steering vehicle dynamics model. The simulation results indicate that the proposed control system has better performance and robustness and can effectively improve the stability and steering safety of the four-wheel independent steering vehicle.

Arc-Search Infeasible Interior-Point Algorithm for Linear Programming

OpenAIRE

Yang, Yaguang

2014-01-01

Mehrotra's algorithm has been the most successful infeasible interior-point algorithm for linear programming since 1990. Most popular interior-point software packages for linear programming are based on Mehrotra's algorithm. This paper proposes an alternative algorithm, arc-search infeasible interior-point algorithm. We will demonstrate, by testing Netlib problems and comparing the test results obtained by arc-search infeasible interior-point algorithm and Mehrotra's algorithm, that the propo...

Quadratic Finite Element Method for 1D Deterministic Transport

International Nuclear Information System (INIS)

Tolar, D R Jr.; Ferguson, J M

2004-01-01

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

A Comparative Analysis of Quadratics Unit in Singaporean, Turkish and IBDP Mathematics Textbooks

Directory of Open Access Journals (Sweden)

Reyhan Sağlam

2012-12-01

Full Text Available The purpose of this study was to analyze and compare the contents of the chapters on quadratics in three mathematics textbooks selected from Turkey, Singapore, and the International Baccalaureate Diploma Program (IBDP through content analysis. The analysis of mathematical content showed that the three textbooks have different approaches and priorities in terms of the positions of chapters and weights of the quadratics units, and the time allocated to them within the respective curricular programs. It was also found that the Turkish textbook covers a greater number of learning outcomes targeted for quadratics among the three mathematics syllabi, showing a detailed treatment of the topic compared to the other two textbooks.Key Words: Content analysis, international comparative studies, mathematics textbooks

Gravitation and quadratic forms

International Nuclear Information System (INIS)

Ananth, Sudarshan; Brink, Lars; Majumdar, Sucheta; Mali, Mahendra; Shah, Nabha

2017-01-01

The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.

Gravitation and quadratic forms

Energy Technology Data Exchange (ETDEWEB)

Ananth, Sudarshan [Indian Institute of Science Education and Research,Pune 411008 (India); Brink, Lars [Department of Physics, Chalmers University of Technology,S-41296 Göteborg (Sweden); Institute of Advanced Studies and Department of Physics & Applied Physics,Nanyang Technological University,Singapore 637371 (Singapore); Majumdar, Sucheta [Indian Institute of Science Education and Research,Pune 411008 (India); Mali, Mahendra [School of Physics, Indian Institute of Science Education and Research,Thiruvananthapuram, Trivandrum 695016 (India); Shah, Nabha [Indian Institute of Science Education and Research,Pune 411008 (India)

2017-03-31

The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.

Primal-dual path-following algorithms for circular programming

Directory of Open Access Journals (Sweden)

Baha Alzalg

2017-06-01

Full Text Available Circular programming problems are a new class of convex optimization problems that include second-order cone programming problems as a special case‎. ‎Alizadeh and Goldfarb [Math‎. ‎Program‎. ‎Ser‎. ‎A 95 (2003 3--51] introduced primal-dual path-following algorithms for solving second-order cone programming problems‎. ‎In this paper‎, ‎we generalize their work by using the machinery of Euclidean Jordan algebras associated with the circular cones to derive primal-dual path-following interior point algorithms for circular programming problems‎. ‎We prove polynomial convergence of the proposed algorithms by showing that the circular logarithmic barrier is a strongly self-concordant barrier‎. ‎The numerical examples show the path-following algorithms are simple and efficient‎.

Separable quadratic stochastic operators

International Nuclear Information System (INIS)

Rozikov, U.A.; Nazir, S.

2009-04-01

We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well known, we mainly study the properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. We also compare our results with known results of the theory of quadratic operators and give some open problems. (author)

Quantum Algorithms for Weighing Matrices and Quadratic Residues

OpenAIRE

van Dam, Wim

2000-01-01

In this article we investigate how we can employ the structure of combinatorial objects like Hadamard matrices and weighing matrices to device new quantum algorithms. We show how the properties of a weighing matrix can be used to construct a problem for which the quantum query complexity is ignificantly lower than the classical one. It is pointed out that this scheme captures both Bernstein & Vazirani's inner-product protocol, as well as Grover's search algorithm. In the second part of the ar...

KENO-VI: A Monte Carlo Criticality Program with generalized quadratic geometry

International Nuclear Information System (INIS)

Hollenbach, D.F.; Petrie, L.M.; Landers, N.F.

1993-01-01

This report discusses KENO-VI which is a new version of the KENO monte Carlo Criticality Safety developed at Oak Ridge National Laboratory. The purpose of KENO-VI is to provide a criticality safety code similar to KENO-V.a that possesses a more general and flexible geometry package. KENO-VI constructs and processes geometry data as sets of quadratic equations. A lengthy set of simple, easy-to-use geometric functions, similar to those provided in KENO-V.a., and the ability to build more complex geometric shapes represented by sets of quadratic equations are the heart of the geometry package in KENO-VI. The code's flexibility is increased by allowing intersecting geometry regions, hexagonal as well as cuboidal arrays, and the ability to specify an array boundary that intersects the array

An enhanced fractal image denoising algorithm

International Nuclear Information System (INIS)

Lu Jian; Ye Zhongxing; Zou Yuru; Ye Ruisong

2008-01-01

In recent years, there has been a significant development in image denoising using fractal-based method. This paper presents an enhanced fractal predictive denoising algorithm for denoising the images corrupted by an additive white Gaussian noise (AWGN) by using quadratic gray-level function. Meanwhile, a quantization method for the fractal gray-level coefficients of the quadratic function is proposed to strictly guarantee the contractivity requirement of the enhanced fractal coding, and in terms of the quality of the fractal representation measured by PSNR, the enhanced fractal image coding using quadratic gray-level function generally performs better than the standard fractal coding using linear gray-level function. Based on this enhanced fractal coding, the enhanced fractal image denoising is implemented by estimating the fractal gray-level coefficients of the quadratic function of the noiseless image from its noisy observation. Experimental results show that, compared with other standard fractal-based image denoising schemes using linear gray-level function, the enhanced fractal denoising algorithm can improve the quality of the restored image efficiently

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

Science.gov (United States)

Liao, Bolin; Zhang, Yunong; Jin, Long

2016-02-01

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

Quadratic Polynomial Regression using Serial Observation Processing:Implementation within DART

Science.gov (United States)

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

2017-12-01

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

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

Energy Technology Data Exchange (ETDEWEB)

Enghauser, Michael [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2016-02-01

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

Linear programming mathematics, theory and algorithms

CERN Document Server

1996-01-01

Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.

Linear programming foundations and extensions

CERN Document Server

Vanderbei, Robert J

2001-01-01

Linear Programming: Foundations and Extensions is an introduction to the field of optimization. The book emphasizes constrained optimization, beginning with a substantial treatment of linear programming, and proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. The book is carefully written. Specific examples and concrete algorithms precede more abstract topics. Topics are clearly developed with a large number of numerical examples worked out in detail. Moreover, Linear Programming: Foundations and Extensions underscores the purpose of optimization: to solve practical problems on a computer. Accordingly, the book is coordinated with free efficient C programs that implement the major algorithms studied: -The two-phase simplex method; -The primal-dual simplex method; -The path-following interior-point method; -The homogeneous self-dual methods. In addition, there are online JAVA applets that illustrate various pivot rules and variants of the simplex m...

Synthesis of concentric circular antenna arrays using dragonfly algorithm

Science.gov (United States)

Babayigit, B.

2018-05-01

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

Multiparametric programming based algorithms for pure integer and mixed-integer bilevel programming problems

KAUST Repository

Domí nguez, Luis F.; Pistikopoulos, Efstratios N.

2010-01-01

continuous multiparametric programming algorithm is then used to solve the reformulated convex inner problem. The second algorithm addresses the mixed-integer case of the bilevel programming problem where integer and continuous variables of the outer problem

Reconstruction of tomographic images from projections of a small number of views by means of mathematical programming

International Nuclear Information System (INIS)

Kobayashi, Fujio; Yamaguchi, Shoichiro

1985-01-01

Fundamental studies have been made on the application of mathematical programming to the reconstruction of tomographic images from projections of a small number of views without requiring any circular symmetry nor periodicity. Linear programming and quadratic programming were applied to minimize the quadratic sum of the residue and to finally obtain optimized reconstruction images. The mathematical algorithms were verified by the method of computer simulation, and the relationship between the number of picture elements and the number of iterations necessary for convergence was also investigated. The methods of linear programming and quadratic programming require fairly simple mathematical procedures, and strict solutions can be obtained within a finite number of iterations. Their only draw back is the requirement of a large quantity of computer memory. But this problem will be desolved by the advent of large fast memory devices in the near future. (Aoki, K.)

An approach of traffic signal control based on NLRSQP algorithm

Science.gov (United States)

Zou, Yuan-Yang; Hu, Yu

2017-11-01

This paper presents a linear program model with linear complementarity constraints (LPLCC) to solve traffic signal optimization problem. The objective function of the model is to obtain the minimization of total queue length with weight factors at the end of each cycle. Then, a combination algorithm based on the nonlinear least regression and sequence quadratic program (NLRSQP) is proposed, by which the local optimal solution can be obtained. Furthermore, four numerical experiments are proposed to study how to set the initial solution of the algorithm that can get a better local optimal solution more quickly. In particular, the results of numerical experiments show that: The model is effective for different arrival rates and weight factors; and the lower bound of the initial solution is, the better optimal solution can be obtained.

Dynamic programming algorithms for biological sequence comparison.

Science.gov (United States)

Pearson, W R; Miller, W

1992-01-01

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

Linear Quadratic Controller with Fault Detection in Compact Disk Players

DEFF Research Database (Denmark)

Vidal, Enrique Sanchez; Hansen, K.G.; Andersen, R.S.

2001-01-01

The design of the positioning controllers in Optical Disk Drives are today subjected to a trade off between an acceptable suppression of external disturbances and an acceptable immunity against surfaces defects. In this paper an algorithm is suggested to detect defects of the disk surface combined...... with an observer and a Linear Quadratic Regulator. As a result, the mentioned trade off is minimized and the playability of the tested compact disk player is considerably enhanced....

Algorithm for programming function generators

International Nuclear Information System (INIS)

Bozoki, E.

1981-01-01

The present paper deals with a mathematical problem, encountered when driving a fully programmable μ-processor controlled function generator. An algorithm is presented to approximate a desired function by a set of straight segments in such a way that additional restrictions (hardware imposed) are also satisfied. A computer program which incorporates this algorithm and automatically generates the necessary input for the function generator for a broad class of desired functions is also described

Optimization of Algorithms Using Extensions of Dynamic Programming

KAUST Repository

AbouEisha, Hassan M.

2017-04-09

We study and answer questions related to the complexity of various important problems such as: multi-frontal solvers of hp-adaptive finite element method, sorting and majority. We advocate the use of dynamic programming as a viable tool to study optimal algorithms for these problems. The main approach used to attack these problems is modeling classes of algorithms that may solve this problem using a discrete model of computation then defining cost functions on this discrete structure that reflect different complexity measures of the represented algorithms. As a last step, dynamic programming algorithms are designed and used to optimize those models (algorithms) and to obtain exact results on the complexity of the studied problems. The first part of the thesis presents a novel model of computation (element partition tree) that represents a class of algorithms for multi-frontal solvers along with cost functions reflecting various complexity measures such as: time and space. It then introduces dynamic programming algorithms for multi-stage and bi-criteria optimization of element partition trees. In addition, it presents results based on optimal element partition trees for famous benchmark meshes such as: meshes with point and edge singularities. New improved heuristics for those benchmark meshes were ob- tained based on insights of the optimal results found by our algorithms. The second part of the thesis starts by introducing a general problem where different problems can be reduced to and show how to use a decision table to model such problem. We describe how decision trees and decision tests for this table correspond to adaptive and non-adaptive algorithms for the original problem. We present exact bounds on the average time complexity of adaptive algorithms for the eight elements sorting problem. Then bounds on adaptive and non-adaptive algorithms for a variant of the majority problem are introduced. Adaptive algorithms are modeled as decision trees whose depth

Factorization method of quadratic template

Science.gov (United States)

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.

Aspects of Quadratic Gravity

CERN Document Server

Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio

2016-01-01

We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...

Sparse Covariance Matrix Estimation by DCA-Based Algorithms.

Science.gov (United States)

Phan, Duy Nhat; Le Thi, Hoai An; Dinh, Tao Pham

2017-11-01

This letter proposes a novel approach using the [Formula: see text]-norm regularization for the sparse covariance matrix estimation (SCME) problem. The objective function of SCME problem is composed of a nonconvex part and the [Formula: see text] term, which is discontinuous and difficult to tackle. Appropriate DC (difference of convex functions) approximations of [Formula: see text]-norm are used that result in approximation SCME problems that are still nonconvex. DC programming and DCA (DC algorithm), powerful tools in nonconvex programming framework, are investigated. Two DC formulations are proposed and corresponding DCA schemes developed. Two applications of the SCME problem that are considered are classification via sparse quadratic discriminant analysis and portfolio optimization. A careful empirical experiment is performed through simulated and real data sets to study the performance of the proposed algorithms. Numerical results showed their efficiency and their superiority compared with seven state-of-the-art methods.

Lambda-Lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, Olivier; Schultz, Ulrik Pagh

2002-01-01

Lambda-lifting is a program transformation used in compilers and in partial evaluators and that operates in cubic time. In this article, we show how to reduce this complexity to quadratic time. Lambda-lifting transforms a block-structured program into a set of recursive equations, one for each...... local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters that yields the cubic factor in the traditional formulation of lambda-lifting, which...... is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity of lambda-lifting from O(n 3 log n)toO(n2 log n), where n is the size of the program. Since a lambda-lifter can output...

2-Phase NSGA II: An Optimized Reward and Risk Measurements Algorithm in Portfolio Optimization

Directory of Open Access Journals (Sweden)

Seyedeh Elham Eftekharian

2017-11-01

Full Text Available Portfolio optimization is a serious challenge for financial engineering and has pulled down special attention among investors. It has two objectives: to maximize the reward that is calculated by expected return and to minimize the risk. Variance has been considered as a risk measure. There are many constraints in the world that ultimately lead to a non–convex search space such as cardinality constraint. In conclusion, parametric quadratic programming could not be applied and it seems essential to apply multi-objective evolutionary algorithm (MOEA. In this paper, a new efficient multi-objective portfolio optimization algorithm called 2-phase NSGA II algorithm is developed and the results of this algorithm are compared with the NSGA II algorithm. It was found that 2-phase NSGA II significantly outperformed NSGA II algorithm.

TEACHING ALGORITHMIZATION AND PROGRAMMING USING PYTHON LANGUAGE

Directory of Open Access Journals (Sweden)

M. Lvov

2014-07-01

Full Text Available The article describes requirements to educational programming languages and considers the use of Python as the first programming language. The issues of introduction of this programming language into teaching and replacing Pascal by Python are examined. The advantages of such approach are regarded. The comparison of popular programming languages is represented from the point of view of their convenience of use for teaching algorithmization and programming. Python supports lots of programming paradigms: structural, object-oriented, functional, imperative and aspect-oriented, and learning can be started without any preparation. There is one more advantage of the language: all algorithms are written easily and structurally in Python. Therefore, due to all mentioned above, it is possible to affirm that Python pretends to become a decent replacement for educational programming language PASCAL both at schools and on the first courses of higher education establishments.

Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks

KAUST Repository

Li, Yanning

2014-03-01

This article presents a new optimal control framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi (H-J) equation and the commonly used triangular fundamental diagram, we pose the problem of controlling the state of the system on a network link, in a finite horizon, as a Linear Program (LP). We then show that this framework can be extended to an arbitrary transportation network, resulting in an LP or a Quadratic Program. Unlike many previously investigated transportation network control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e., discontinuities in the state of the system). As it leverages the intrinsic properties of the H-J equation used to model the state of the system, it does not require any approximation, unlike classical methods that are based on discretizations of the model. The computational efficiency of the method is illustrated on a transportation network. © 2014 IEEE.

Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks

KAUST Repository

Li, Yanning; Canepa, Edward S.; Claudel, Christian

2014-01-01

This article presents a new optimal control framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi (H-J) equation and the commonly used triangular fundamental diagram, we pose the problem of controlling the state of the system on a network link, in a finite horizon, as a Linear Program (LP). We then show that this framework can be extended to an arbitrary transportation network, resulting in an LP or a Quadratic Program. Unlike many previously investigated transportation network control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e., discontinuities in the state of the system). As it leverages the intrinsic properties of the H-J equation used to model the state of the system, it does not require any approximation, unlike classical methods that are based on discretizations of the model. The computational efficiency of the method is illustrated on a transportation network. © 2014 IEEE.

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

Science.gov (United States)

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

2013-01-01

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

A numerical algorithm to find all feedback Nash equilibria in scalar affine quadratic differential games

NARCIS (Netherlands)

Engwerda, Jacob

2015-01-01

This note deals with solving scalar coupled algebraic Riccati equations. These equations arise in finding linear feedback Nash equilibria of the scalar N-player affine quadratic differential game. A numerical procedure is provided to compute all the stabilizing solutions. The main idea is to

Constrained Quadratic Programming and Neurodynamics-Based Solver for Energy Optimization of Biped Walking Robots

Directory of Open Access Journals (Sweden)

Liyang Wang

2017-01-01

Full Text Available The application of biped robots is always trapped by their high energy consumption. This paper makes a contribution by optimizing the joint torques to decrease the energy consumption without changing the biped gaits. In this work, a constrained quadratic programming (QP problem for energy optimization is formulated. A neurodynamics-based solver is presented to solve the QP problem. Differing from the existing literatures, the proposed neurodynamics-based energy optimization (NEO strategy minimizes the energy consumption and guarantees the following three important constraints simultaneously: (i the force-moment equilibrium equation of biped robots, (ii frictions applied by each leg on the ground to hold the biped robot without slippage and tipping over, and (iii physical limits of the motors. Simulations demonstrate that the proposed strategy is effective for energy-efficient biped walking.

An Extended Quadratic Frobenius Primality Test with Average Case Error Estimates

DEFF Research Database (Denmark)

Damgård, Ivan Bjerre; Frandsen, Gudmund Skovbjerg

2001-01-01

We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to an extends the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham. EQFT takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability, namely 256/331776t for t...... for the error probability of this algorithm as well as a general closed expression bounding the error. For instance, it is at most 2-143 for k = 500, t = 2. Compared to earlier similar results for the Miller-Rabin test, the results indicates that our test in the average case has the effect of 9 Miller......-Rabin tests, while only taking time equivalent to about 2 such tests. We also give bounds for the error in case a prime is sought by incremental search from a random starting point....

A Fast Condensing Method for Solution of Linear-Quadratic Control Problems

DEFF Research Database (Denmark)

Frison, Gianluca; Jørgensen, John Bagterp

2013-01-01

consider a condensing (or state elimination) method to solve an extended version of the LQ control problem, and we show how to exploit the structure of this problem to both factorize the dense Hessian matrix and solve the system. Furthermore, we present two efficient implementations. The first......In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is usually the main computational effort. In this paper we...... implementation is formally identical to the Riccati recursion based solver and has a computational complexity that is linear in the control horizon length and cubic in the number of states. The second implementation has a computational complexity that is quadratic in the control horizon length as well...

ANALYSIS AND PERFORMANCE MEASUREMENT OF EXISTING SOLUTION METHODS OF QUADRATIC ASSIGNMENT PROBLEM

Directory of Open Access Journals (Sweden)

Morteza KARAMI

2014-01-01

Full Text Available Quadratic Assignment Problem (QAP is known as one of the most difficult combinatorial optimization problems that is classified in the category of NP-hard problems. Quadratic Assignment Problem Library (QAPLIB is a full database of QAPs which contains several problems from different authors and different sizes. Many exact and meta-heuristic solution methods have been introduced to solve QAP. In this study we focus on previously introduced solution methods of QAP e.g. Branch and Bound (B&B, Simulated Annealing (SA Algorithm, Greedy Randomized Adaptive Search Procedure (GRASP for dense and sparse QAPs. The codes of FORTRAN for these methods were downloaded from QAPLIB. All problems of QAPLIB were solved by the abovementioned methods. Several results were obtained from the computational experiments part. The Results show that the Branch and Bound method is able to introduce a feasible solution for all problems while Simulated Annealing Algorithm and GRASP methods are not able to find any solution for some problems. On the other hand, Simulated Annealing and GRASP methods have shorter run time comparing to the Branch and Bound method. In addition, the performance of the methods on the objective function value is discussed.

Input-constrained model predictive control via the alternating direction method of multipliers

DEFF Research Database (Denmark)

Sokoler, Leo Emil; Frison, Gianluca; Andersen, Martin S.

2014-01-01

This paper presents an algorithm, based on the alternating direction method of multipliers, for the convex optimal control problem arising in input-constrained model predictive control. We develop an efficient implementation of the algorithm for the extended linear quadratic control problem (LQCP......) with input and input-rate limits. The algorithm alternates between solving an extended LQCP and a highly structured quadratic program. These quadratic programs are solved using a Riccati iteration procedure, and a structure-exploiting interior-point method, respectively. The computational cost per iteration...... is quadratic in the dimensions of the controlled system, and linear in the length of the prediction horizon. Simulations show that the approach proposed in this paper is more than an order of magnitude faster than several state-of-the-art quadratic programming algorithms, and that the difference in computation...

Synthesizing Dynamic Programming Algorithms from Linear Temporal Logic Formulae

Science.gov (United States)

Rosu, Grigore; Havelund, Klaus

2001-01-01

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

DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers

Science.gov (United States)

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

2016-10-01

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

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

Science.gov (United States)

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

2017-04-01

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

A new algorithm for generalized fractional programs

NARCIS (Netherlands)

J.B.G. Frenk (Hans); A.I. Barros (Ana); S. Schaible; S. Zhang (Shuzhong)

1996-01-01

textabstractA new dual problem for convex generalized fractional programs with no duality gap is presented and it is shown how this dual problem can be efficiently solved using a parametric approach. The resulting algorithm can be seen as “dual” to the Dinkelbach-type algorithm for generalized

AES ALGORITHM IMPLEMENTATION IN PROGRAMMING LANGUAGES

Directory of Open Access Journals (Sweden)

Luminiţa DEFTA

2010-12-01

Full Text Available Information encryption represents the usage of an algorithm to convert an unknown message into an encrypted one. It is used to protect the data against unauthorized access. Protected data can be stored on a media device or can be transmitted through the network. In this paper we describe a concrete implementation of the AES algorithm in the Java programming language (available from Java Development Kit 6 libraries and C (using the OpenSSL library. AES (Advanced Encryption Standard is an asymmetric key encryption algorithm formally adopted by the U.S. government and was elected after a long process of standardization.

On the Distribution of Indefinite Quadratic Forms in Gaussian Random Variables

KAUST Repository

Al-Naffouri, Tareq Y.

2015-10-30

© 2015 IEEE. In this work, we propose a unified approach to evaluating the CDF and PDF of indefinite quadratic forms in Gaussian random variables. Such a quantity appears in many applications in communications, signal processing, information theory, and adaptive filtering. For example, this quantity appears in the mean-square-error (MSE) analysis of the normalized least-meansquare (NLMS) adaptive algorithm, and SINR associated with each beam in beam forming applications. The trick of the proposed approach is to replace inequalities that appear in the CDF calculation with unit step functions and to use complex integral representation of the the unit step function. Complex integration allows us then to evaluate the CDF in closed form for the zero mean case and as a single dimensional integral for the non-zero mean case. Utilizing the saddle point technique allows us to closely approximate such integrals in non zero mean case. We demonstrate how our approach can be extended to other scenarios such as the joint distribution of quadratic forms and ratios of such forms, and to characterize quadratic forms in isotropic distributed random variables.We also evaluate the outage probability in multiuser beamforming using our approach to provide an application of indefinite forms in communications.

Portfolio optimization by using linear programing models based on genetic algorithm

Science.gov (United States)

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

2018-01-01

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

Pattern Nulling of Linear Antenna Arrays Using Backtracking Search Optimization Algorithm

Directory of Open Access Journals (Sweden)

Kerim Guney

2015-01-01

Full Text Available An evolutionary method based on backtracking search optimization algorithm (BSA is proposed for linear antenna array pattern synthesis with prescribed nulls at interference directions. Pattern nulling is obtained by controlling only the amplitude, position, and phase of the antenna array elements. BSA is an innovative metaheuristic technique based on an iterative process. Various numerical examples of linear array patterns with the prescribed single, multiple, and wide nulls are given to illustrate the performance and flexibility of BSA. The results obtained by BSA are compared with the results of the following seventeen algorithms: particle swarm optimization (PSO, genetic algorithm (GA, modified touring ant colony algorithm (MTACO, quadratic programming method (QPM, bacterial foraging algorithm (BFA, bees algorithm (BA, clonal selection algorithm (CLONALG, plant growth simulation algorithm (PGSA, tabu search algorithm (TSA, memetic algorithm (MA, nondominated sorting GA-2 (NSGA-2, multiobjective differential evolution (MODE, decomposition with differential evolution (MOEA/D-DE, comprehensive learning PSO (CLPSO, harmony search algorithm (HSA, seeker optimization algorithm (SOA, and mean variance mapping optimization (MVMO. The simulation results show that the linear antenna array synthesis using BSA provides low side-lobe levels and deep null levels.

Extending the Scope of Robust Quadratic Optimization

NARCIS (Netherlands)

Marandi, Ahmadreza; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand

In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in

A New Finite Continuation Algorithm for Linear Programming

DEFF Research Database (Denmark)

Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa

1996-01-01

We describe a new finite continuation algorithm for linear programming. The dual of the linear programming problem with unit lower and upper bounds is formulated as an $\\ell_1$ minimization problem augmented with the addition of a linear term. This nondifferentiable problem is approximated...... by a smooth problem. It is shown that the minimizers of the smooth problem define a family of piecewise-linear paths as a function of a smoothing parameter. Based on this property, a finite algorithm that traces these paths to arrive at an optimal solution of the linear program is developed. The smooth...

Quadratic residues and non-residues selected topics

CERN Document Server

Wright, Steve

2016-01-01

This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.

Mathematical programming methods for large-scale topology optimization problems

DEFF Research Database (Denmark)

Rojas Labanda, Susana

for mechanical problems, but has rapidly extended to many other disciplines, such as fluid dynamics and biomechanical problems. However, the novelty and improvements of optimization methods has been very limited. It is, indeed, necessary to develop of new optimization methods to improve the final designs......, and at the same time, reduce the number of function evaluations. Nonlinear optimization methods, such as sequential quadratic programming and interior point solvers, have almost not been embraced by the topology optimization community. Thus, this work is focused on the introduction of this kind of second...... for the classical minimum compliance problem. Two of the state-of-the-art optimization algorithms are investigated and implemented for this structural topology optimization problem. A Sequential Quadratic Programming (TopSQP) and an interior point method (TopIP) are developed exploiting the specific mathematical...

Students' Understanding of Quadratic Equations

Science.gov (United States)

López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

2016-01-01

Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

A superlinear interior points algorithm for engineering design optimization

Science.gov (United States)

Herskovits, J.; Asquier, J.

1990-01-01

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

PACE: A dynamic programming algorithm for hardware/software partitioning

DEFF Research Database (Denmark)

Knudsen, Peter Voigt; Madsen, Jan

1996-01-01

This paper presents the PACE partitioning algorithm which is used in the LYCOS co-synthesis system for partitioning control/dataflow graphs into hardware and software parts. The algorithm is a dynamic programming algorithm which solves both the problem of minimizing system execution time...

Guam Community Coral Reef Monitoring Program, Benthic Quadrat Surveys at Guam in 2013

Data.gov (United States)

National Oceanic and Atmospheric Administration, Department of Commerce — Guam community members gathered benthic cover data using a 0.25m2 quadrat with 6 intersecting points at each meter along a 25-meter transect. Members identified...

Empirical study of self-configuring genetic programming algorithm performance and behaviour

International Nuclear Information System (INIS)

KrasnoyarskiyRabochiy prospect, Krasnoyarsk, 660014 (Russian Federation))" data-affiliation=" (Siberian State Aerospace University named after Academician M.F. Reshetnev 31 KrasnoyarskiyRabochiy prospect, Krasnoyarsk, 660014 (Russian Federation))" >Semenkin, E; KrasnoyarskiyRabochiy prospect, Krasnoyarsk, 660014 (Russian Federation))" data-affiliation=" (Siberian State Aerospace University named after Academician M.F. Reshetnev 31 KrasnoyarskiyRabochiy prospect, Krasnoyarsk, 660014 (Russian Federation))" >Semenkina, M

2015-01-01

The behaviour of the self-configuring genetic programming algorithm with a modified uniform crossover operator that implements a selective pressure on the recombination stage, is studied over symbolic programming problems. The operator's probabilistic rates interplay is studied and the role of operator variants on algorithm performance is investigated. Algorithm modifications based on the results of investigations are suggested. The performance improvement of the algorithm is demonstrated by the comparative analysis of suggested algorithms on the benchmark and real world problems

Dynamical invariants for variable quadratic Hamiltonians

International Nuclear Information System (INIS)

Suslov, Sergei K

2010-01-01

We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.

A Primal-Dual Interior Point-Linear Programming Algorithm for MPC

DEFF Research Database (Denmark)

Edlund, Kristian; Sokoler, Leo Emil; Jørgensen, John Bagterp

2009-01-01

Constrained optimal control problems for linear systems with linear constraints and an objective function consisting of linear and l1-norm terms can be expressed as linear programs. We develop an efficient primal-dual interior point algorithm for solution of such linear programs. The algorithm...

Orthogonality preserving infinite dimensional quadratic stochastic operators

International Nuclear Information System (INIS)

Akın, Hasan; Mukhamedov, Farrukh

2015-01-01

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

Polyhedral combinatorics of the cardinality constrained quadratic knapsack problem and the quadratic selective travelling salesman problem

DEFF Research Database (Denmark)

Mak, Vicky; Thomadsen, Tommy

2006-01-01

This paper considers the cardinality constrained quadratic knapsack problem (QKP) and the quadratic selective travelling salesman problem (QSTSP). The QKP is a generalization of the knapsack problem and the QSTSP is a generalization of the travelling salesman problem. Thus, both problems are NP...

Quadratically convergent MCSCF scheme using Fock operators

International Nuclear Information System (INIS)

Das, G.

1981-01-01

A quadratically convergent formulation of the MCSCF method using Fock operators is presented. Among its advantages the present formulation is quadratically convergent unlike the earlier ones based on Fock operators. In contrast to other quadratically convergent schemes as well as the one based on generalized Brillouin's theorem, this method leads easily to a hybrid scheme where the weakly coupled orbitals (such as the core) are handled purely by Fock equations, while the rest of the orbitals are treated by a quadratically convergent approach with a truncated virtual space obtained by the use of the corresponding Fock equations

Quadratic brackets from symplectic forms

International Nuclear Information System (INIS)

Alekseev, Anton Yu.; Todorov, Ivan T.

1994-01-01

We give a physicist oriented survey of Poisson-Lie symmetries of classical systems. We consider finite-dimensional geometric actions and the chiral WZNW model as examples for the general construction. An essential point is the appearance of quadratic Poisson brackets for group-like variables. It is believed that upon quantization they lead to quadratic exchange algebras. ((orig.))

An Extended Quadratic Frobenius Primality Test with Average and Worst Case Error Estimates

DEFF Research Database (Denmark)

Damgård, Ivan Bjerre; Frandsen, Gudmund Skovbjerg

2003-01-01

We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to an extends the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham. EQFT takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability, namely 256/331776t for t...... for the error probability of this algorithm as well as a general closed expression bounding the error. For instance, it is at most 2-143 for k = 500, t = 2. Compared to earlier similar results for the Miller-Rabin test, the results indicates that our test in the average case has the effect of 9 Miller......-Rabin tests, while only taking time equivalent to about 2 such tests. We also give bounds for the error in case a prime is sought by incremental search from a random starting point....

An Extended Quadratic Frobenius Primality Test with Average- and Worst-Case Error Estimate

DEFF Research Database (Denmark)

Damgård, Ivan Bjerre; Frandsen, Gudmund Skovbjerg

2006-01-01

We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to an extends the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham. EQFT takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability, namely 256/331776t for t...... for the error probability of this algorithm as well as a general closed expression bounding the error. For instance, it is at most 2-143 for k = 500, t = 2. Compared to earlier similar results for the Miller-Rabin test, the results indicates that our test in the average case has the effect of 9 Miller......-Rabin tests, while only taking time equivalent to about 2 such tests. We also give bounds for the error in case a prime is sought by incremental search from a random starting point....

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

Science.gov (United States)

Rey, Martin P.; Pontzen, Andrew

2018-02-01

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

Quantum-circuit model of Hamiltonian search algorithms

International Nuclear Information System (INIS)

Roland, Jeremie; Cerf, Nicolas J.

2003-01-01

We analyze three different quantum search algorithms, namely, the traditional circuit-based Grover's algorithm, its continuous-time analog by Hamiltonian evolution, and the quantum search by local adiabatic evolution. We show that these algorithms are closely related in the sense that they all perform a rotation, at a constant angular velocity, from a uniform superposition of all states to the solution state. This makes it possible to implement the two Hamiltonian-evolution algorithms on a conventional quantum circuit, while keeping the quadratic speedup of Grover's original algorithm. It also clarifies the link between the adiabatic search algorithm and Grover's algorithm

Linear programming algorithms and applications

CERN Document Server

Vajda, S

1981-01-01

This text is based on a course of about 16 hours lectures to students of mathematics, statistics, and/or operational research. It is intended to introduce readers to the very wide range of applicability of linear programming, covering problems of manage­ ment, administration, transportation and a number of other uses which are mentioned in their context. The emphasis is on numerical algorithms, which are illustrated by examples of such modest size that the solutions can be obtained using pen and paper. It is clear that these methods, if applied to larger problems, can also be carried out on automatic (electronic) computers. Commercially available computer packages are, in fact, mainly based on algorithms explained in this book. The author is convinced that the user of these algorithms ought to be knowledgeable about the underlying theory. Therefore this volume is not merely addressed to the practitioner, but also to the mathematician who is interested in relatively new developments in algebraic theory and in...

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

Science.gov (United States)

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

2009-11-01

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

A Quasi-Dynamic Optimal Control Strategy for Non-Linear Multivariable Processes Based upon Non-Quadratic Objective Functions

Directory of Open Access Journals (Sweden)

Jens G. Balchen

1984-10-01

Full Text Available The problem of systematic derivation of a quasi-dynamic optimal control strategy for a non-linear dynamic process based upon a non-quadratic objective function is investigated. The wellknown LQG-control algorithm does not lead to an optimal solution when the process disturbances have non-zero mean. The relationships between the proposed control algorithm and LQG-control are presented. The problem of how to constrain process variables by means of 'penalty' - terms in the objective function is dealt with separately.

Projection of curves on B-spline surfaces using quadratic reparameterization

KAUST Repository

Yang, Yijun

2010-09-01

Curves on surfaces play an important role in computer aided geometric design. In this paper, we present a hyperbola approximation method based on the quadratic reparameterization of Bézier surfaces, which generates reasonable low degree curves lying completely on the surfaces by using iso-parameter curves of the reparameterized surfaces. The Hausdorff distance between the projected curve and the original curve is controlled under the user-specified distance tolerance. The projected curve is T-G 1 continuous, where T is the user-specified angle tolerance. Examples are given to show the performance of our algorithm. © 2010 Elsevier Inc. All rights reserved.

Quadratic Boost A-Source Impedance Network

DEFF Research Database (Denmark)

Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii

2016-01-01

A novel quadratic boost A-source impedance network is proposed to realize converters that demand very high voltage gain. To satisfy the requirement, the network uses an autotransformer where the obtained gain is quadratically dependent on the duty ratio and is unmatched by any existing impedance...

Group leaders optimization algorithm

Science.gov (United States)

Daskin, Anmer; Kais, Sabre

2011-03-01

We present a new global optimization algorithm in which the influence of the leaders in social groups is used as an inspiration for the evolutionary technique which is designed into a group architecture. To demonstrate the efficiency of the method, a standard suite of single and multi-dimensional optimization functions along with the energies and the geometric structures of Lennard-Jones clusters are given as well as the application of the algorithm on quantum circuit design problems. We show that as an improvement over previous methods, the algorithm scales as N 2.5 for the Lennard-Jones clusters of N-particles. In addition, an efficient circuit design is shown for a two-qubit Grover search algorithm which is a quantum algorithm providing quadratic speedup over the classical counterpart.

Quadratic Diophantine equations

CERN Document Server

Andreescu, Titu

2015-01-01

This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.

A Numerical Algorithm to find All Scalar Feedback Nash Equilibria

NARCIS (Netherlands)

Engwerda, J.C.

2013-01-01

Abstract: In this note we generalize a numerical algorithm presented in [9] to calculate all solutions of the scalar algebraic Riccati equations that play an important role in finding feedback Nash equilibria of the scalar N-player linear affine-quadratic differential game. The algorithm is based on

A discretized algorithm for the solution of a constrained, continuous ...

African Journals Online (AJOL)

A discretized algorithm for the solution of a constrained, continuous quadratic control problem. ... The results obtained show that the Discretized constrained algorithm (DCA) is much more accurate and more efficient than some of these techniques, particularly the FSA. Journal of the Nigerian Association of Mathematical ...

A review on quantum search algorithms

Science.gov (United States)

Giri, Pulak Ranjan; Korepin, Vladimir E.

2017-12-01

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

Algorithmic Trading with Developmental and Linear Genetic Programming

Science.gov (United States)

Wilson, Garnett; Banzhaf, Wolfgang

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

A scalable parallel algorithm for multiple objective linear programs

Science.gov (United States)

Wiecek, Malgorzata M.; Zhang, Hong

1994-01-01

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

Parallel Implementation of Riccati Recursion for Solving Linear-Quadratic Control Problems

DEFF Research Database (Denmark)

Frison, Gianluca; Jørgensen, John Bagterp

2013-01-01

In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is usually the main computational effort. In this paper...... an alternative version of the Riccati recursion solver for LQ control problems is presented. The performance of both the classical and the alternative version is analyzed from a theoretical as well as a numerical point of view, and the alternative version is found to be approximately 50% faster than...

A backtracking algorithm for the stream AND-parallel execution of logic programs

Energy Technology Data Exchange (ETDEWEB)

Somogyi, Z.; Ramamohanarao, K.; Vaghani, J. (Univ. of Melbourne, Parkville (Australia))

1988-06-01

The authors present the first backtracking algorithm for stream AND-parallel logic programs. It relies on compile-time knowledge of the data flow graph of each clause to let it figure out efficiently which goals to kill or restart when a goal fails. This crucial information, which they derive from mode declarations, was not available at compile-time in any previous stream AND-parallel system. They show that modes can increase the precision of the backtracking algorithm, though their algorithm allows this precision to be traded off against overhead on a procedure-by-procedure and call-by-call basis. The modes also allow their algorithm to handle efficiently programs that manipulate partially instantiated data structures and an important class of programs with circular dependency graphs. On code that does not need backtracking, the efficiency of their algorithm approaches that of the committed-choice languages; on code that does need backtracking its overhead is comparable to that of the independent AND-parallel backtracking algorithms.

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

Science.gov (United States)

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

2018-04-01

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

Quadratic maximization on the unit simplex: structure, stability, genericity and application in biology

NARCIS (Netherlands)

Still, Georg J.; Ahmed, F.

The paper deals with the simple but important problem of maximizing a (nonconvex) quadratic function on the unit simplex. This program is directly related to the concept of evolutionarily stable strategies (ESS) in biology. We discuss this relation and study optimality conditions, stability and

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

Science.gov (United States)

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

2017-09-08

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

Rational hybrid Monte Carlo algorithm for theories with unknown spectral bounds

International Nuclear Information System (INIS)

Kogut, J. B.; Sinclair, D. K.

2006-01-01

The Rational Hybrid Monte Carlo (RHMC) algorithm extends the Hybrid Monte Carlo algorithm for lattice QCD simulations to situations involving fractional powers of the determinant of the quadratic Dirac operator. This avoids the updating increment (dt) dependence of observables which plagues the Hybrid Molecular-dynamics (HMD) method. The RHMC algorithm uses rational approximations to fractional powers of the quadratic Dirac operator. Such approximations are only available when positive upper and lower bounds to the operator's spectrum are known. We apply the RHMC algorithm to simulations of 2 theories for which a positive lower spectral bound is unknown: lattice QCD with staggered quarks at finite isospin chemical potential and lattice QCD with massless staggered quarks and chiral 4-fermion interactions (χQCD). A choice of lower bound is made in each case, and the properties of the RHMC simulations these define are studied. Justification of our choices of lower bounds is made by comparing measurements with those from HMD simulations, and by comparing different choices of lower bounds

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

Science.gov (United States)

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

2016-01-01

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

Stability in quadratic torsion theories

Energy Technology Data Exchange (ETDEWEB)

Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)

2017-11-15

We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)

Stability in quadratic torsion theories

International Nuclear Information System (INIS)

Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado

2017-01-01

We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)

Finite element method with quadratic quadrilateral unit for solving two dimensional incompressible N-S equation

International Nuclear Information System (INIS)

Tao Ganqiang; Yu Qing; Xiao Xiao

2011-01-01

Viscous and incompressible fluid flow is important for numerous engineering mechanics problems. Because of high non linear and incompressibility for Navier-Stokes equation, it is very difficult to solve Navier-Stokes equation by numerical method. According to its characters of Navier-Stokes equation, quartic derivation controlling equation of the two dimensional incompressible Navier-Stokes equation is set up firstly. The method solves the problem for dealing with vorticity boundary and automatically meets incompressibility condition. Then Finite Element equation for Navier-Stokes equation is proposed by using quadratic quadrilateral unit with 8 nodes in which the unit function is quadratic and non linear.-Based on it, the Finite Element program of quadratic quadrilateral unit with 8 nodes is developed. Lastly, numerical experiment proves the accuracy and dependability of the method and also shows the method has good application prospect in computational fluid mechanics. (authors)

Efficient Implementation of the Riccati Recursion for Solving Linear-Quadratic Control Problems

DEFF Research Database (Denmark)

Frison, Gianluca; Jørgensen, John Bagterp

2013-01-01

In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is typically the main computational effort at each iteration....... In this paper, we compare a number of solvers for an extended formulation of the LQ control problem: a Riccati recursion based solver can be considered the best choice for the general problem with dense matrices. Furthermore, we present a novel version of the Riccati solver, that makes use of the Cholesky...... factorization of the Pn matrices to reduce the number of flops. When combined with regularization and mixed precision, this algorithm can solve large instances of the LQ control problem up to 3 times faster than the classical Riccati solver....

Optimisation in radiotherapy II: Programmed and inversion optimisation algorithms

International Nuclear Information System (INIS)

Ebert, M.

1997-01-01

This is the second article in a three part examination of optimisation in radiotherapy. The previous article established the bases of optimisation in radiotherapy, and the formulation of the optimisation problem. This paper outlines several algorithms that have been used in radiotherapy, for searching for the best irradiation strategy within the full set of possible strategies. Two principle classes of algorithm are considered - those associated with mathematical programming which employ specific search techniques, linear programming type searches or artificial intelligence - and those which seek to perform a numerical inversion of the optimisation problem, finishing with deterministic iterative inversion. (author)

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

Science.gov (United States)

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

2016-05-04

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

An example in linear quadratic optimal control

NARCIS (Netherlands)

Weiss, George; Zwart, Heiko J.

1998-01-01

We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme

ACCEPT: a three-dimensional finite element program for large deformation elastic-plastic-creep analysis of pressurized tubes (LWBR/AWBA Development Program)

International Nuclear Information System (INIS)

Hutula, D.N.; Wiancko, B.E.

1980-03-01

ACCEPT is a three-dimensional finite element computer program for analysis of large-deformation elastic-plastic-creep response of Zircaloy tubes subjected to temperature, surface pressures, and axial force. A twenty-mode, tri-quadratic, isoparametric element is used along with a Zircaloy materials model. A linear time-incremental procedure with residual force correction is used to solve for the time-dependent response. The program features an algorithm which automatically chooses the time step sizes to control the accuracy and numerical stability of the solution. A contact-separation capability allows modeling of interaction of reactor fuel rod cladding with fuel pellets or external supports

Radiotherapy treatment planning linear-quadratic radiobiology

CERN Document Server

Chapman, J Donald

2015-01-01

Understand Quantitative Radiobiology from a Radiation Biophysics PerspectiveIn the field of radiobiology, the linear-quadratic (LQ) equation has become the standard for defining radiation-induced cell killing. Radiotherapy Treatment Planning: Linear-Quadratic Radiobiology describes tumor cell inactivation from a radiation physics perspective and offers appropriate LQ parameters for modeling tumor and normal tissue responses.Explore the Latest Cell Killing Numbers for Defining Iso-Effective Cancer TreatmentsThe book compil

A Branch-and-Bound Algorithm Embedded with DCA for DC Programming

Directory of Open Access Journals (Sweden)

Meihua Wang

2012-01-01

Full Text Available The special importance of Difference of Convex (DC functions programming has been recognized in recent studies on nonconvex optimization problems. In this work, a class of DC programming derived from the portfolio selection problems is studied. The most popular method applied to solve the problem is the Branch-and-Bound (B&B algorithm. However, “the curse of dimensionality” will affect the performance of the B&B algorithm. DC Algorithm (DCA is an efficient method to get a local optimal solution. It has been applied to many practical problems, especially for large-scale problems. A B&B-DCA algorithm is proposed by embedding DCA into the B&B algorithms, the new algorithm improves the computational performance and obtains a global optimal solution. Computational results show that the proposed B&B-DCA algorithm has the superiority of the branch number and computational time than general B&B. The nice features of DCA (inexpensiveness, reliability, robustness, globality of computed solutions, etc. provide crucial support to the combined B&B-DCA for accelerating the convergence of B&B.

A Partitioning and Bounded Variable Algorithm for Linear Programming

Science.gov (United States)

Sheskin, Theodore J.

2006-01-01

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

A synthesis/design optimization algorithm for Rankine cycle based energy systems

International Nuclear Information System (INIS)

Toffolo, Andrea

2014-01-01

The algorithm presented in this work has been developed to search for the optimal topology and design parameters of a set of Rankine cycles forming an energy system that absorbs/releases heat at different temperature levels and converts part of the absorbed heat into electricity. This algorithm can deal with several applications in the field of energy engineering: e.g., steam cycles or bottoming cycles in combined/cogenerative plants, steam networks, low temperature organic Rankine cycles. The main purpose of this algorithm is to overcome the limitations of the search space introduced by the traditional mixed-integer programming techniques, which assume that possible solutions are derived from a single superstructure embedding them all. The algorithm presented in this work is a hybrid evolutionary/traditional optimization algorithm organized in two levels. A complex original codification of the topology and the intensive design parameters of the system is managed by the upper level evolutionary algorithm according to the criteria set by the HEATSEP method, which are used for the first time to automatically synthesize a “basic” system configuration from a set of elementary thermodynamic cycles. The lower SQP (sequential quadratic programming) algorithm optimizes the objective function(s) with respect to cycle mass flow rates only, taking into account the heat transfer feasibility constraint within the undefined heat transfer section. A challenging example of application is also presented to show the capabilities of the algorithm. - Highlights: • Energy systems based on Rankine cycles are used in many applications. • A hybrid algorithm is proposed to optimize the synthesis/design of such systems. • The topology of the candidate solutions is not limited by a superstructure. • Topology is managed by the genetic operators of the upper level algorithm. • The effectiveness of the algorithm is proved in a complex test case

Generic Optimization Program User Manual Version 3.0.0

International Nuclear Information System (INIS)

Wetter, Michael

2009-01-01

GenOpt is an optimization program for the minimization of a cost function that is evaluated by an external simulation program. It has been developed for optimization problems where the cost function is computationally expensive and its derivatives are not available or may not even exist. GenOpt can be coupled to any simulation program that reads its input from text files and writes its output to text files. The independent variables can be continuous variables (possibly with lower and upper bounds), discrete variables, or both, continuous and discrete variables. Constraints on dependent variables can be implemented using penalty or barrier functions. GenOpt uses parallel computing to evaluate the simulations. GenOpt has a library with local and global multi-dimensional and one-dimensional optimization algorithms, and algorithms for doing parametric runs. An algorithm interface allows adding new minimization algorithms without knowing the details of the program structure. GenOpt is written in Java so that it is platform independent. The platform independence and the general interface make GenOpt applicable to a wide range of optimization problems. GenOpt has not been designed for linear programming problems, quadratic programming problems, and problems where the gradient of the cost function is available. For such problems, as well as for other problems, special tailored software exists that is more efficient

Generic Optimization Program User Manual Version 3.0.0

Energy Technology Data Exchange (ETDEWEB)

Wetter, Michael

2009-05-11

GenOpt is an optimization program for the minimization of a cost function that is evaluated by an external simulation program. It has been developed for optimization problems where the cost function is computationally expensive and its derivatives are not available or may not even exist. GenOpt can be coupled to any simulation program that reads its input from text files and writes its output to text files. The independent variables can be continuous variables (possibly with lower and upper bounds), discrete variables, or both, continuous and discrete variables. Constraints on dependent variables can be implemented using penalty or barrier functions. GenOpt uses parallel computing to evaluate the simulations. GenOpt has a library with local and global multi-dimensional and one-dimensional optimization algorithms, and algorithms for doing parametric runs. An algorithm interface allows adding new minimization algorithms without knowing the details of the program structure. GenOpt is written in Java so that it is platform independent. The platform independence and the general interface make GenOpt applicable to a wide range of optimization problems. GenOpt has not been designed for linear programming problems, quadratic programming problems, and problems where the gradient of the cost function is available. For such problems, as well as for other problems, special tailored software exists that is more efficient.

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

Science.gov (United States)

Zhang, Yongjun; Lu, Zhixin

2017-10-01

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

Dynamic Economic Dispatch Pada Sistem Kelistrikan Microgrid Dengan Penambahan Media Penyimpan Energi Menggunakan Quadratic Programming

Directory of Open Access Journals (Sweden)

Fakhruddin Wirakusuma

2017-01-01

Full Text Available Kebutuhan daya listrik saat ini meningkat pesat seiring dengan perkembangan teknologi. Peningkatan kebutuhan daya listrik ini bertolak belakang dengan menipisnya ketersediaan sumber energy minyak dan batu bara. Permasalahan ini berdampak pada ketahanan listrik nasional. Untuk memenuhi kebutuhan daya listrik yang besar dengan cakupan wilayah yang luas diperlukan pembangkit tersebar berskala kecil. Pembangkit tersebar ini diupayakan bersumber pada energi terbarukan untuk meminimalkan pemakaian dari sumber energy minyak dan batu bara lalu dihubungkan ke Micro Grid serta digunakan baterai sebagai power balance. Oleh karena banyaknya pembangkit tersebar dan penggunaan baterai maka penting untuk menentukan besarnya pembangkitan daya listrik yang optimal dari masing-masing pembangkit serta penggunaan baterai berdasarkan kapasitas yang optimal sehingga kebutuhan daya listrik dapat dipenuhi dengan biaya yang minimal tiap waktunya. Optimisasi ini dikenal dengan istilah Dynamic Economic Dispatch. Optimisasi ini sudah banyak dilakukan dilakukan dengan berbagai macam metode Artificial Intelligence. Pada penelitian ini, metode Artificial Intellegence yang diaplikasikan yakni Quadratic Programming. Metode ini diterapkan pada software MATLAB. Dengan metode tersebut, diketahui bahwa penggunaan baterai mampu mengurangi total biaya pembangkitan.

Adiabatic quantum search algorithm for structured problems

International Nuclear Information System (INIS)

Roland, Jeremie; Cerf, Nicolas J.

2003-01-01

The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an unstructured search problem with a quadratic speedup over a classical search, just as Grover's algorithm. In this paper, we study how the structure of the search problem may be exploited to further improve the efficiency of these quantum adiabatic algorithms. We show that by nesting a partial search over a reduced set of variables into a global search, it is possible to devise quantum adiabatic algorithms with a complexity that, although still exponential, grows with a reduced order in the problem size

Quadratic independence of coordinate functions of certain ...

Indian Academy of Sciences (India)

... are `quadratically independent' in the sense that they do not satisfy any nontrivial homogeneous quadratic relations among them. Using this, it is proved that there is no genuine compact quantum group which can act faithfully on C ( M ) such that the action leaves invariant the linear span of the above coordinate functions.

A solution to the economic dispatch using EP based SA algorithm on large scale power system

Energy Technology Data Exchange (ETDEWEB)

Christober Asir Rajan, C. [Department of EEE, Pondicherry Engineering College, Pondicherry 605 014 (India)

2010-07-15

This paper develops a new approach for solving the Economic Load Dispatch (ELD) using an integrated algorithm based on Evolutionary Programming (EP) and Simulated Annealing (SA) on large scale power system. Classical methods employed for solving Economic Load Dispatch are calculus-based. For generator units having quadratic fuel cost functions, the classical techniques ignore or flatten out the portions of the incremental fuel cost curves and so may be have difficulties in the determination of the global optimum solution for non-differentiable fuel cost functions. To overcome these problems, the intelligent techniques, namely, Evolutionary Programming and Simulated Annealing are employed. The above said optimization techniques are capable of determining the global or near global optimum dispatch solutions. The validity and effectiveness of the proposed integrated algorithm has been tested with 66-bus Indian utility system, IEEE 5-bus, 30-bus, 118-bus system. And the test results are compared with the results obtained from other methods. Numerical results show that the proposed integrated algorithm can provide accurate solutions within reasonable time for any type of fuel cost functions. (author)

Exact cancellation of quadratic divergences in top condensation models

International Nuclear Information System (INIS)

Blumhofer, A.

1995-01-01

We discuss the hierarchy problem and the corresponding quadratic divergences in the top mode Standard Model. Quadratic divergences appear at each order 1/N c since fermionic and bosonic contributions are of different order 1/N c . It is shown that the full dynamical system to all orders in 1/N c admits a solution, where the sum of all quadratic divergent contributions disappears. ((orig.))

Sibling curves of quadratic polynomials | Wiggins | Quaestiones ...

African Journals Online (AJOL)

Sibling curves were demonstrated in [1, 2] as a novel way to visualize the zeroes of real valued functions. In [3] it was shown that a polynomial of degree n has n sibling curves. This paper focuses on the algebraic and geometric properites of the sibling curves of real and complex quadratic polynomials. Key words: Quadratic ...

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

Science.gov (United States)

Armstrong, E. S.

1978-01-01

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

Parallel Algorithm for Incremental Betweenness Centrality on Large Graphs

KAUST Repository

Jamour, Fuad Tarek; Skiadopoulos, Spiros; Kalnis, Panos

2017-01-01

: they either require excessive memory (i.e., quadratic to the size of the input graph) or perform unnecessary computations rendering them prohibitively slow. We propose iCentral; a novel incremental algorithm for computing betweenness centrality in evolving

Quadratic adaptive algorithm for solving cardiac action potential models.

Science.gov (United States)

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

2016-10-01

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

Testing Algorithmic Skills in Traditional and Non-Traditional Programming Environments

Science.gov (United States)

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

2015-01-01

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

Mathematical programming models for solving in equal-sized facilities layout problems. A genetic search method

International Nuclear Information System (INIS)

Tavakkoli-Moghaddam, R.

1999-01-01

This paper present unequal-sized facilities layout solutions generated by a genetic search program. named Layout Design using a Genetic Algorithm) 9. The generalized quadratic assignment problem requiring pre-determined distance and material flow matrices as the input data and the continuous plane model employing a dynamic distance measure and a material flow matrix are discussed. Computational results on test problems are reported as compared with layout solutions generated by the branch - and bound algorithm a hybrid method merging simulated annealing and local search techniques, and an optimization process of an enveloped block

Solitons in quadratic nonlinear photonic crystals

DEFF Research Database (Denmark)

Corney, Joel Frederick; Bang, Ole

2001-01-01

We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families....... Because of these induced cubic terms, solitons still exist even when the effective quadratic nonlinearity vanishes and conventional theory predicts that there can be no soliton. We demonstrate that both bright and dark forms of these solitons can propagate stably....

Algorithm Building and Learning Programming Languages Using a New Educational Paradigm

Science.gov (United States)

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

2011-08-01

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

Quadratic tracer dynamical models tobacco growth

International Nuclear Information System (INIS)

Qiang Jiyi; Hua Cuncai; Wang Shaohua

2011-01-01

In order to study the non-uniformly transferring process of some tracer dosages, we assume that the absorption of some tracer by tobacco is a quadratic function of the tracer quantity of the tracer in the case of fast absorption, whereas the exclusion of the tracer from tobacco is a linear function of the tracer quantity in the case of slow exclusion, after the tracer is introduced into tobacco once at zero time. A single-compartment quadratic dynamical model of Logistic type is established for the leaves of tobacco. Then, a two-compartment quadratic dynamical model is established for leaves and calms of the tobacco. Qualitative analysis of the models shows that the tracer applied to the leaves of the tobacco is excluded finally; however, the tracer stays at the tobacco for finite time. Two methods are also given for computing the parameters in the models. Finally, the results of the models are verified by the 32 P experiment for the absorption of tobacco. (authors)

Image Processing Algorithms in the Secondary School Programming Education

Science.gov (United States)

Gerják, István

2017-01-01

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

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

Science.gov (United States)

Beitz, Janice M; van Rijswijk, Lia

2012-01-01

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

Bilevel programming problems theory, algorithms and applications to energy networks

CERN Document Server

Dempe, Stephan; Pérez-Valdés, Gerardo A; Kalashnykova, Nataliya; Kalashnikova, Nataliya

2015-01-01

This book describes recent theoretical findings relevant to bilevel programming in general, and in mixed-integer bilevel programming in particular. It describes recent applications in energy problems, such as the stochastic bilevel optimization approaches used in the natural gas industry. New algorithms for solving linear and mixed-integer bilevel programming problems are presented and explained.

Quantum algorithms for the ordered search problem via semidefinite programming

International Nuclear Information System (INIS)

Childs, Andrew M.; Landahl, Andrew J.; Parrilo, Pablo A.

2007-01-01

One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log 2 N queries to the list, a quantum computer can solve the problem using a constant factor fewer queries. However, the precise value of this constant is unknown. By characterizing a class of quantum query algorithms for the ordered search problem in terms of a semidefinite program, we find quantum algorithms for small instances of the ordered search problem. Extending these algorithms to arbitrarily large instances using recursion, we show that there is an exact quantum ordered search algorithm using 4 log 605 N≅0.433 log 2 N queries, which improves upon the previously best known exact algorithm

Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

Science.gov (United States)

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…

A perturbative solution for gravitational waves in quadratic gravity

International Nuclear Information System (INIS)

Neto, Edgard C de Rey; Aguiar, Odylio D; Araujo, Jose C N de

2003-01-01

We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to Einstein's linearized field equations. We show that only the Ricci-squared quadratic invariant contributes to give a different solution to those found in Einstein's general relativity. The perturbative solution is written as a power series in the β parameter, the coefficient of the Ricci-squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency ω, the perturbative solution can be summed out to give an exact solution to the linearized version of quadratic gravity, for 0 1/2 . This result may lead to implications for the predictions for gravitational wave backgrounds of cosmological origin

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

Science.gov (United States)

Reeves, Anthony P.

1987-01-01

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

A primal-dual exterior point algorithm for linear programming problems

Directory of Open Access Journals (Sweden)

Samaras Nikolaos

2009-01-01

Full Text Available The aim of this paper is to present a new simplex type algorithm for the Linear Programming Problem. The Primal - Dual method is a Simplex - type pivoting algorithm that generates two paths in order to converge to the optimal solution. The first path is primal feasible while the second one is dual feasible for the original problem. Specifically, we use a three-phase-implementation. The first two phases construct the required primal and dual feasible solutions, using the Primal Simplex algorithm. Finally, in the third phase the Primal - Dual algorithm is applied. Moreover, a computational study has been carried out, using randomly generated sparse optimal linear problems, to compare its computational efficiency with the Primal Simplex algorithm and also with MATLAB's Interior Point Method implementation. The algorithm appears to be very promising since it clearly shows its superiority to the Primal Simplex algorithm as well as its robustness over the IPM algorithm.

Improved dynamic-programming-based algorithms for segmentation of masses in mammograms

International Nuclear Information System (INIS)

Dominguez, Alfonso Rojas; Nandi, Asoke K.

2007-01-01

In this paper, two new boundary tracing algorithms for segmentation of breast masses are presented. These new algorithms are based on the dynamic programming-based boundary tracing (DPBT) algorithm proposed in Timp and Karssemeijer, [S. Timp and N. Karssemeijer, Med. Phys. 31, 958-971 (2004)] The DPBT algorithm contains two main steps: (1) construction of a local cost function, and (2) application of dynamic programming to the selection of the optimal boundary based on the local cost function. The validity of some assumptions used in the design of the DPBT algorithm is tested in this paper using a set of 349 mammographic images. Based on the results of the tests, modifications to the computation of the local cost function have been designed and have resulted in the Improved-DPBT (IDPBT) algorithm. A procedure for the dynamic selection of the strength of the components of the local cost function is presented that makes these parameters independent of the image dataset. Incorporation of this dynamic selection procedure has produced another new algorithm which we have called ID 2 PBT. Methods for the determination of some other parameters of the DPBT algorithm that were not covered in the original paper are presented as well. The merits of the new IDPBT and ID 2 PBT algorithms are demonstrated experimentally by comparison against the DPBT algorithm. The segmentation results are evaluated with base on the area overlap measure and other segmentation metrics. Both of the new algorithms outperform the original DPBT; the improvements in the algorithms performance are more noticeable around the values of the segmentation metrics corresponding to the highest segmentation accuracy, i.e., the new algorithms produce more optimally segmented regions, rather than a pronounced increase in the average quality of all the segmented regions

Solutions of the Schrödinger equation with inversely quadratic Hellmann plus inversely quadratic potential using Nikiforov-Uvarov method

International Nuclear Information System (INIS)

Ita, B. I.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.

2014-01-01

By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained

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

Science.gov (United States)

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

2014-01-01

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

A Thrust Allocation Method for Efficient Dynamic Positioning of a Semisubmersible Drilling Rig Based on the Hybrid Optimization Algorithm

Directory of Open Access Journals (Sweden)

Luman Zhao

2015-01-01

Full Text Available A thrust allocation method was proposed based on a hybrid optimization algorithm to efficiently and dynamically position a semisubmersible drilling rig. That is, the thrust allocation was optimized to produce the generalized forces and moment required while at the same time minimizing the total power consumption under the premise that forbidden zones should be taken into account. An optimization problem was mathematically formulated to provide the optimal thrust allocation by introducing the corresponding design variables, objective function, and constraints. A hybrid optimization algorithm consisting of a genetic algorithm and a sequential quadratic programming (SQP algorithm was selected and used to solve this problem. The proposed method was evaluated by applying it to a thrust allocation problem for a semisubmersible drilling rig. The results indicate that the proposed method can be used as part of a cost-effective strategy for thrust allocation of the rig.

Generalized SMO algorithm for SVM-based multitask learning.

Science.gov (United States)

Cai, Feng; Cherkassky, Vladimir

2012-06-01

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

The stability of quadratic-reciprocal functional equation

Science.gov (United States)

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.

Robustness analysis of the Zhang neural network for online time-varying quadratic optimization

International Nuclear Information System (INIS)

Zhang Yunong; Ruan Gongqin; Li Kene; Yang Yiwen

2010-01-01

A general type of recurrent neural network (termed as Zhang neural network, ZNN) has recently been proposed by Zhang et al for the online solution of time-varying quadratic-minimization (QM) and quadratic-programming (QP) problems. Global exponential convergence of the ZNN could be achieved theoretically in an ideal error-free situation. In this paper, with the normal differentiation and dynamics-implementation errors considered, the robustness properties of the ZNN model are investigated for solving these time-varying problems. In addition, linear activation functions and power-sigmoid activation functions could be applied to such a perturbed ZNN model. Both theoretical-analysis and computer-simulation results demonstrate the good ZNN robustness and superior performance for online time-varying QM and QP problem solving, especially when using power-sigmoid activation functions.

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

Science.gov (United States)

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

2017-09-01

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

A deep cut ellipsoid algorithm for convex programming : Theory and applications

NARCIS (Netherlands)

J.B.G. Frenk (Hans); J.A.S. Gromicho (Joaquim); S. Zhang (Shuzhong)

1994-01-01

textabstractThis paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules

A DEEP CUT ELLIPSOID ALGORITHM FOR CONVEX-PROGRAMMING - THEORY AND APPLICATIONS

NARCIS (Netherlands)

FRENK, JBG; GROMICHO, J; ZHANG, S

1994-01-01

This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent

A Deep Cut Ellipsoid Algorithm for convex Programming: theory and Applications

NARCIS (Netherlands)

Frenk, J.B.G.; Gromicho Dos Santos, J.A.; Zhang, S.

1994-01-01

This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent

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

Science.gov (United States)

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

2016-01-01

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

Orthogonal and Scaling Transformations of Quadratic Functions with ...

African Journals Online (AJOL)

In this paper we present a non-singular transformation that can reduce a given quadratic function defined on Rn to another simpler quadratic function and study the impact of the transformation in relation to the problem of minimization of the function. In particular, we construct a non-singular transformation that can reduce a ...

A Quadratic Spring Equation

Science.gov (United States)

Fay, Temple H.

2010-01-01

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

Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier

DEFF Research Database (Denmark)

Neumeyer, Stefan; Sorokin, Vladislav; Thomsen, Jon Juel

2016-01-01

We consider the performance of a parametric amplifier with perfect tuning (two-to-one ratio between the parametric and direct excitation frequencies) and quadratic and cubic nonlinearities. A forced Duffing–Mathieu equation with appended quadratic nonlinearity is considered as the model system......, and approximate analytical steady-state solutions and corresponding stabilities are obtained by the method of varying amplitudes. Some general effects of pure quadratic, and mixed quadratic and cubic nonlinearities on parametric amplification are shown. In particular, the effects of mixed quadratic and cubic...... nonlinearities may generate additional amplitude–frequency solutions. In this case an increased response and a more phase sensitive amplitude (phase between excitation frequencies) is obtained, as compared to the case with either pure quadratic or cubic nonlinearity. Furthermore, jumps and bi...

Design of reinforced areas of concrete column using quadratic polynomials

Science.gov (United States)

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

2017-11-01

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

Indirect quantum tomography of quadratic Hamiltonians

Energy Technology Data Exchange (ETDEWEB)

Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)

2011-01-15

A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.

Nonlinear dynamics of quadratically cubic systems

International Nuclear Information System (INIS)

Rudenko, O V

2013-01-01

We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)

On orthogonality preserving quadratic stochastic operators

Energy Technology Data Exchange (ETDEWEB)

Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)

2015-05-15

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

On orthogonality preserving quadratic stochastic operators

International Nuclear Information System (INIS)

Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

2015-01-01

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

Parallelizing Gene Expression Programming Algorithm in Enabling Large-Scale Classification

Directory of Open Access Journals (Sweden)

Lixiong Xu

2017-01-01

Full Text Available As one of the most effective function mining algorithms, Gene Expression Programming (GEP algorithm has been widely used in classification, pattern recognition, prediction, and other research fields. Based on the self-evolution, GEP is able to mine an optimal function for dealing with further complicated tasks. However, in big data researches, GEP encounters low efficiency issue due to its long time mining processes. To improve the efficiency of GEP in big data researches especially for processing large-scale classification tasks, this paper presents a parallelized GEP algorithm using MapReduce computing model. The experimental results show that the presented algorithm is scalable and efficient for processing large-scale classification tasks.

Quadratic Twists of Rigid Calabi–Yau Threefolds Over

DEFF Research Database (Denmark)

Gouvêa, Fernando Q.; Kiming, Ian; Yui, Noriko

2013-01-01

of weight 4 on some Γ 0(N). We show that quadratic twisting of a threefold corresponds to twisting the attached newform by quadratic characters and illustrate with a number of obvious and not so obvious examples. The question is motivated by the deeper question of which newforms of weight 4 on some Γ 0(N...

Effects of a random noisy oracle on search algorithm complexity

International Nuclear Information System (INIS)

Shenvi, Neil; Brown, Kenneth R.; Whaley, K. Birgitta

2003-01-01

Grover's algorithm provides a quadratic speed-up over classical algorithms for unstructured database or library searches. This paper examines the robustness of Grover's search algorithm to a random phase error in the oracle and analyzes the complexity of the search process as a function of the scaling of the oracle error with database or library size. Both the discrete- and continuous-time implementations of the search algorithm are investigated. It is shown that unless the oracle phase error scales as O(N -1/4 ), neither the discrete- nor the continuous-time implementation of Grover's algorithm is scalably robust to this error in the absence of error correction

Convergence Analysis for the Multiplicative Schwarz Preconditioned Inexact Newton Algorithm

KAUST Repository

Liu, Lulu

2016-10-26

The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm, based on decomposition by field type rather than by subdomain, was recently introduced to improve the convergence of systems with unbalanced nonlinearities. This paper provides a convergence analysis of the MSPIN algorithm. Under reasonable assumptions, it is shown that MSPIN is locally convergent, and desired superlinear or even quadratic convergence can be obtained when the forcing terms are picked suitably.

Convergence Analysis for the Multiplicative Schwarz Preconditioned Inexact Newton Algorithm

KAUST Repository

Liu, Lulu; Keyes, David E.

2016-01-01

The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm, based on decomposition by field type rather than by subdomain, was recently introduced to improve the convergence of systems with unbalanced nonlinearities. This paper provides a convergence analysis of the MSPIN algorithm. Under reasonable assumptions, it is shown that MSPIN is locally convergent, and desired superlinear or even quadratic convergence can be obtained when the forcing terms are picked suitably.

On Convex Quadratic Approximation

NARCIS (Netherlands)

den Hertog, D.; de Klerk, E.; Roos, J.

2000-01-01

In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of

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

Science.gov (United States)

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

2016-02-01

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

The Model and Quadratic Stability Problem of Buck Converter in DCM

Directory of Open Access Journals (Sweden)

Li Xiaojing

2016-01-01

Full Text Available Quadratic stability is an important performance for control systems. At first, the model of Buck Converter in DCM is built based on the theories of hybrid systems and switched linear systems primarily. Then quadratic stability of SLS and hybrid feedback switching rule are introduced. The problem of Buck Converter’s quadratic stability is researched afterwards. In the end, the simulation analysis and verification are provided. Both experimental verification and theoretical analysis results indicate that the output of Buck Converter in DCM has an excellent performance via quadratic stability control and switching rules.

Newton-Raphson based modified Laplace Adomian decomposition method for solving quadratic Riccati differential equations

Directory of Open Access Journals (Sweden)

Mishra Vinod

2016-01-01

Full Text Available Numerical Laplace transform method is applied to approximate the solution of nonlinear (quadratic Riccati differential equations mingled with Adomian decomposition method. A new technique is proposed in this work by reintroducing the unknown function in Adomian polynomial with that of well known Newton-Raphson formula. The solutions obtained by the iterative algorithm are exhibited in an infinite series. The simplicity and efficacy of method is manifested with some examples in which comparisons are made among the exact solutions, ADM (Adomian decomposition method, HPM (Homotopy perturbation method, Taylor series method and the proposed scheme.

On Exponential Hedging and Related Quadratic Backward Stochastic Differential Equations

International Nuclear Information System (INIS)

Sekine, Jun

2006-01-01

The dual optimization problem for the exponential hedging problem is addressed with a cone constraint. Without boundedness conditions on the terminal payoff and the drift of the Ito-type controlled process, the backward stochastic differential equation, which has a quadratic growth term in the drift, is derived as a necessary and sufficient condition for optimality via a variational method and dynamic programming. Further, solvable situations are given, in which the value and the optimizer are expressed in closed forms with the help of the Clark-Haussmann-Ocone formula

Linear quadratic optimization for positive LTI system

Science.gov (United States)

Muhafzan, Yenti, Syafrida Wirma; Zulakmal

2017-05-01

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

Nearly Quadratic n-Derivations on Non-Archimedean Banach Algebras

Directory of Open Access Journals (Sweden)

Madjid Eshaghi Gordji

2012-01-01

Full Text Available Let n>1 be an integer, let A be an algebra, and X be an A-module. A quadratic function D:A→X is called a quadratic n-derivation if D(∏i=1nai=D(a1a22⋯an2+a12D(a2a32⋯an2+⋯+a12a22⋯an−12D(an for all a1,...,an∈A. We investigate the Hyers-Ulam stability of quadratic n-derivations from non-Archimedean Banach algebras into non-Archimedean Banach modules by using the Banach fixed point theorem.

Comparison between linear quadratic and early time dose models

International Nuclear Information System (INIS)

Chougule, A.A.; Supe, S.J.

1993-01-01

During the 70s, much interest was focused on fractionation in radiotherapy with the aim of improving tumor control rate without producing unacceptable normal tissue damage. To compare the radiobiological effectiveness of various fractionation schedules, empirical formulae such as Nominal Standard Dose, Time Dose Factor, Cumulative Radiation Effect and Tumour Significant Dose, were introduced and were used despite many shortcomings. It has been claimed that a recent linear quadratic model is able to predict the radiobiological responses of tumours as well as normal tissues more accurately. We compared Time Dose Factor and Tumour Significant Dose models with the linear quadratic model for tumour regression in patients with carcinomas of the cervix. It was observed that the prediction of tumour regression estimated by the Tumour Significant Dose and Time Dose factor concepts varied by 1.6% from that of the linear quadratic model prediction. In view of the lack of knowledge of the precise values of the parameters of the linear quadratic model, it should be applied with caution. One can continue to use the Time Dose Factor concept which has been in use for more than a decade as its results are within ±2% as compared to that predicted by the linear quadratic model. (author). 11 refs., 3 figs., 4 tabs

Algorithms and programs for consequence diagram and fault tree construction

International Nuclear Information System (INIS)

Hollo, E.; Taylor, J.R.

1976-12-01

A presentation of algorithms and programs for consequence diagram and sequential fault tree construction that are intended for reliability and disturbance analysis of large systems. The system to be analyzed must be given as a block diagram formed by mini fault trees of individual system components. The programs were written in LISP programming language and run on a PDP8 computer with 8k words of storage. A description is given of the methods used and of the program construction and working. (author)

Algorithms

Indian Academy of Sciences (India)

polynomial) division have been found in Vedic Mathematics which are dated much before Euclid's algorithm. A programming language Is used to describe an algorithm for execution on a computer. An algorithm expressed using a programming.

Quantum Algorithms for Compositional Natural Language Processing

Directory of Open Access Journals (Sweden)

William Zeng

2016-08-01

Full Text Available We propose a new application of quantum computing to the field of natural language processing. Ongoing work in this field attempts to incorporate grammatical structure into algorithms that compute meaning. In (Coecke, Sadrzadeh and Clark, 2010, the authors introduce such a model (the CSC model based on tensor product composition. While this algorithm has many advantages, its implementation is hampered by the large classical computational resources that it requires. In this work we show how computational shortcomings of the CSC approach could be resolved using quantum computation (possibly in addition to existing techniques for dimension reduction. We address the value of quantum RAM (Giovannetti,2008 for this model and extend an algorithm from Wiebe, Braun and Lloyd (2012 into a quantum algorithm to categorize sentences in CSC. Our new algorithm demonstrates a quadratic speedup over classical methods under certain conditions.

Guises and disguises of quadratic divergences

Energy Technology Data Exchange (ETDEWEB)

Cherchiglia, A.L., E-mail: adriano@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Vieira, A.R., E-mail: arvieira@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Hiller, Brigitte, E-mail: brigitte@teor.fis.uc.pt [Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, 3004-516 Coimbra (Portugal); Baêta Scarpelli, A.P., E-mail: scarpelli.apbs@dpf.gov.br [Setor Técnico-Científico, Departamento de Polícia Federal, Rua Hugo D’Antola, 95 - Lapa, São Paulo (Brazil); Sampaio, Marcos, E-mail: marcos.sampaio@durham.ac.uk [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road Durham DH1 3LE (United Kingdom)

2014-12-15

In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

Visualising the Roots of Quadratic Equations with Complex Coefficients

Science.gov (United States)

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…

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

Science.gov (United States)

Reeves, Anthony P.

1986-01-01

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

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

Science.gov (United States)

Gog, Simon; Bader, Martin

2008-10-01

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

Scale-Invariant Rotating Black Holes in Quadratic Gravity

Directory of Open Access Journals (Sweden)

Guido Cognola

2015-07-01

Full Text Available Black hole solutions in pure quadratic theories of gravity are interesting since they allow the formulation of a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.

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

Science.gov (United States)

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

2017-06-21

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

Local multiplicative Schwarz algorithms for convection-diffusion equations

Science.gov (United States)

Cai, Xiao-Chuan; Sarkis, Marcus

1995-01-01

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

Algorithmic differentiation of pragma-defined parallel regions differentiating computer programs containing OpenMP

CERN Document Server

Förster, Michael

2014-01-01

Numerical programs often use parallel programming techniques such as OpenMP to compute the program's output values as efficient as possible. In addition, derivative values of these output values with respect to certain input values play a crucial role. To achieve code that computes not only the output values simultaneously but also the derivative values, this work introduces several source-to-source transformation rules. These rules are based on a technique called algorithmic differentiation. The main focus of this work lies on the important reverse mode of algorithmic differentiation. The inh

Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems

International Nuclear Information System (INIS)

Marquette, Ian

2011-01-01

There exists a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude and the Schroedinger equation. We obtain the relativistic energy spectrum for the four relativistic quantum Smorodinsky-Winternitz systems from their quasi-Hamiltonian and the quadratic algebras studied by Daskaloyannis in the nonrelativistic context. We also apply the quadratic algebra approach directly to the initial Dirac equation for these four systems and show that the quadratic algebras obtained are the same than those obtained from the quasi-Hamiltonians. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras can be applied to the quantum relativistic case.

Geometric Approaches to Quadratic Equations from Other Times and Places.

Science.gov (United States)

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)

Approximate *-derivations and approximate quadratic *-derivations on C*-algebras

Directory of Open Access Journals (Sweden)

Park Choonkil

2011-01-01

Full Text Available Abstract In this paper, we prove the stability of *-derivations and of quadratic *-derivations on Banach *-algebras. We moreover prove the superstability of *-derivations and of quadratic *-derivations on C*-algebras. 2000 Mathematics Subject Classification: 39B52; 47B47; 46L05; 39B72.

Optimally stopped variational quantum algorithms

Science.gov (United States)

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.

Applications and algorithms for mixed integer nonlinear programming

International Nuclear Information System (INIS)

Leyffer, Sven; Munson, Todd; Linderoth, Jeff; Luedtke, James; Miller, Andrew

2009-01-01

The mathematical modeling of systems often requires the use of both nonlinear and discrete components. Discrete decision variables model dichotomies, discontinuities, and general logical relationships. Nonlinear functions are required to accurately represent physical properties such as pressure, stress, temperature, and equilibrium. Problems involving both discrete variables and nonlinear constraint functions are known as mixed-integer nonlinear programs (MINLPs) and are among the most challenging computational optimization problems faced by researchers and practitioners. In this paper, we describe relevant scientific applications that are naturally modeled as MINLPs, we provide an overview of available algorithms and software, and we describe ongoing methodological advances for solving MINLPs. These algorithmic advances are making increasingly larger instances of this important family of problems tractable.

Analysis of Students' Error in Learning of Quadratic Equations

Science.gov (United States)

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…

Quadratic hamiltonians and relativistic quantum mechanics

International Nuclear Information System (INIS)

Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.

1981-01-01

For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru

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

Science.gov (United States)

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

2018-03-01

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

A chaos-based evolutionary algorithm for general nonlinear programming problems

International Nuclear Information System (INIS)

El-Shorbagy, M.A.; Mousa, A.A.; Nasr, S.M.

2016-01-01

In this paper we present a chaos-based evolutionary algorithm (EA) for solving nonlinear programming problems named chaotic genetic algorithm (CGA). CGA integrates genetic algorithm (GA) and chaotic local search (CLS) strategy to accelerate the optimum seeking operation and to speed the convergence to the global solution. The integration of global search represented in genetic algorithm and CLS procedures should offer the advantages of both optimization methods while offsetting their disadvantages. By this way, it is intended to enhance the global convergence and to prevent to stick on a local solution. The inherent characteristics of chaos can enhance optimization algorithms by enabling it to escape from local solutions and increase the convergence to reach to the global solution. Twelve chaotic maps have been analyzed in the proposed approach. The simulation results using the set of CEC’2005 show that the application of chaotic mapping may be an effective strategy to improve the performances of EAs.

Swarm, genetic and evolutionary programming algorithms applied to multiuser detection

Directory of Open Access Journals (Sweden)

Paul Jean Etienne Jeszensky

2005-02-01

Full Text Available In this paper, the particles swarm optimization technique, recently published in the literature, and applied to Direct Sequence/Code Division Multiple Access systems (DS/CDMA with multiuser detection (MuD is analyzed, evaluated and compared. The Swarm algorithm efficiency when applied to the DS-CDMA multiuser detection (Swarm-MuD is compared through the tradeoff performance versus computational complexity, being the complexity expressed in terms of the number of necessary operations in order to reach the performance obtained through the optimum detector or the Maximum Likelihood detector (ML. The comparison is accomplished among the genetic algorithm, evolutionary programming with cloning and Swarm algorithm under the same simulation basis. Additionally, it is proposed an heuristics-MuD complexity analysis through the number of computational operations. Finally, an analysis is carried out for the input parameters of the Swarm algorithm in the attempt to find the optimum parameters (or almost-optimum for the algorithm applied to the MuD problem.

AUTOMATION PROGRAM FOR RECOGNITION OF ALGORITHM SOLUTION OF MATHEMATIC TASK

Directory of Open Access Journals (Sweden)

Denis N. Butorin

2014-01-01

Full Text Available In the article are been describing technology for manage of testing task in computer program. It was found for recognition of algorithm solution of mathematic task. There are been justifi ed the using hierarchical structure for a special set of testing questions. Also, there has been presented the release of the described tasks in the computer program openSEE. 

AUTOMATION PROGRAM FOR RECOGNITION OF ALGORITHM SOLUTION OF MATHEMATIC TASK

OpenAIRE

Denis N. Butorin

2014-01-01

In the article are been describing technology for manage of testing task in computer program. It was found for recognition of algorithm solution of mathematic task. There are been justifi ed the using hierarchical structure for a special set of testing questions. Also, there has been presented the release of the described tasks in the computer program openSEE. 

Essential algorithms a practical approach to computer algorithms

CERN Document Server

Stephens, Rod

2013-01-01

A friendly and accessible introduction to the most useful algorithms Computer algorithms are the basic recipes for programming. Professional programmers need to know how to use algorithms to solve difficult programming problems. Written in simple, intuitive English, this book describes how and when to use the most practical classic algorithms, and even how to create new algorithms to meet future needs. The book also includes a collection of questions that can help readers prepare for a programming job interview. Reveals methods for manipulating common data structures s

Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares

Science.gov (United States)

Orr, Jeb S.

2012-01-01

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

Relaxation Methods for Strictly Convex Regularizations of Piecewise Linear Programs

International Nuclear Information System (INIS)

Kiwiel, K. C.

1998-01-01

We give an algorithm for minimizing the sum of a strictly convex function and a convex piecewise linear function. It extends several dual coordinate ascent methods for large-scale linearly constrained problems that occur in entropy maximization, quadratic programming, and network flows. In particular, it may solve exact penalty versions of such (possibly inconsistent) problems, and subproblems of bundle methods for nondifferentiable optimization. It is simple, can exploit sparsity, and in certain cases is highly parallelizable. Its global convergence is established in the recent framework of B -functions (generalized Bregman functions)

A program package for solving linear optimization problems

International Nuclear Information System (INIS)

Horikami, Kunihiko; Fujimura, Toichiro; Nakahara, Yasuaki

1980-09-01

Seven computer programs for the solution of linear, integer and quadratic programming (four programs for linear programming, one for integer programming and two for quadratic programming) have been prepared and tested on FACOM M200 computer, and auxiliary programs have been written to make it easy to use the optimization program package. The characteristics of each program are explained and the detailed input/output descriptions are given in order to let users know how to use them. (author)

Sketching the General Quadratic Equation Using Dynamic Geometry Software

Science.gov (United States)

Stols, G. H.

2005-01-01

This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…

Tangent Lines without Derivatives for Quadratic and Cubic Equations

Science.gov (United States)

Carroll, William J.

2009-01-01

In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

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

Science.gov (United States)

Moore, J H

1995-06-01

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

Constant-work-space algorithms for geometric problems

Directory of Open Access Journals (Sweden)

Tetsuo Asano

2011-07-01

Full Text Available Constant-work-space algorithms may use only constantly many cells of storage in addition to their input, which is provided as a read-only array. We show how to construct several geometric structures efficiently in the constant-work-space model. Traditional algorithms process the input into a suitable data structure (like a doubly-connected edge list that allows efficient traversal of the structure at hand. In the constant-work-space setting, however, we cannot afford to do this. Instead, we provide operations that compute the desired features on the fly by accessing the input with no extra space. The whole geometric structure can be obtained by using these operations to enumerate all the features. Of course, we must pay for the space savings by slower running times. While the standard data structure allows us to implement traversal operations in constant time, our schemes typically take linear time to read the input data in each step.We begin with two simple problems: triangulating a planar point set and finding the trapezoidal decomposition of a simple polygon. In both cases adjacent features can be enumerated in linear time per step, resulting in total quadratic running time to output the whole structure. Actually, we show that the former result carries over to the Delaunay triangulation, and hence the Voronoi diagram. This also means that we can compute the largest empty circle of a planar point set in quadratic time and constant work-space. As another application, we demonstrate how to enumerate the features of an Euclidean minimum spanning tree (EMST in quadratic time per step, so that the whole EMST can be found in cubic time using constant work-space.Finally, we describe how to compute a shortest geodesic path between two points in a simple polygon. Although the shortest path problem in general graphs is NL-complete (Jakoby and Tantau 2003, this constrained problem can be solved in quadratic time using only constant work-space.

Methods of using the quadratic assignment problem solution

Directory of Open Access Journals (Sweden)

Izabela Kudelska

2012-09-01

Full Text Available Background: Quadratic assignment problem (QAP is one of the most interesting of combinatorial optimization. Was presented by Koopman and Beckamanna in 1957, as a mathematical model of the location of indivisible tasks. This problem belongs to the class NP-hard issues. This forces the application to the solution already approximate methods for tasks with a small size (over 30. Even though it is much harder than other combinatorial optimization problems, it enjoys wide interest because it models the important class of decision problems. Material and methods: The discussion was an artificial intelligence tool that allowed to solve the problem QAP, among others are: genetic algorithms, Tabu Search, Branch and Bound. Results and conclusions: QAP did not arise directly as a model for certain actions, but he found its application in many areas. Examples of applications of the problem is: arrangement of buildings on the campus of the university, layout design of electronic components in systems with large scale integration (VLSI, design a hospital, arrangement of keys on the keyboard.

Noise-induced chaos in a quadratically nonlinear oscillator

International Nuclear Information System (INIS)

Gan Chunbiao

2006-01-01

The present paper focuses on the noise-induced chaos in a quadratically nonlinear oscillator. Simple zero points of the stochastic Melnikov integral theoretically mean the necessary rising of noise-induced chaotic response in the system based on the stochastic Melnikov method. To quantify the noise-induced chaos, the boundary of the system's safe basin is firstly studied and it is shown to be incursively fractal when chaos arises. Three cases are considered in simulating the safe basin of the system, i.e., the system is excited only by the harmonic excitation, by both the harmonic and the Gaussian white noise excitations, and only by the Gaussian white noise excitation. Secondly, the leading Lyapunov exponent by Rosenstein's algorithm is shown to quantify the chaotic nature of the sample time series of the system. The results show that the boundary of the safe basin can also be fractal even if the system is excited only by the external Gaussian white noise. Most importantly, the almost-harmonic, the noise-induced chaotic and the thoroughly random responses can be found in the system

Linear Programming, the Simplex Algorithm and Simple Polytopes

Directory of Open Access Journals (Sweden)

Das Bhusan

2010-09-01

Full Text Available In the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concurring the simplex algorithm. We describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes.

Python algorithms mastering basic algorithms in the Python language

CERN Document Server

Hetland, Magnus Lie

2014-01-01

Python Algorithms, Second Edition explains the Python approach to algorithm analysis and design. Written by Magnus Lie Hetland, author of Beginning Python, this book is sharply focused on classical algorithms, but it also gives a solid understanding of fundamental algorithmic problem-solving techniques. The book deals with some of the most important and challenging areas of programming and computer science in a highly readable manner. It covers both algorithmic theory and programming practice, demonstrating how theory is reflected in real Python programs. Well-known algorithms and data struc

Impurity solitons with quadratic nonlinearities

DEFF Research Database (Denmark)

Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis

1998-01-01

We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton...

Algorithmic Approach to Abstracting Linear Systems by Timed Automata

DEFF Research Database (Denmark)

Sloth, Christoffer; Wisniewski, Rafael

2011-01-01

This paper proposes an LMI-based algorithm for abstracting dynamical systems by timed automata, which enables automatic formal verification of linear systems. The proposed abstraction is based on partitioning the state space of the system using positive invariant sets, generated by Lyapunov...... functions. This partitioning ensures that the vector field of the dynamical system is transversal to all facets of the cells, which induces some desirable properties of the abstraction. The algorithm is based on identifying intersections of level sets of quadratic Lyapunov functions, and determining...

Cascaded Quadratic Soliton Compression in Waveguide Structures

DEFF Research Database (Denmark)

Guo, Hairun

between the Kerr nonlinear effects and the dispersive effects in the medium. A Kerr-like nonlinearity is produced through the cascaded phase mismatched quadratic process, e.g. the second harmonic generation process, which can be flexibly tuned in both the sign and the amplitude, making possible a strong......-phase-matching technology is not necessarily needed. In large-RI-changed waveguides, CQSC is extended to the mid-infrared range to generate single-cycle pulses with purely nonlinear interactions, since an all-normal dispersion profile could be achieved within the guidance band. We believe that CQSC in quadratic waveguides...

A linear programming algorithm to test for jamming in hard-sphere packings

International Nuclear Information System (INIS)

Donev, Aleksandar; Torquato, Salvatore.; Stillinger, Frank H.; Connelly, Robert

2004-01-01

Jamming in hard-particle packings has been the subject of considerable interest in recent years. In a paper by Torquato and Stillinger [J. Phys. Chem. B 105 (2001)], a classification scheme of jammed packings into hierarchical categories of locally, collectively and strictly jammed configurations has been proposed. They suggest that these jamming categories can be tested using numerical algorithms that analyze an equivalent contact network of the packing under applied displacements, but leave the design of such algorithms as a future task. In this work, we present a rigorous and practical algorithm to assess whether an ideal hard-sphere packing in two or three dimensions is jammed according to the aforementioned categories. The algorithm is based on linear programming and is applicable to regular as well as random packings of finite size with hard-wall and periodic boundary conditions. If the packing is not jammed, the algorithm yields representative multi-particle unjamming motions. Furthermore, we extend the jamming categories and the testing algorithm to packings with significant interparticle gaps. We describe in detail two variants of the proposed randomized linear programming approach to test for jamming in hard-sphere packings. The first algorithm treats ideal packings in which particles form perfect contacts. Another algorithm treats the case of jamming in packings with significant interparticle gaps. This extended algorithm allows one to explore more fully the nature of the feasible particle displacements. We have implemented the algorithms and applied them to ordered as well as random packings of circular disks and spheres with periodic boundary conditions. Some representative results for large disordered disk and sphere packings are given, but more robust and efficient implementations as well as further applications (e.g., non-spherical particles) are anticipated for the future

The quadratic reciprocity law a collection of classical proofs

CERN Document Server

Baumgart, Oswald

2015-01-01

This book is the English translation of Baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise”), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart’s comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory.

Research of Smart Payment System of Power Grid Using Strongly Sub-feasible SQP Algorithm

Directory of Open Access Journals (Sweden)

Yang Fang

2017-01-01

Full Text Available With the continuous development and perfection of “Internet + Electricity”, the regional grid operation has gradually realized the Internet-based automation. In order to improve the smart level of regional grid operation, this paper analyzes the status quo of power grid terminal in Fujian local power (group company, and introduces the strongly sub-feasible sequence quadratic programming (SQP. The smart payment system based on strongly sub-feasible SQP algorithm is described by its structure, function and implementation process. Through the information technology to improve the efficiency of the service, so that payment staff and smart terminal of self-service payment system has been information between the interactive mode, the actual operation effect is good.

On quadratic variation of martingales

Indian Academy of Sciences (India)

On quadratic variation of martingales. 459. The proof relied on the theory of stochastic integration. Subsequently, in Karandikar. [4], the formula was derived using only Doob's maximal inequality. Thus this could be the starting point for the development of stochastic calculus for continuous semimartingales without bringing in ...

Quadratic prediction of factor scores

NARCIS (Netherlands)

Wansbeek, T

1999-01-01

Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. II is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic

The regular indefinite linear-quadratic problem with linear endpoint constraints

NARCIS (Netherlands)

Soethoudt, J.M.; Trentelman, H.L.

1989-01-01

This paper deals with the infinite horizon linear-quadratic problem with indefinite cost. Given a linear system, a quadratic cost functional and a subspace of the state space, we consider the problem of minimizing the cost functional over all inputs for which the state trajectory converges to that

Fast Detection of Compressively Sensed IR Targets Using Stochastically Trained Least Squares and Compressed Quadratic Correlation Filters

KAUST Repository

Millikan, Brian; Dutta, Aritra; Sun, Qiyu; Foroosh, Hassan

2017-01-01

Target detection of potential threats at night can be deployed on a costly infrared focal plane array with high resolution. Due to the compressibility of infrared image patches, the high resolution requirement could be reduced with target detection capability preserved. For this reason, a compressive midwave infrared imager (MWIR) with a low-resolution focal plane array has been developed. As the most probable coefficient indices of the support set of the infrared image patches could be learned from the training data, we develop stochastically trained least squares (STLS) for MWIR image reconstruction. Quadratic correlation filters (QCF) have been shown to be effective for target detection and there are several methods for designing a filter. Using the same measurement matrix as in STLS, we construct a compressed quadratic correlation filter (CQCF) employing filter designs for compressed infrared target detection. We apply CQCF to the U.S. Army Night Vision and Electronic Sensors Directorate dataset. Numerical simulations show that the recognition performance of our algorithm matches that of the standard full reconstruction methods, but at a fraction of the execution time.

Fast Detection of Compressively Sensed IR Targets Using Stochastically Trained Least Squares and Compressed Quadratic Correlation Filters

KAUST Repository

Millikan, Brian

2017-05-02

Target detection of potential threats at night can be deployed on a costly infrared focal plane array with high resolution. Due to the compressibility of infrared image patches, the high resolution requirement could be reduced with target detection capability preserved. For this reason, a compressive midwave infrared imager (MWIR) with a low-resolution focal plane array has been developed. As the most probable coefficient indices of the support set of the infrared image patches could be learned from the training data, we develop stochastically trained least squares (STLS) for MWIR image reconstruction. Quadratic correlation filters (QCF) have been shown to be effective for target detection and there are several methods for designing a filter. Using the same measurement matrix as in STLS, we construct a compressed quadratic correlation filter (CQCF) employing filter designs for compressed infrared target detection. We apply CQCF to the U.S. Army Night Vision and Electronic Sensors Directorate dataset. Numerical simulations show that the recognition performance of our algorithm matches that of the standard full reconstruction methods, but at a fraction of the execution time.

Penalty Algorithm Based on Conjugate Gradient Method for Solving Portfolio Management Problem

Directory of Open Access Journals (Sweden)

Wang YaLin

2009-01-01

Full Text Available A new approach was proposed to reformulate the biobjectives optimization model of portfolio management into an unconstrained minimization problem, where the objective function is a piecewise quadratic polynomial. We presented some properties of such an objective function. Then, a class of penalty algorithms based on the well-known conjugate gradient methods was developed to find the solution of portfolio management problem. By implementing the proposed algorithm to solve the real problems from the stock market in China, it was shown that this algorithm is promising.

Eigenfunctions of quadratic hamiltonians in Wigner representation

International Nuclear Information System (INIS)

Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.

1984-01-01

Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail

Remarks on second-order quadratic systems in algebras

Directory of Open Access Journals (Sweden)

Art Sagle

2017-10-01

Full Text Available This paper is an addendum to our earlier paper [8], where a systematic study of quadratic systems of second order ordinary differential equations defined in commutative algebras was presented. Here we concentrate on special solutions and energy considerations of some quadratic systems defined in algebras which need not be commutative, however, we shall throughout assume the algebra to be associative. We here also give a positive answer to an open question, concerning periodic motions of such systems, posed in our earlier paper.

Estimating sample size for a small-quadrat method of botanical ...

African Journals Online (AJOL)

Reports the results of a study conducted to determine an appropriate sample size for a small-quadrat method of botanical survey for application in the Mixed Bushveld of South Africa. Species density and grass density were measured using a small-quadrat method in eight plant communities in the Nylsvley Nature Reserve.

Efficient Dual Domain Decoding of Linear Block Codes Using Genetic Algorithms

Directory of Open Access Journals (Sweden)

Ahmed Azouaoui

2012-01-01

Full Text Available A computationally efficient algorithm for decoding block codes is developed using a genetic algorithm (GA. The proposed algorithm uses the dual code in contrast to the existing genetic decoders in the literature that use the code itself. Hence, this new approach reduces the complexity of decoding the codes of high rates. We simulated our algorithm in various transmission channels. The performance of this algorithm is investigated and compared with competitor decoding algorithms including Maini and Shakeel ones. The results show that the proposed algorithm gives large gains over the Chase-2 decoding algorithm and reach the performance of the OSD-3 for some quadratic residue (QR codes. Further, we define a new crossover operator that exploits the domain specific information and compare it with uniform and two point crossover. The complexity of this algorithm is also discussed and compared to other algorithms.

Theoretical and algorithmic advances in multi-parametric programming and control

KAUST Repository

Pistikopoulos, Efstratios N.; Dominguez, Luis; Panos, Christos; Kouramas, Konstantinos; Chinchuluun, Altannar

2012-01-01

This paper presents an overview of recent theoretical and algorithmic advances, and applications in the areas of multi-parametric programming and explicit/multi-parametric model predictive control (mp-MPC). In multi-parametric programming, advances include areas such as nonlinear multi-parametric programming (mp-NLP), bi-level programming, dynamic programming and global optimization for multi-parametric mixed-integer linear programming problems (mp-MILPs). In multi-parametric/explicit MPC (mp-MPC), advances include areas such as robust multi-parametric control, multi-parametric nonlinear MPC (mp-NMPC) and model reduction in mp-MPC. A comprehensive framework for multi-parametric programming and control is also presented. Recent applications include a hydrogen storage device, a fuel cell power generation system, an unmanned autonomous vehicle (UAV) and a hybrid pressure swing adsorption (PSA) system. © 2012 Springer-Verlag.

Theoretical and algorithmic advances in multi-parametric programming and control

KAUST Repository

Pistikopoulos, Efstratios N.

2012-04-21

This paper presents an overview of recent theoretical and algorithmic advances, and applications in the areas of multi-parametric programming and explicit/multi-parametric model predictive control (mp-MPC). In multi-parametric programming, advances include areas such as nonlinear multi-parametric programming (mp-NLP), bi-level programming, dynamic programming and global optimization for multi-parametric mixed-integer linear programming problems (mp-MILPs). In multi-parametric/explicit MPC (mp-MPC), advances include areas such as robust multi-parametric control, multi-parametric nonlinear MPC (mp-NMPC) and model reduction in mp-MPC. A comprehensive framework for multi-parametric programming and control is also presented. Recent applications include a hydrogen storage device, a fuel cell power generation system, an unmanned autonomous vehicle (UAV) and a hybrid pressure swing adsorption (PSA) system. © 2012 Springer-Verlag.

A multithreaded parallel implementation of a dynamic programming algorithm for sequence comparison.

Science.gov (United States)

Martins, W S; Del Cuvillo, J B; Useche, F J; Theobald, K B; Gao, G R

2001-01-01

This paper discusses the issues involved in implementing a dynamic programming algorithm for biological sequence comparison on a general-purpose parallel computing platform based on a fine-grain event-driven multithreaded program execution model. Fine-grain multithreading permits efficient parallelism exploitation in this application both by taking advantage of asynchronous point-to-point synchronizations and communication with low overheads and by effectively tolerating latency through the overlapping of computation and communication. We have implemented our scheme on EARTH, a fine-grain event-driven multithreaded execution and architecture model which has been ported to a number of parallel machines with off-the-shelf processors. Our experimental results show that the dynamic programming algorithm can be efficiently implemented on EARTH systems with high performance (e.g., speedup of 90 on 120 nodes), good programmability and reasonable cost.

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

Science.gov (United States)

Abejuela, Harmony Raylen; Osser, David N

2016-01-01

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

Quadratic divergences and dimensional regularisation

International Nuclear Information System (INIS)

Jack, I.; Jones, D.R.T.

1990-01-01

We present a detailed analysis of quadratic and quartic divergences in dimensionally regulated renormalisable theories. We perform explicit three-loop calculations for a general theory of scalars and fermions. We find that the higher-order quartic divergences are related to the lower-order ones by the renormalisation group β-functions. (orig.)

Facets for the Cardinality Constrained Quadratic Knapsack Problem and the Quadratic Selective Travelling Salesman Problem

DEFF Research Database (Denmark)

Mak, Vicky; Thomadsen, Tommy

2004-01-01

A well-known extension of the Travelling Salesman Problem (TSP) is the Selective (or Prize-collecting) TSP: In addition to the edge-costs, each node has an associated reward (denoted the node-reward) and instead of visiting all nodes, only profitable nodes are visited. The Quadratic Selective TSP...

Pair- ${v}$ -SVR: A Novel and Efficient Pairing nu-Support Vector Regression Algorithm.

Science.gov (United States)

Hao, Pei-Yi

This paper proposes a novel and efficient pairing nu-support vector regression (pair--SVR) algorithm that combines successfully the superior advantages of twin support vector regression (TSVR) and classical -SVR algorithms. In spirit of TSVR, the proposed pair--SVR solves two quadratic programming problems (QPPs) of smaller size rather than a single larger QPP, and thus has faster learning speed than classical -SVR. The significant advantage of our pair--SVR over TSVR is the improvement in the prediction speed and generalization ability by introducing the concepts of the insensitive zone and the regularization term that embodies the essence of statistical learning theory. Moreover, pair--SVR has additional advantage of using parameter for controlling the bounds on fractions of SVs and errors. Furthermore, the upper bound and lower bound functions of the regression model estimated by pair--SVR capture well the characteristics of data distributions, thus facilitating automatic estimation of the conditional mean and predictive variance simultaneously. This may be useful in many cases, especially when the noise is heteroscedastic and depends strongly on the input values. The experimental results validate the superiority of our pair--SVR in both training/prediction speed and generalization ability.This paper proposes a novel and efficient pairing nu-support vector regression (pair--SVR) algorithm that combines successfully the superior advantages of twin support vector regression (TSVR) and classical -SVR algorithms. In spirit of TSVR, the proposed pair--SVR solves two quadratic programming problems (QPPs) of smaller size rather than a single larger QPP, and thus has faster learning speed than classical -SVR. The significant advantage of our pair--SVR over TSVR is the improvement in the prediction speed and generalization ability by introducing the concepts of the insensitive zone and the regularization term that embodies the essence of statistical learning theory

Design of problem-specific evolutionary algorithm/mixed-integer programming hybrids: two-stage stochastic integer programming applied to chemical batch scheduling

Science.gov (United States)

Urselmann, Maren; Emmerich, Michael T. M.; Till, Jochen; Sand, Guido; Engell, Sebastian

2007-07-01

Engineering optimization often deals with large, mixed-integer search spaces with a rigid structure due to the presence of a large number of constraints. Metaheuristics, such as evolutionary algorithms (EAs), are frequently suggested as solution algorithms in such cases. In order to exploit the full potential of these algorithms, it is important to choose an adequate representation of the search space and to integrate expert-knowledge into the stochastic search operators, without adding unnecessary bias to the search. Moreover, hybridisation with mathematical programming techniques such as mixed-integer programming (MIP) based on a problem decomposition can be considered for improving algorithmic performance. In order to design problem-specific EAs it is desirable to have a set of design guidelines that specify properties of search operators and representations. Recently, a set of guidelines has been proposed that gives rise to so-called Metric-based EAs (MBEAs). Extended by the minimal moves mutation they allow for a generalization of EA with self-adaptive mutation strength in discrete search spaces. In this article, a problem-specific EA for process engineering task is designed, following the MBEA guidelines and minimal moves mutation. On the background of the application, the usefulness of the design framework is discussed, and further extensions and corrections proposed. As a case-study, a two-stage stochastic programming problem in chemical batch process scheduling is considered. The algorithm design problem can be viewed as the choice of a hierarchical decision structure, where on different layers of the decision process symmetries and similarities can be exploited for the design of minimal moves. After a discussion of the design approach and its instantiation for the case-study, the resulting problem-specific EA/MIP is compared to a straightforward application of a canonical EA/MIP and to a monolithic mathematical programming algorithm. In view of the

Isotropy of quadratic forms

Indian Academy of Sciences (India)

V. Suresh University Of Hyderabad Hyderabad

2008-10-31

Oct 31, 2008 ... We say that (a1,··· ,an) is a zero of the polynomial f if f (a1,··· ,an) = 0. One of the main problems in Mathematics is to determine whether the given polynomial has a (non-trivial) zero or not. For example, let us recall the Fermat's last theorem: V. Suresh University Of Hyderabad Hyderabad. Isotropy of quadratic ...

A GENETIC ALGORITHM USING THE LOCAL SEARCH HEURISTIC IN FACILITIES LAYOUT PROBLEM: A MEMETİC ALGORİTHM APPROACH

Directory of Open Access Journals (Sweden)

Orhan TÜRKBEY

2002-02-01

Full Text Available Memetic algorithms, which use local search techniques, are hybrid structured algorithms like genetic algorithms among evolutionary algorithms. In this study, for Quadratic Assignment Problem (QAP, a memetic structured algorithm using a local search heuristic like 2-opt is developed. Developed in the algorithm, a crossover operator that has not been used before for QAP is applied whereas, Eshelman procedure is used in order to increase thesolution variability. The developed memetic algorithm is applied on test problems taken from QAP-LIB, the results are compared with the present techniques in the literature.

Dynamical correlation functions of the quadratic coupling spin-Boson model

Science.gov (United States)

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 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).

STRUCTURE OPTIMIZATION OF RESERVATION BY PRECISE QUADRATIC REGULARIZATION

Directory of Open Access Journals (Sweden)

KOSOLAP A. I.

2015-11-01

Full Text Available The problem of optimization of the structure of systems redundancy elements. Such problems arise in the design of complex systems. To improve the reliability of operation of such systems of its elements are duplicated. This increases system cost and improves its reliability. When optimizing these systems is maximized probability of failure of the entire system while limiting its cost or the cost is minimized for a given probability of failure-free operation. A mathematical model of the problem is a discrete backup multiextremal. To search for the global extremum of currently used methods of Lagrange multipliers, coordinate descent, dynamic programming, random search. These methods guarantee a just and local solutions are used in the backup tasks of small dimension. In the work for solving redundancy uses a new method for accurate quadratic regularization. This method allows you to convert the original discrete problem to the maximization of multi vector norm on a convex set. This means that the diversity of the tasks given to the problem of redundancy maximize vector norm on a convex set. To solve the problem, a reformed straightdual interior point methods. Currently, it is the best method for local optimization of nonlinear problems. Transformed the task includes a new auxiliary variable, which is determined by dichotomy. There have been numerous comparative numerical experiments in problems with the number of redundant subsystems to one hundred. These experiments confirm the effectiveness of the method of precise quadratic regularization for solving problems of redundancy.

New robust chaotic system with exponential quadratic term

International Nuclear Information System (INIS)

Bao Bocheng; Li Chunbiao; Liu Zhong; Xu Jianping

2008-01-01

This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic attractor with only two equilibria, and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent. Some basic dynamical properties and chaotic behaviour of novel attractor are studied. By numerical simulation, this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviours by a constant controller. (general)

Effects of Classroom Instruction on Students' Understanding of Quadratic Equations

Science.gov (United States)

Vaiyavutjamai, Pongchawee; Clements, M. A.

2006-01-01

Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…

Quadratic Functionals with General Boundary Conditions

International Nuclear Information System (INIS)

Dosla, Z.; Dosly, O.

1997-01-01

The purpose of this paper is to give the Reid 'Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in terms of Riccati equation solutions

Multi-task feature selection in microarray data by binary integer programming.

Science.gov (United States)

Lan, Liang; Vucetic, Slobodan

2013-12-20

A major challenge in microarray classification is that the number of features is typically orders of magnitude larger than the number of examples. In this paper, we propose a novel feature filter algorithm to select the feature subset with maximal discriminative power and minimal redundancy by solving a quadratic objective function with binary integer constraints. To improve the computational efficiency, the binary integer constraints are relaxed and a low-rank approximation to the quadratic term is applied. The proposed feature selection algorithm was extended to solve multi-task microarray classification problems. We compared the single-task version of the proposed feature selection algorithm with 9 existing feature selection methods on 4 benchmark microarray data sets. The empirical results show that the proposed method achieved the most accurate predictions overall. We also evaluated the multi-task version of the proposed algorithm on 8 multi-task microarray datasets. The multi-task feature selection algorithm resulted in significantly higher accuracy than when using the single-task feature selection methods.

Spatial statistics of pitting corrosion patterning: Quadrat counts and the non-homogeneous Poisson process

International Nuclear Information System (INIS)

Lopez de la Cruz, J.; Gutierrez, M.A.

2008-01-01

This paper presents a stochastic analysis of spatial point patterns as effect of localized pitting corrosion. The Quadrat Counts method is studied with two empirical pit patterns. The results are dependent on the quadrat size and bias is introduced when empty quadrats are accounted for the analysis. The spatially inhomogeneous Poisson process is used to improve the performance of the Quadrat Counts method. The latter combines Quadrat Counts with distance-based statistics in the analysis of pit patterns. The Inter-Event and the Nearest-Neighbour statistics are here implemented in order to compare their results. Further, the treatment of patterns in irregular domains is discussed

A Constraint programming-based genetic algorithm for capacity output optimization

Directory of Open Access Journals (Sweden)

Kate Ean Nee Goh

2014-10-01

Full Text Available Purpose: The manuscript presents an investigation into a constraint programming-based genetic algorithm for capacity output optimization in a back-end semiconductor manufacturing company.Design/methodology/approach: In the first stage, constraint programming defining the relationships between variables was formulated into the objective function. A genetic algorithm model was created in the second stage to optimize capacity output. Three demand scenarios were applied to test the robustness of the proposed algorithm.Findings: CPGA improved both the machine utilization and capacity output once the minimum requirements of a demand scenario were fulfilled. Capacity outputs of the three scenarios were improved by 157%, 7%, and 69%, respectively.Research limitations/implications: The work relates to aggregate planning of machine capacity in a single case study. The constraints and constructed scenarios were therefore industry-specific.Practical implications: Capacity planning in a semiconductor manufacturing facility need to consider multiple mutually influenced constraints in resource availability, process flow and product demand. The findings prove that CPGA is a practical and an efficient alternative to optimize the capacity output and to allow the company to review its capacity with quick feedback.Originality/value: The work integrates two contemporary computational methods for a real industry application conventionally reliant on human judgement.

Algorithms and programs of dynamic mixture estimation unified approach to different types of components

CERN Document Server

Nagy, Ivan

2017-01-01

This book provides a general theoretical background for constructing the recursive Bayesian estimation algorithms for mixture models. It collects the recursive algorithms for estimating dynamic mixtures of various distributions and brings them in the unified form, providing a scheme for constructing the estimation algorithm for a mixture of components modeled by distributions with reproducible statistics. It offers the recursive estimation of dynamic mixtures, which are free of iterative processes and close to analytical solutions as much as possible. In addition, these methods can be used online and simultaneously perform learning, which improves their efficiency during estimation. The book includes detailed program codes for solving the presented theoretical tasks. Codes are implemented in the open source platform for engineering computations. The program codes given serve to illustrate the theory and demonstrate the work of the included algorithms.

Temporal quadratic expansion nodal Green's function method

International Nuclear Information System (INIS)

Liu Cong; Jing Xingqing; Xu Xiaolin

2000-01-01

A new approach is presented to efficiently solve the three-dimensional space-time reactor dynamics equation which overcomes the disadvantages of current methods. In the Temporal Quadratic Expansion Nodal Green's Function Method (TQE/NGFM), the Quadratic Expansion Method (QEM) is used for the temporal solution with the Nodal Green's Function Method (NGFM) employed for the spatial solution. Test calculational results using TQE/NGFM show that its time step size can be 5-20 times larger than that of the Fully Implicit Method (FIM) for similar precision. Additionally, the spatial mesh size with NGFM can be nearly 20 times larger than that using the finite difference method. So, TQE/NGFM is proved to be an efficient reactor dynamics analysis method

On wave-packet dynamics in a decaying quadratic potential

DEFF Research Database (Denmark)

Møller, Klaus Braagaard; Henriksen, Niels Engholm

1997-01-01

We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics.......We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics....

Burgers' turbulence problem with linear or quadratic external potential

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole Eiler; Leonenko, N.N.

2005-01-01

We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.......We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions....

Geometrical Solutions of Some Quadratic Equations with Non-Real Roots

Science.gov (United States)

Pathak, H. K.; Grewal, A. S.

2002-01-01

This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

Hybrid SOA-SQP algorithm for dynamic economic dispatch with valve-point effects

Energy Technology Data Exchange (ETDEWEB)

Sivasubramani, S.; Swarup, K.S. [Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai 600036 (India)

2010-12-15

This paper proposes a hybrid technique combining a new heuristic algorithm named seeker optimization algorithm (SOA) and sequential quadratic programming (SQP) method for solving dynamic economic dispatch problem with valve-point effects. The SOA is based on the concept of simulating the act of human searching, where the search direction is based on the empirical gradient (EG) by evaluating the response to the position changes and the step length is based on uncertainty reasoning by using a simple fuzzy rule. In this paper, SOA is used as a base level search, which can give a good direction to the optimal global region and SQP as a local search to fine tune the solution obtained from SOA. Thus SQP guides SOA to find optimal or near optimal solution in the complex search space. Two test systems i.e., 5 unit with losses and 10 unit without losses, have been taken to validate the efficiency of the proposed hybrid method. Simulation results clearly show that the proposed method outperforms the existing method in terms of solution quality. (author)

Geometrical and Graphical Solutions of Quadratic Equations.

Science.gov (United States)

Hornsby, E. John, Jr.

1990-01-01

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

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

Directory of Open Access Journals (Sweden)

Fulong Jing

2017-06-01

Full Text Available 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.

Commuting quantum traces for quadratic algebras

International Nuclear Information System (INIS)

Nagy, Zoltan; Avan, Jean; Doikou, Anastasia; Rollet, Genevieve

2005-01-01

Consistent tensor products on auxiliary spaces, hereafter denoted 'fusion procedures', and commuting transfer matrices are defined for general quadratic algebras, nondynamical and dynamical, inspired by results on reflection algebras. Applications of these procedures then yield integer-indexed families of commuting Hamiltonians

AUTOMATA PROGRAMS CONSTRUCTION FROM SPECIFICATION WITH AN ANT COLONY OPTIMIZATION ALGORITHM BASED ON MUTATION GRAPH

Directory of Open Access Journals (Sweden)

Daniil S. Chivilikhin

2014-11-01

Full Text Available The procedure of testing traditionally used in software engineering cannot guarantee program correctness; therefore verification is used at the excess requirements to programs reliability. Verification makes it possible to check certain properties of programs in all possible computational states; however, this process is very complex. In the model checking method a model of the program is built (often, manually and requirements in terms of temporal logic are formulated. Such temporal properties of the model can be checked automatically. The main issue in this framework is the gap between the program and its model. Automata-based programming paradigm gives the possibility to overcome this limitation. In this paradigm, program logic is represented using finite-state machines. The advantage of finite-state machines is that their models can be constructed automatically. The paper deals with the application of mutation-based ant colony optimization algorithm to the problem of finite-state machine construction from their specification, defined by test scenarios and temporal properties. The presented approach has been tested on the elevator doors control problem as well as on randomly generated data. Obtained results show the ant colony algorithm is two-three times faster than the previously used genetic algorithm. The proposed approach can be recommended for inferring control programs for critical systems.

Mathematical models and algorithms for the computer program 'WOLF'

International Nuclear Information System (INIS)

Halbach, K.

1975-12-01

The computer program FLOW finds the nonrelativistic self- consistent set of two-dimensional ion trajectories and electric fields (including space charges from ions and electrons) for a given set of initial and boundary conditions for the particles and fields. The combination of FLOW with the optimization code PISA gives the program WOLF, which finds the shape of the emitter which is consistent with the plasma forming it, and in addition varies physical characteristics such as electrode position, shapes, and potentials so that some performance characteristics are optimized. The motivation for developing these programs was the desire to design optimum ion source extractor/accelerator systems in a systematic fashion. The purpose of this report is to explain and derive the mathematical models and algorithms which approximate the real physical processes. It serves primarily to document the computer programs. 10 figures

Isotropic harmonic oscillator plus inverse quadratic potential in N-dimensional spaces

International Nuclear Information System (INIS)

Oyewumi, K.A.; Bangudu, E.A.

2003-01-01

Some aspects of the N-dimensional isotropic harmonic plus inverse quadratic potential were discussed. The hyperradial equation for isotropic harmonic oscillator plus inverse quadratic potential is solved by transformation into the confluent hypergeometric equation to obtain the normalized hyperradial solution. Together with the hyperangular solutions (hyperspherical harmonics), these form the complete energy eigenfunctions of the N-dimensional isotropic harmonic oscillator plus inverse quadratic potential and the energy eigenvalues are also obtained. These are dimensionally dependent. The dependence of radial solution on the dimensions or potential strength and the degeneracy of the energy levels are discussed. (author)

Superlinear convergence of a symmetric primal-dual path following algorithm for semidefinite programming

NARCIS (Netherlands)

Z-Q. Luo; J.F. Sturm; S. Zhang (Shuzhong)

1996-01-01

textabstractThis paper establishes the superlinear convergence of a symmetric primal-dual path following algorithm for semidefinite programming under the assumptions that the semidefinite program has a strictly complementary primal-dual optimal solution and that the size of the central path

Resolving Actuator Redundancy - Control Allocation vs. Linear Quadratic Control

OpenAIRE

Härkegård, Ola

2004-01-01

When designing control laws for systems with more inputs than controlled variables, one issue to consider is how to deal with actuator redundancy. Two tools for distributing the control effort among a redundant set of actuators are control allocation and linear quadratic control design. In this paper, we investigate the relationship between these two design tools when a quadratic performance index is used for control allocation. We show that for a particular class of linear systems, they give...

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

Science.gov (United States)

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

1979-01-01

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

Optimization and experimental realization of the quantum permutation algorithm

Science.gov (United States)

Yalçınkaya, I.; Gedik, Z.

2017-12-01

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

Quadratic spatial soliton interactions

Science.gov (United States)

Jankovic, Ladislav

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

Fixed-point image orthorectification algorithms for reduced computational cost

Science.gov (United States)

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

Quadratic Interpolation and Linear Lifting Design

Directory of Open Access Journals (Sweden)

Joel Solé

2007-03-01

Full Text Available A quadratic image interpolation method is stated. The formulation is connected to the optimization of lifting steps. This relation triggers the exploration of several interpolation possibilities within the same context, which uses the theory of convex optimization to minimize quadratic functions with linear constraints. The methods consider possible knowledge available from a given application. A set of linear equality constraints that relate wavelet bases and coefficients with the underlying signal is introduced in the formulation. As a consequence, the formulation turns out to be adequate for the design of lifting steps. The resulting steps are related to the prediction minimizing the detail signal energy and to the update minimizing the l2-norm of the approximation signal gradient. Results are reported for the interpolation methods in terms of PSNR and also, coding results are given for the new update lifting steps.

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

Science.gov (United States)

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

2018-04-01

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

The cyclicity of period annulus of a quadratic reversible Lotka–Volterra system

International Nuclear Information System (INIS)

Li, Chengzhi; Llibre, Jaume

2009-01-01

We prove that by perturbing the periodic annulus of the quadratic polynomial reversible Lotka–Volterra differential system, inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles

Quadratic contributions of softly broken supersymmetry in the light of loop regularization

Energy Technology Data Exchange (ETDEWEB)

Bai, Dong [Chinese Academy of Sciences, Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Beijing (China); University of Chinese Academy of Sciences, School of Physical Sciences, Beijing (China); Wu, Yue-Liang [Chinese Academy of Sciences, Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Beijing (China); International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), Beijing (China); University of Chinese Academy of Sciences, School of Physical Sciences, Beijing (China)

2017-09-15

Loop regularization (LORE) is a novel regularization scheme in modern quantum field theories. It makes no change to the spacetime structure and respects both gauge symmetries and supersymmetry. As a result, LORE should be useful in calculating loop corrections in supersymmetry phenomenology. To further demonstrate its power, in this article we revisit in the light of LORE the old issue of the absence of quadratic contributions (quadratic divergences) in softly broken supersymmetric field theories. It is shown explicitly by Feynman diagrammatic calculations that up to two loops the Wess-Zumino model with soft supersymmetry breaking terms (WZ' model), one of the simplest models with the explicit supersymmetry breaking, is free of quadratic contributions. All the quadratic contributions cancel with each other perfectly, which is consistent with results dictated by the supergraph techniques. (orig.)

On quadratic residue codes and hyperelliptic curves

Directory of Open Access Journals (Sweden)

David Joyner

2008-01-01

Full Text Available For an odd prime p and each non-empty subset S⊂GF(p, consider the hyperelliptic curve X S defined by y 2 =f S (x, where f S (x = ∏ a∈S (x-a. Using a connection between binary quadratic residue codes and hyperelliptic curves over GF(p, this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S⊂GF(p for which the bound |X S (GF(p| > 1.39p holds. We also use the quasi-quadratic residue codes defined below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the ``Riemann hypothesis.''

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

Science.gov (United States)

Mohammad, Othman; Osser, David N

2014-01-01

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

A multilevel search algorithm for the maximization of submodular functions applied to the quadratic cost partition problem

NARCIS (Netherlands)

Goldengorin, B.; Ghosh, D.

Maximization of submodular functions on a ground set is a NP-hard combinatorial optimization problem. Data correcting algorithms are among the several algorithms suggested for solving this problem exactly and approximately. From the point of view of Hasse diagrams data correcting algorithms use

Configuration space analysis of common cost functions in radiotherapy beam-weight optimization algorithms

Energy Technology Data Exchange (ETDEWEB)

Rowbottom, Carl Graham [Joint Department of Physics, Institute of Cancer Research and the Royal Marsden NHS Trust, Sutton, Surrey (United Kingdom); Webb, Steve [Joint Department of Physics, Institute of Cancer Research and the Royal Marsden NHS Trust, Sutton, Surrey (United Kingdom)

2002-01-07

The successful implementation of downhill search engines in radiotherapy optimization algorithms depends on the absence of local minima in the search space. Such techniques are much faster than stochastic optimization methods but may become trapped in local minima if they exist. A technique known as 'configuration space analysis' was applied to examine the search space of cost functions used in radiotherapy beam-weight optimization algorithms. A downhill-simplex beam-weight optimization algorithm was run repeatedly to produce a frequency distribution of final cost values. By plotting the frequency distribution as a function of final cost, the existence of local minima can be determined. Common cost functions such as the quadratic deviation of dose to the planning target volume (PTV), integral dose to organs-at-risk (OARs), dose-threshold and dose-volume constraints for OARs were studied. Combinations of the cost functions were also considered. The simple cost function terms such as the quadratic PTV dose and integral dose to OAR cost function terms are not susceptible to local minima. In contrast, dose-threshold and dose-volume OAR constraint cost function terms are able to produce local minima in the example case studied. (author)

New bidding strategy formulation for day-ahead energy and reserve markets based on evolutionary programming

International Nuclear Information System (INIS)

Attaviriyanupap, Pathom; Kita, Hiroyuki; Tanaka, Eiichi; Hasegawa, Jun

2005-01-01

In this paper, a new bidding strategy for a day-ahead market is formulated. The proposed algorithm is developed from the viewpoint of a generation company wishing to maximize a profit as a participant in the deregulated power and reserve markets. Separate power and reserve markets are considered, both are operated by clearing price auction system. The optimal bidding parameters for both markets are determined by solving an optimization problem that takes unit commitment constraints such as generating limits and unit minimum up/down time constraints into account. This is a non-convex and non-differentiable which is difficult to solve by traditional optimization techniques. In this paper, evolutionary programming is used to solve the problem. The algorithm is applied to both single-sided and double-sided auctions, numerical simulations are carried out to demonstrate the performance of the proposed scheme compared with those obtained from a sequential quadratic programming. (author)

Schur Stability Regions for Complex Quadratic Polynomials

Science.gov (United States)

Cheng, Sui Sun; Huang, Shao Yuan

2010-01-01

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

A Novel Single Switch Transformerless Quadratic DC/DC Buck-Boost Converter

DEFF Research Database (Denmark)

Mostaan, Ali; A. Gorji, Saman; N. Soltani, Mohsen

2017-01-01

A novel quadratic buck-boost DC/DC converter is presented in this study. The proposed converter utilizes only one active switch and can step-up/down the input voltage, while the existing single switch quadratic buck/boost converters can only work in step-up or step-down mode. First, the proposed ...

Facial Affect Recognition Using Regularized Discriminant Analysis-Based Algorithms

Directory of Open Access Journals (Sweden)

Cheng-Yuan Shih

2010-01-01

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

Measurement of quadratic electrogyration effect in castor oil

Science.gov (United States)

Izdebski, Marek; Ledzion, Rafał; Górski, Piotr

2015-07-01

This work presents a detailed analysis of electrogyration measurement in liquids with the usage of an optical polarimetric technique. Theoretical analysis of the optical response to an applied electric field is illustrated by experimental data for castor oil which exhibits natural optical activity, quadratic electro-optic effect and quadratic electrogyration effect. Moreover, the experimental data show that interaction of the oil with a pair of flat electrodes induces a significant dichroism and natural linear birefringence. The combination of these effects occurring at the same time complicates the procedure of measurements. It has been found that a single measurement is insufficient to separate the contribution of the electrogyration effect, but it is possible on the basis of several measurements performed with various orientations of the polarizer and the analyser. The obtained average values of the quadratic electrogyration coefficient β13 in castor oil at room temperature are from - 0.92 ×10-22 to - 1.44 ×10-22m2V-2 depending on the origin of the oil. Although this study is focused on measurements in castor oil, the presented analysis is much more general.

Large N saddle formulation of quadratic building block theories

International Nuclear Information System (INIS)

Halpern, M.B.

1980-01-01

I develop a large N saddle point formulation for the broad class of 'theories of quadratic building blocks'. Such theories are those on which the sums over internal indices are contained in quadratic building blocks, e.g. PHI 2 = Σsup(N)sub(a-1)PHi sup(a)sup(a). The formulation applies as well to fermions, derivative coupling and non-polynomial interactions. In a related development, closed Schwinger-Dyson equations for Green functions of the building blocks are derived and solved for large N. (orig.)

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

Science.gov (United States)

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

2014-01-01

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

A comparative analysis of quadratics in mathematics textbooks from Turkey, Singapore, and the international baccalaureate diploma programme

OpenAIRE

Sağlam, Reyhan

2012-01-01

Ankara : The Program of Curriculum and Instruction, Bilkent University, 2012. Thesis (Master's) -- Bilkent University, 2012. Includes bibliographical references leaves 110-118. The purpose of this study was to analyze and compare the chapters on quadratics in three mathematics textbooks selected from Turkey, Singapore, and the International Baccalaureate Diploma Programme (IBDP) in terms of content, organization, and presentation style through content analysis. The analys...

Quadratic measurement and conditional state preparation in an optomechanical system

DEFF Research Database (Denmark)

A. Brawley, George; Vanner, Michael A.; Bowen, Warwick P.

2014-01-01

We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator.......We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator....

Dose calculation algorithm for the Department of Energy Laboratory Accreditation Program

International Nuclear Information System (INIS)

Moscovitch, M.; Tawil, R.A.; Thompson, D.; Rhea, T.A.

1991-01-01

The dose calculation algorithm for a symmetric four-element LiF:Mg,Ti based thermoluminescent dosimeter is presented. The algorithm is based on the parameterization of the response of the dosimeter when exposed to both pure and mixed fields of various types and compositions. The experimental results were then used to develop the algorithm as a series of empirical response functions. Experiments to determine the response of the dosimeter and to test the dose calculation algorithm were performed according to the standard established by the Department of Energy Laboratory Accreditation Program (DOELAP). The test radiation fields include: 137 Cs gamma rays, 90 Sr/ 90 Y and 204 Tl beta particles, low energy photons of 20-120 keV and moderated 252 Cf neutron fields. The accuracy of the system has been demonstrated in an official DOELAP blind test conducted at Sandia National Laboratory. The test results were well within DOELAP tolerance limits. The results of this test are presented and discussed

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

Science.gov (United States)

Fedrowitz, Christian H.

1994-11-01

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

Computer program for regional assessment of lung perfusion defect. Part II - verification of the algorithm

International Nuclear Information System (INIS)

Stefaniak, B.

2002-01-01

As described earlier, a dedicated computer program was developed for quantitative evaluation of regional lung perfusion defects, visualized by pulmonary scintigraphy. The correctness of the basic assumptions accepted to construct the algorithms and of the all program functions needed to be checked, before application of the program into the clinical routine. The aim of this study was to verified the program using various software instruments and physical models. Evaluation of the proposed method was performed using software procedures, physical lung phantom, and selected lung image.The reproducibility of lung regions, defined by the program was found excellent. No significant distortion of registered data was observed after ROI transformation into the circle and retransformation into the original shape. The obtained results comprised parametric presentation of activity defects as well as a set of numerical indices which defined extent and intensity of decreased counts density. Among these indices PD2 and DM* were proved the most suitable for the above purposes. The obtained results indicate that the algorithms used for the program construction were correct and suitable for the aim of the study. The above algorithms enable function under study to be presented graphically with true imaging of activity distribution, as well as numerical indices, defining extent and intensity of activity defects to calculated. (author)

The Quadratic Selective Travelling Salesman Problem

DEFF Research Database (Denmark)

Thomadsen, Tommy; Stidsen, Thomas K.

2003-01-01

A well-known extension of the Travelling Salesman Problem (TSP) is the Selective TSP (STSP): Each node has an associated profit and instead of visiting all nodes, the most profitable set of nodes, taking into account the tour cost, is visited. The Quadratic STSP (QSTSP) adds the additional...

Exact solutions to quadratic gravity

Czech Academy of Sciences Publication Activity Database

Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

2017-01-01

Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025

On Quadratic Variation of Martingales

Indian Academy of Sciences (India)

where D ( [ 0 , ∞ ) , R ) denotes the class of real valued r.c.l.l. functions on [ 0 , ∞ ) such that for a locally square integrable martingale ( M t ) with r.c.l.l. paths,. Ψ ( M . ( ) ) = A . ( ). gives the quadratic variation process (written usually as [ M , M ] t ) of ( M t ) . We also show that this process ( A t ) is the unique increasing ...

Exact solutions to quadratic gravity

Czech Academy of Sciences Publication Activity Database

Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

2017-01-01

Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025

Estimating nonlinear selection gradients using quadratic regression coefficients: double or nothing?

Science.gov (United States)

Stinchcombe, John R; Agrawal, Aneil F; Hohenlohe, Paul A; Arnold, Stevan J; Blows, Mark W

2008-09-01

The use of regression analysis has been instrumental in allowing evolutionary biologists to estimate the strength and mode of natural selection. Although directional and correlational selection gradients are equal to their corresponding regression coefficients, quadratic regression coefficients must be doubled to estimate stabilizing/disruptive selection gradients. Based on a sample of 33 papers published in Evolution between 2002 and 2007, at least 78% of papers have not doubled quadratic regression coefficients, leading to an appreciable underestimate of the strength of stabilizing and disruptive selection. Proper treatment of quadratic regression coefficients is necessary for estimation of fitness surfaces and contour plots, canonical analysis of the gamma matrix, and modeling the evolution of populations on an adaptive landscape.

Quantum tomography and classical propagator for quadratic quantum systems

International Nuclear Information System (INIS)

Man'ko, O.V.

1999-03-01

The classical propagator for tomographic probability (which describes the quantum state instead of wave function or density matrix) is presented for quadratic quantum systems and its relation to the quantum propagator is considered. The new formalism of quantum mechanics, based on the probability representation of the state, is applied to particular quadratic systems - the harmonic oscillator, particle's free motion, problems of an ion in a Paul trap and in asymmetric Penning trap, and to the process of stimulated Raman scattering. The classical propagator for these systems is written in an explicit form. (author)

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

Science.gov (United States)

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

2016-01-01

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

Development of transmission dose estimation algorithm for in vivo dosimetry in high energy radiation treatment

International Nuclear Information System (INIS)

Yun, Hyong Geun; Shin, Kyo Chul; Hun, Soon Nyung; Woo, Hong Gyun; Ha, Sung Whan; Lee, Hyoung Koo

2004-01-01

In vivo dosimetry is very important for quality assurance purpose in high energy radiation treatment. Measurement of transmission dose is a new method of in vivo dosimetry which is noninvasive and easy for daily performance. This study is to develop a tumor dose estimation algorithm using measured transmission dose for open radiation field. For basic beam data, transmission dose was measured with various field size (FS) of square radiation field, phantom thickness (Tp), and phantom chamber distance (PCD) with a acrylic phantom for 6 MV and 10 MV X-ray. Source to chamber distance (SCD) was set to 150 cm. Measurement was conducted with a 0.6 cc Farmer type ion chamber. By using regression analysis of measured basic beam data, a transmission dose estimation algorithm was developed. Accuracy of the algorithm was tested with flat solid phantom with various thickness in various settings of rectangular fields and various PCD. In our developed algorithm, transmission dose was equated to quadratic function of log(A/P) (where A/P is area-perimeter ratio) and the coefficients of the quadratic functions were equated to tertiary functions of PCD. Our developed algorithm could estimate the radiation dose with the errors within ±0.5% for open square field, and with the errors within ±1.0% for open elongated radiation field. Developed algorithm could accurately estimate the transmission dose in open radiation fields with various treatment settings of high energy radiation treatment. (author)

Phase retrieval via incremental truncated amplitude flow algorithm

Science.gov (United States)

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

2017-10-01

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

A LINEAR PROGRAMMING ALGORITHM FOR LEAST-COST SCHEDULING

Directory of Open Access Journals (Sweden)

AYMAN H AL-MOMANI

1999-12-01

Full Text Available In this research, some concepts of linear programming and critical path method are reviewed to describe recent modeling structures that have been of great value in analyzing extended planning horizon project time-cost trade-offs problems. A simplified representation of a small project and a linear programming model is formulated to represent this system. Procedures to solve these various problems formulations were cited and the final solution is obtained using LINDO program. The model developed represents many restrictions and management considerations of the project. It could be used by construction managers in a planning stage to explore numerous possible opportunities to the contractor and predict the effect of a decision on the construction to facilitate a preferred operating policy given different management objectives. An implementation using this method is shown to outperform several other techniques and a large class of test problems. Linear programming show that the algorithm is very promising in practice on a wide variety of time-cost trade-offs problems. This method is simple, applicable to a large network, and generates a shorter computational time at low cost, along with an increase in robustness.

On a New Family of Kalman Filter Algorithms for Integrated Navigation

Science.gov (United States)

Mahboub, V.; Saadatseresht, M.; Ardalan, A. A.

2017-09-01

Here we present a review on a new family of Kalman filter algorithms which recently developed for integrated navigation. In particular it is useful for vision based navigation due to the type of data. Here we mainly focus on three algorithms namely weighted Total Kalman filter (WTKF), integrated Kalman filter (IKF) and constrained integrated Kalman filter (CIKF). The common characteristic of these algorithms is that they can consider the neglected random observed quantities which may appear in the dynamic model. Moreover, our approach makes use of condition equations and straightforward variance propagation rules. The WTKF algorithm can deal with problems with arbitrary weight matrixes. Both of the observation equations and system equations can be dynamic-errors-in-variables (DEIV) models in the IKF algorithms. In some problems a quadratic constraint may exist. They can be solved by CIKF algorithm. Finally, we compare four algorithms WTKF, IKF, CIKF and EKF in numerical examples.

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

Directory of Open Access Journals (Sweden)

Yong Li

2014-01-01

Full Text Available 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.

Examinations on Applications of Manual Calculation Programs on Lung Cancer Radiation Therapy Using Analytical Anisotropic Algorithm

Energy Technology Data Exchange (ETDEWEB)

Kim, Jung Min; Kim, Dae Sup; Hong, Dong Ki; Back, Geum Mun; Kwak, Jung Won [Dept. of Radiation Oncology, , Seoul (Korea, Republic of)

2012-03-15

There was a problem with using MU verification programs for the reasons that there were errors of MU when using MU verification programs based on Pencil Beam Convolution (PBC) Algorithm with radiation treatment plans around lung using Analytical Anisotropic Algorithm (AAA). On this study, we studied the methods that can verify the calculated treatment plans using AAA. Using Eclipse treatment planning system (Version 8.9, Varian, USA), for each 57 fields of 7 cases of Lung Stereotactic Body Radiation Therapy (SBRT), we have calculated using PBC and AAA with dose calculation algorithm. By developing MU of established plans, we compared and analyzed with MU of manual calculation programs. We have analyzed relationship between errors and 4 variables such as field size, lung path distance of radiation, Tumor path distance of radiation, effective depth that can affect on errors created from PBC algorithm and AAA using commonly used programs. Errors of PBC algorithm have showned 0.2{+-}1.0% and errors of AAA have showned 3.5{+-}2.8%. Moreover, as a result of analyzing 4 variables that can affect on errors, relationship in errors between lung path distance and MU, connection coefficient 0.648 (P=0.000) has been increased and we could calculate MU correction factor that is A.E=L.P 0.00903+0.02048 and as a result of replying for manual calculation program, errors of 3.5{+-}2.8% before the application has been decreased within 0.4{+-}2.0%. On this study, we have learned that errors from manual calculation program have been increased as lung path distance of radiation increases and we could verified MU of AAA with a simple method that is called MU correction factor.

Examinations on Applications of Manual Calculation Programs on Lung Cancer Radiation Therapy Using Analytical Anisotropic Algorithm

International Nuclear Information System (INIS)

Kim, Jung Min; Kim, Dae Sup; Hong, Dong Ki; Back, Geum Mun; Kwak, Jung Won

2012-01-01

There was a problem with using MU verification programs for the reasons that there were errors of MU when using MU verification programs based on Pencil Beam Convolution (PBC) Algorithm with radiation treatment plans around lung using Analytical Anisotropic Algorithm (AAA). On this study, we studied the methods that can verify the calculated treatment plans using AAA. Using Eclipse treatment planning system (Version 8.9, Varian, USA), for each 57 fields of 7 cases of Lung Stereotactic Body Radiation Therapy (SBRT), we have calculated using PBC and AAA with dose calculation algorithm. By developing MU of established plans, we compared and analyzed with MU of manual calculation programs. We have analyzed relationship between errors and 4 variables such as field size, lung path distance of radiation, Tumor path distance of radiation, effective depth that can affect on errors created from PBC algorithm and AAA using commonly used programs. Errors of PBC algorithm have showned 0.2±1.0% and errors of AAA have showned 3.5±2.8%. Moreover, as a result of analyzing 4 variables that can affect on errors, relationship in errors between lung path distance and MU, connection coefficient 0.648 (P=0.000) has been increased and we could calculate MU correction factor that is A.E=L.P 0.00903+0.02048 and as a result of replying for manual calculation program, errors of 3.5±2.8% before the application has been decreased within 0.4±2.0%. On this study, we have learned that errors from manual calculation program have been increased as lung path distance of radiation increases and we could verified MU of AAA with a simple method that is called MU correction factor.

Towards Merging Binary Integer Programming Techniques with Genetic Algorithms

Directory of Open Access Journals (Sweden)

Reza Zamani

2017-01-01

Full Text Available This paper presents a framework based on merging a binary integer programming technique with a genetic algorithm. The framework uses both lower and upper bounds to make the employed mathematical formulation of a problem as tight as possible. For problems whose optimal solutions cannot be obtained, precision is traded with speed through substituting the integrality constrains in a binary integer program with a penalty. In this way, instead of constraining a variable u with binary restriction, u is considered as real number between 0 and 1, with the penalty of Mu(1-u, in which M is a large number. Values not near to the boundary extremes of 0 and 1 make the component of Mu(1-u large and are expected to be avoided implicitly. The nonbinary values are then converted to priorities, and a genetic algorithm can use these priorities to fill its initial pool for producing feasible solutions. The presented framework can be applied to many combinatorial optimization problems. Here, a procedure based on this framework has been applied to a scheduling problem, and the results of computational experiments have been discussed, emphasizing the knowledge generated and inefficiencies to be circumvented with this framework in future.

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

Science.gov (United States)

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.

Optimal Control of Complex Systems Based on Improved Dual Heuristic Dynamic Programming Algorithm

Directory of Open Access Journals (Sweden)

Hui Li

2017-01-01

Full Text Available When applied to solving the data modeling and optimal control problems of complex systems, the dual heuristic dynamic programming (DHP technique, which is based on the BP neural network algorithm (BP-DHP, has difficulty in prediction accuracy, slow convergence speed, poor stability, and so forth. In this paper, a dual DHP technique based on Extreme Learning Machine (ELM algorithm (ELM-DHP was proposed. Through constructing three kinds of network structures, the paper gives the detailed realization process of the DHP technique in the ELM. The controller designed upon the ELM-DHP algorithm controlled a molecular distillation system with complex features, such as multivariability, strong coupling, and nonlinearity. Finally, the effectiveness of the algorithm is verified by the simulation that compares DHP and HDP algorithms based on ELM and BP neural network. The algorithm can also be applied to solve the data modeling and optimal control problems of similar complex systems.

Quadratic time dependent Hamiltonians and separation of variables

International Nuclear Information System (INIS)

Anzaldo-Meneses, A.

2017-01-01

Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green’s function is obtained and a comparison with the classical Hamilton–Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei–Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü–Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems. - Highlights: • Exact unitary transformation reducing time dependent quadratic quantum Hamiltonian to zero. • New separation of variables method and simultaneous uncoupling of modes. • Explicit examples of transformations for one to four dimensional problems. • New general evolution equation for quadratic form in the action, respectively Green’s function.

Staff turnover in hotels : exploring the quadratic and linear relationships.

OpenAIRE

Mohsin, A.; Lengler, J.F.B.; Aguzzoli, R.L.

2015-01-01

The aim of this study is to assess whether the relationship between intention to leave the job and its antecedents is quadratic or linear. To explore those relationships a theoretical model (see Fig. 1) and eight hypotheses are proposed. Each linear hypothesis is followed by an alternative quadratic hypothesis. The alternative hypotheses propose that the relationship between the four antecedent constructs and intention to leave the job might not be linear, as the existing literature suggests....

Optimization for decision making linear and quadratic models

CERN Document Server

Murty, Katta G

2010-01-01

While maintaining the rigorous linear programming instruction required, Murty's new book is unique in its focus on developing modeling skills to support valid decision-making for complex real world problems, and includes solutions to brand new algorithms.

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

Science.gov (United States)

Navon, I. M.; Yu, Jian

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

Quadratic forms for Feynman-Kac semigroups

International Nuclear Information System (INIS)

Hibey, Joseph L.; Charalambous, Charalambos D.

2006-01-01

Some problems in a stochastic setting often involve the need to evaluate the Feynman-Kac formula that follows from models described in terms of stochastic differential equations. Equivalent representations in terms of partial differential equations are also of interest, and these establish the well-known connection between probabilistic and deterministic formulations of these problems. In this Letter, this connection is studied in terms of the quadratic form associated with the Feynman-Kac semigroup. The probability measures that naturally arise in this approach, and thus define how Brownian motion is killed at a specified rate while exiting a set, are interpreted as a random time change of the original stochastic differential equation. Furthermore, since random time changes alter the diffusion coefficients in stochastic differential equations while Girsanov-type measure transformations alter their drift coefficients, their simultaneous use should lead to more tractable solutions for some classes of problems. For example, the minimization of some quadratic forms leads to solutions that satisfy certain partial differential equations and, therefore, the techniques discussed provide a variational approach for finding these solutions

Algorithms

Indian Academy of Sciences (India)

to as 'divide-and-conquer'. Although there has been a large effort in realizing efficient algorithms, there are not many universally accepted algorithm design paradigms. In this article, we illustrate algorithm design techniques such as balancing, greedy strategy, dynamic programming strategy, and backtracking or traversal of ...

Decay constants for pulsed monoenergetic neutron systems with quadratically anisotropic scattering

International Nuclear Information System (INIS)

Sjoestrand, N.G.

1977-06-01

The eigenvalues of the time-dependent transport equation for monoenergetic neutrons have been studied numerically for various combinations of linearly and quadratically anisotropic scattering assuming a space dependence of e β . The results, presented in the form of tables and graphs, show that quadratic anisotropy leads to a more complicated eigenvalue spectrum. However, no drastic changes occur in comparison to purely linear anistropy.(author)

Permanent vegetation quadrats on Olkiluoto island. Establishment and results from the first inventory

Energy Technology Data Exchange (ETDEWEB)

Huhta, A.P.; Korpela, L. [Finnish Forest Research Institute, Helsinki (Finland)

2006-05-15

This report describes in detail the vegetation quadrats established inside the permanent, follow-up sample plots (Forest Extensive High-level monitoring plots, FEH) on Olkiluoto Island. During summer 2005 a total of 94 sample plots (a 30 m{sup 2}), each containing eight quadrats (a 1m{sup 2}), were investigated. The total number of sampled quadrats was 752. Seventy of the 94 plots represent coniferous stands: 57 Norway spruce-dominated and 13 Scots pine-dominated stands. Ten of the plots represent deciduous, birch-dominated (Betula spp.) stands, 7 plots common alder-dominated (Alnus glutinosa) stands, and seven plots are mires. The majority of the coniferous tree stands were growing on sites representing various succession stages of the Myrtillus, Vaccinium-Myrtillus and Deschampsia-Myrtillus forest site types. The pine-dominated stands growing on exposed bedrock clearly differed from the other coniferous stands: the vegetation was characterised by the Cladina, Calluna-Cladina and Empetrum-Vaccinium vitis-idaea/Vaccinium Myrtillus forest site types. The deciduous stands were characterized by tall grasses, especially Calamagrostis epigejos, C. purpurea and Deschampsia flexuosa. The vegetation of the deciduous stands dominated by common alder represented grove-like sites and seashore groves. Typical species for mires included Calamagrostis purpurea, Calla palustris, Equisetum sylvaticum, and especially white mosses (Sphagnum spp.). A total of 184 vascular plant species were found growing within the quadrats. Due to the high number of quadrats in these forests, the spruce stands had the highest total number of species, but the birch and alder-dominated forests had the highest average number of species per quadrat. This basic inventory of the permanent vegetation quadrats on Olkiluoto Island provides a sound starting point for future vegetation surveys. Guidelines for future inventories and supplementary sampling are given in the discussion part of this report. (orig.)

Permanent vegetation quadrats on Olkiluoto island. Establishment and results from the first inventory

International Nuclear Information System (INIS)

Huhta, A.P.; Korpela, L.

2006-05-01

This report describes in detail the vegetation quadrats established inside the permanent, follow-up sample plots (Forest Extensive High-level monitoring plots, FEH) on Olkiluoto Island. During summer 2005 a total of 94 sample plots (a 30 m 2 ), each containing eight quadrats (a 1m 2 ), were investigated. The total number of sampled quadrats was 752. Seventy of the 94 plots represent coniferous stands: 57 Norway spruce-dominated and 13 Scots pine-dominated stands. Ten of the plots represent deciduous, birch-dominated (Betula spp.) stands, 7 plots common alder-dominated (Alnus glutinosa) stands, and seven plots are mires. The majority of the coniferous tree stands were growing on sites representing various succession stages of the Myrtillus, Vaccinium-Myrtillus and Deschampsia-Myrtillus forest site types. The pine-dominated stands growing on exposed bedrock clearly differed from the other coniferous stands: the vegetation was characterised by the Cladina, Calluna-Cladina and Empetrum-Vaccinium vitis-idaea/Vaccinium Myrtillus forest site types. The deciduous stands were characterized by tall grasses, especially Calamagrostis epigejos, C. purpurea and Deschampsia flexuosa. The vegetation of the deciduous stands dominated by common alder represented grove-like sites and seashore groves. Typical species for mires included Calamagrostis purpurea, Calla palustris, Equisetum sylvaticum, and especially white mosses (Sphagnum spp.). A total of 184 vascular plant species were found growing within the quadrats. Due to the high number of quadrats in these forests, the spruce stands had the highest total number of species, but the birch and alder-dominated forests had the highest average number of species per quadrat. This basic inventory of the permanent vegetation quadrats on Olkiluoto Island provides a sound starting point for future vegetation surveys. Guidelines for future inventories and supplementary sampling are given in the discussion part of this report. (orig.)

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

Science.gov (United States)

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

Estimating factors influencing the detection probability of semiaquatic freshwater snails using quadrat survey methods

Science.gov (United States)

Roesler, Elizabeth L.; Grabowski, Timothy B.

2018-01-01

Developing effective monitoring methods for elusive, rare, or patchily distributed species requires extra considerations, such as imperfect detection. Although detection is frequently modeled, the opportunity to assess it empirically is rare, particularly for imperiled species. We used Pecos assiminea (Assiminea pecos), an endangered semiaquatic snail, as a case study to test detection and accuracy issues surrounding quadrat searches. Quadrats (9 × 20 cm; n = 12) were placed in suitable Pecos assiminea habitat and randomly assigned a treatment, defined as the number of empty snail shells (0, 3, 6, or 9). Ten observers rotated through each quadrat, conducting 5-min visual searches for shells. The probability of detecting a shell when present was 67.4 ± 3.0%, but it decreased with the increasing litter depth and fewer number of shells present. The mean (± SE) observer accuracy was 25.5 ± 4.3%. Accuracy was positively correlated to the number of shells in the quadrat and negatively correlated to the number of times a quadrat was searched. The results indicate quadrat surveys likely underrepresent true abundance, but accurately determine the presence or absence. Understanding detection and accuracy of elusive, rare, or imperiled species improves density estimates and aids in monitoring and conservation efforts.

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

International Nuclear Information System (INIS)

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

2017-01-01

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

Improved algorithms for approximate string matching (extended abstract

Directory of Open Access Journals (Sweden)

Papamichail Georgios

2009-01-01

Full Text Available Abstract Background The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants of the problem, including comparison of two strings, approximate pattern identification in a string or calculation of the longest common subsequence that two strings share. Results We designed an output sensitive algorithm solving the edit distance problem between two strings of lengths n and m respectively in time O((s - |n - m|·min(m, n, s + m + n and linear space, where s is the edit distance between the two strings. This worst-case time bound sets the quadratic factor of the algorithm independent of the longest string length and improves existing theoretical bounds for this problem. The implementation of our algorithm also excels in practice, especially in cases where the two strings compared differ significantly in length. Conclusion We have provided the design, analysis and implementation of a new algorithm for calculating the edit distance of two strings with both theoretical and practical implications. Source code of our algorithm is available online.

Transmission dose estimation algorithm for in vivo dosimetry

International Nuclear Information System (INIS)

Yun, Hyong Geun; Shin, Kyo Chul; Huh, Soon Nyung; Woo, Hong Gyun; Ha, Sung Whan; Lee, Hyoung Koo

2002-01-01

Measurement of transmission dose is useful for in vivo dosimetry of QA purpose. The objective of this study is to develope an algorithm for estimation of tumor dose using measured transmission dose for open radiation field. Transmission dose was measured with various field size (FS), phantom thickness (Tp), and phantom chamber distance (PCD) with an acrylic phantom for 6 MV and 10 MV X-ray. Source to chamber distance (SCD) was set to 150 cm. Measurement was conducted with a 0.6 cc Farmer type ion chamber. Using measured data and regression analysis, an algorithm was developed for estimation of expected reading of transmission dose. Accuracy of the algorithm was tested with flat solid phantom with various settings. The algorithm consisted of quadratic function of log(A/P) (where A/P is area-perimeter ratio) and tertiary function of PCD. The algorithm could estimate dose with very high accuracy for open square field, with errors within ±0.5%. For elongated radiation field, the errors were limited to ±1.0%. The developed algorithm can accurately estimate the transmission dose in open radiation fields with various treatment settings

Transmission dose estimation algorithm for in vivo dosimetry

Energy Technology Data Exchange (ETDEWEB)

Yun, Hyong Geun; Shin, Kyo Chul [Dankook Univ., Seoul (Korea, Republic of); Huh, Soon Nyung; Woo, Hong Gyun; Ha, Sung Whan [Seoul National Univ., Seoul (Korea, Republic of); Lee, Hyoung Koo [Catholic Univ., Seoul (Korea, Republic of)

2002-07-01

Measurement of transmission dose is useful for in vivo dosimetry of QA purpose. The objective of this study is to develope an algorithm for estimation of tumor dose using measured transmission dose for open radiation field. Transmission dose was measured with various field size (FS), phantom thickness (Tp), and phantom chamber distance (PCD) with an acrylic phantom for 6 MV and 10 MV X-ray. Source to chamber distance (SCD) was set to 150 cm. Measurement was conducted with a 0.6 cc Farmer type ion chamber. Using measured data and regression analysis, an algorithm was developed for estimation of expected reading of transmission dose. Accuracy of the algorithm was tested with flat solid phantom with various settings. The algorithm consisted of quadratic function of log(A/P) (where A/P is area-perimeter ratio) and tertiary function of PCD. The algorithm could estimate dose with very high accuracy for open square field, with errors within {+-}0.5%. For elongated radiation field, the errors were limited to {+-}1.0%. The developed algorithm can accurately estimate the transmission dose in open radiation fields with various treatment settings.

Coherent states of systems with quadratic Hamiltonians

Energy Technology Data Exchange (ETDEWEB)

Bagrov, V.G., E-mail: bagrov@phys.tsu.ru [Department of Physics, Tomsk State University, Tomsk (Russian Federation); Gitman, D.M., E-mail: gitman@if.usp.br [Tomsk State University, Tomsk (Russian Federation); Pereira, A.S., E-mail: albertoufcg@hotmail.com [Universidade de Sao Paulo (USP), Sao Paulo, SP (Brazil). Instituto de Fisica

2015-06-15

Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)

Coherent states of systems with quadratic Hamiltonians

International Nuclear Information System (INIS)

Bagrov, V.G.; Gitman, D.M.; Pereira, A.S.

2015-01-01

Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)

Game-based programming towards developing algorithmic thinking skills in primary education

Directory of Open Access Journals (Sweden)

Hariklia Tsalapatas

2012-06-01

Full Text Available This paper presents cMinds, a learning intervention that deploys game-based visual programming towards building analytical, computational, and critical thinking skills in primary education. The proposed learning method exploits the structured nature of programming, which is inherently logical and transcends cultural barriers, towards inclusive learning that exposes learners to algorithmic thinking. A visual programming environment, entitled ‘cMinds Learning Suite’, has been developed aimed for classroom use. Feedback from the deployment of the learning methods and tools in classrooms in several European countries demonstrates elevated learner motivation for engaging in logical learning activities, fostering of creativity and an entrepreneurial spirit, and promotion of problem-solving capacity

Recursive algorithms for phylogenetic tree counting.

Science.gov (United States)

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

2013-10-28

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

Automated detection and classification of cryptographic algorithms in binary programs through machine learning

OpenAIRE

Hosfelt, Diane Duros

2015-01-01

Threats from the internet, particularly malicious software (i.e., malware) often use cryptographic algorithms to disguise their actions and even to take control of a victim's system (as in the case of ransomware). Malware and other threats proliferate too quickly for the time-consuming traditional methods of binary analysis to be effective. By automating detection and classification of cryptographic algorithms, we can speed program analysis and more efficiently combat malware. This thesis wil...

Vertical partitioning of relational OLTP databases using integer programming

DEFF Research Database (Denmark)

Amossen, Rasmus Resen

2010-01-01

A way to optimize performance of relational row store databases is to reduce the row widths by vertically partition- ing tables into table fractions in order to minimize the number of irrelevant columns/attributes read by each transaction. This pa- per considers vertical partitioning algorithms...... for relational row- store OLTP databases with an H-store-like architecture, meaning that we would like to maximize the number of single-sited transactions. We present a model for the vertical partitioning problem that, given a schema together with a vertical partitioning and a workload, estimates the costs...... applied to the TPC-C benchmark and the heuristic is shown to obtain solutions with costs close to the ones found using the quadratic program....

Convergence analysis of variational and non-variational multigrid algorithms for the Laplace-Beltrami operator

KAUST Repository

Bonito, Andrea

2012-09-01

We design and analyze variational and non-variational multigrid algorithms for the Laplace-Beltrami operator on a smooth and closed surface. In both cases, a uniform convergence for the V -cycle algorithm is obtained provided the surface geometry is captured well enough by the coarsest grid. The main argument hinges on a perturbation analysis from an auxiliary variational algorithm defined directly on the smooth surface. In addition, the vanishing mean value constraint is imposed on each level, thereby avoiding singular quadratic forms without adding additional computational cost. Numerical results supporting our analysis are reported. In particular, the algorithms perform well even when applied to surfaces with a large aspect ratio. © 2011 American Mathematical Society.

Performance and Complexity Analysis of Blind FIR Channel Identification Algorithms Based on Deterministic Maximum Likelihood in SIMO Systems

DEFF Research Database (Denmark)

De Carvalho, Elisabeth; Omar, Samir; Slock, Dirk

2013-01-01

We analyze two algorithms that have been introduced previously for Deterministic Maximum Likelihood (DML) blind estimation of multiple FIR channels. The first one is a modification of the Iterative Quadratic ML (IQML) algorithm. IQML gives biased estimates of the channel and performs poorly at low...... to the initialization. Its asymptotic performance does not reach the DML performance though. The second strategy, called Pseudo-Quadratic ML (PQML), is naturally denoised. The denoising in PQML is furthermore more efficient than in DIQML: PQML yields the same asymptotic performance as DML, as opposed to DIQML......, but requires a consistent initialization. We furthermore compare DIQML and PQML to the strategy of alternating minimization w.r.t. symbols and channel for solving DML (AQML). An asymptotic performance analysis, a complexity evaluation and simulation results are also presented. The proposed DIQML and PQML...

Joint shape segmentation with linear programming

KAUST Repository

Huang, Qixing

2011-01-01

We present an approach to segmenting shapes in a heterogenous shape database. Our approach segments the shapes jointly, utilizing features from multiple shapes to improve the segmentation of each. The approach is entirely unsupervised and is based on an integer quadratic programming formulation of the joint segmentation problem. The program optimizes over possible segmentations of individual shapes as well as over possible correspondences between segments from multiple shapes. The integer quadratic program is solved via a linear programming relaxation, using a block coordinate descent procedure that makes the optimization feasible for large databases. We evaluate the presented approach on the Princeton segmentation benchmark and show that joint shape segmentation significantly outperforms single-shape segmentation techniques. © 2011 ACM.

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

Science.gov (United States)

Phillips, M. R.

1972-01-01

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

Numerical solution of large nonlinear boundary value problems by quadratic minimization techniques

International Nuclear Information System (INIS)

Glowinski, R.; Le Tallec, P.

1984-01-01

The objective of this paper is to describe the numerical treatment of large highly nonlinear two or three dimensional boundary value problems by quadratic minimization techniques. In all the different situations where these techniques were applied, the methodology remains the same and is organized as follows: 1) derive a variational formulation of the original boundary value problem, and approximate it by Galerkin methods; 2) transform this variational formulation into a quadratic minimization problem (least squares methods) or into a sequence of quadratic minimization problems (augmented lagrangian decomposition); 3) solve each quadratic minimization problem by a conjugate gradient method with preconditioning, the preconditioning matrix being sparse, positive definite, and fixed once for all in the iterative process. This paper will illustrate the methodology above on two different examples: the description of least squares solution methods and their application to the solution of the unsteady Navier-Stokes equations for incompressible viscous fluids; the description of augmented lagrangian decomposition techniques and their application to the solution of equilibrium problems in finite elasticity

Subgroups of class groups of algebraic quadratic function fields

International Nuclear Information System (INIS)

Wang Kunpeng; Zhang Xianke

2001-09-01

Ideal class groups H(K) of algebraic quadratic function fields K are studied, by using mainly the theory of continued fractions of algebraic functions. Properties of such continued fractions are discussed first. Then a necessary and sufficient condition is given for the class group H(K) to contain a cyclic subgroup of any order n, this criterion condition holds true for both real and imaginary fields K. Furthermore, several series of function fields K, including real, inertia imaginary, as well as ramified imaginary quadratic function fields, are given, and their class groups H(K) are proved to contain cyclic subgroups of order n. (author)

Maze solving algorithm and its programs using Z-80 assembler language for a robot

Energy Technology Data Exchange (ETDEWEB)

Takeno, J; Mukaidono, M

1982-01-01

In the first part the formation of a maze problem is introduced and the outline of this algorithm to solve a maze is explained in the second part. The third part describes the detail of this program, and the final part shows the program which has been developed using Z-80 assembler language. This program has portability for other robots using Z-80 microprocessors. 7 references.

A novel hybrid approach based on Particle Swarm Optimization and Ant Colony Algorithm to forecast energy demand of Turkey

International Nuclear Information System (INIS)

Kıran, Mustafa Servet; Özceylan, Eren; Gündüz, Mesut; Paksoy, Turan

2012-01-01

Highlights: ► PSO and ACO algorithms are hybridized for forecasting energy demands of Turkey. ► Linear and quadratic forms are developed to meet the fluctuations of indicators. ► GDP, population, export and import have significant impacts on energy demand. ► Quadratic form provides better fit solution than linear form. ► Proposed approach gives lower estimation error than ACO and PSO, separately. - Abstract: This paper proposes a new hybrid method (HAP) for estimating energy demand of Turkey using Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO). Proposed energy demand model (HAPE) is the first model which integrates two mentioned meta-heuristic techniques. While, PSO, developed for solving continuous optimization problems, is a population based stochastic technique; ACO, simulating behaviors between nest and food source of real ants, is generally used for discrete optimizations. Hybrid method based PSO and ACO is developed to estimate energy demand using gross domestic product (GDP), population, import and export. HAPE is developed in two forms which are linear (HAPEL) and quadratic (HAPEQ). The future energy demand is estimated under different scenarios. In order to show the accuracy of the algorithm, a comparison is made with ACO and PSO which are developed for the same problem. According to obtained results, relative estimation errors of the HAPE model are the lowest of them and quadratic form (HAPEQ) provides better-fit solutions due to fluctuations of the socio-economic indicators.

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

Science.gov (United States)

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

2015-08-01

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

Electron laser acceleration in vacuum by a quadratically chirped laser pulse

International Nuclear Information System (INIS)

Salamin, Yousef I; Jisrawi, Najeh M

2014-01-01

Single MeV electrons in vacuum subjected to single high-intensity quadratically chirped laser pulses are shown to gain multi-GeV energies. The laser pulses are modelled by finite-duration trapezoidal and cos  2 pulse-shapes and the equations of motion are solved numerically. It is found that, typically, the maximum energy gain from interaction with a quadratic chirp is about half of what would be gained from a linear chirp. (paper)

Quadratic reactivity fuel cycle model

International Nuclear Information System (INIS)

Lewins, J.D.

1985-01-01

For educational purposes it is highly desirable to provide simple yet realistic models for fuel cycle and fuel economy. In particular, a lumped model without recourse to detailed spatial calculations would be very helpful in providing the student with a proper understanding of the purposes of fuel cycle calculations. A teaching model for fuel cycle studies based on a lumped model assuming the summability of partial reactivities with a linear dependence of reactivity usefully illustrates fuel utilization concepts. The linear burnup model does not satisfactorily represent natural enrichment reactors. A better model, showing the trend of initial plutonium production before subsequent fuel burnup and fission product generation, is a quadratic fit. The study of M-batch cycles, reloading 1/Mth of the core at end of cycle, is now complicated by nonlinear equations. A complete account of the asymptotic cycle for any order of M-batch refueling can be given and compared with the linear model. A complete account of the transient cycle can be obtained readily in the two-batch model and this exact solution would be useful in verifying numerical marching models. It is convenient to treat the parabolic fit rho = 1 - tau 2 as a special case of the general quadratic fit rho = 1 - C/sub tau/ - (1 - C)tau 2 in suitably normalized reactivity and cycle time units. The parabolic results are given in this paper

Effect of fractional parameter on neutron transport in finite disturbed reactors with quadratic scattering

International Nuclear Information System (INIS)

Sallah, M.; Margeanu, C. A.

2016-01-01

The space-fractional neutron transport equation is used to describe the neutrons transport in finite disturbed reactors. It is approximated using the Pomraning-Eddington technique to yield two space-fractional differential equations, in terms of neutron density and net neutron flux. These resultant equations are coupled into a fractional diffusion-like equation for the neutron density whose solution is obtained by using Laplace transformation method. The solution is represented in terms of the Mittag-Leffler function and its different orders. The scattering is considered as quadratic scattering to offer a more realistic, compact representation of the system, and to increase the accuracy of the estimated neutronic parameters. The results are presented graphically to illustrate the fractional parameter effect in addition to the effect of radiative-transfer properties on the physical parameters of interest (reflection coefficient, transmission coefficient, neutron energy, and net neutron flux). The neutron transport problem in finite disturbed reactor with quadratic scattering is considered in investigating the shielding effectiveness, by using MAVRIC shielding module from SCALE6 programs package. The fractional parameter can be used to adjust the analysed data on neutron energy and flux, both for the theoretical model and the neutron transport application. (authors)

Integrable Hamiltonian systems and interactions through quadratic constraints

International Nuclear Information System (INIS)

Pohlmeyer, K.

1975-08-01

Osub(n)-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems. (orig.) [de

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

Science.gov (United States)

Huang, Dayu; Xue, Anke; Guo, Yunfei

2012-01-01

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

Penalty Dynamic Programming Algorithm for Dim Targets Detection in Sensor Systems

Directory of Open Access Journals (Sweden)

Yunfei Guo

2012-04-01

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

The genetic algorithm for the nonlinear programming of water pollution control system

Energy Technology Data Exchange (ETDEWEB)

Wei, J.; Zhang, J. [China University of Geosciences (China)

1999-08-01

In the programming of water pollution control system the combined method of optimization with simulation is used generally. It is not only laborious in calculation, but also the global optimum of the obtained solution is guaranteed difficult. In this paper, the genetic algorithm (GA) used in the nonlinear programming of water pollution control system is given, by which the preferred conception for the programming of waste water system is found in once-through operation. It is more succinct than the conventional method and the global optimum of the obtained solution could be ensured. 6 refs., 4 figs., 3 tabs.

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

International Nuclear Information System (INIS)

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

2016-01-01

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

An algorithm and program for finding sequence specific oligo-nucleotide probes for species identification

Directory of Open Access Journals (Sweden)

Tautz Diethard

2002-03-01

Full Text Available Abstract Background The identification of species or species groups with specific oligo-nucleotides as molecular signatures is becoming increasingly popular for bacterial samples. However, it shows also great promise for other small organisms that are taxonomically difficult to tract. Results We have devised here an algorithm that aims to find the optimal probes for any given set of sequences. The program requires only a crude alignment of these sequences as input and is optimized for performance to deal also with very large datasets. The algorithm is designed such that the position of mismatches in the probes influences the selection and makes provision of single nucleotide outloops. Program implementations are available for Linux and Windows.

Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

Science.gov (United States)

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.

Accurate nonlocal theory for cascaded quadratic soliton compression

DEFF Research Database (Denmark)

Bache, Morten; Bang, Ole; Moses, Jeffrey

2007-01-01

We study soliton compression in bulk quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion....

Modification of Brueschweiler quantum searching algorithm and realization by NMR experiment

International Nuclear Information System (INIS)

Yang Xiaodong; Wei Daxiu; Luo Jun; Miao Xijia

2002-01-01

In recent years, quantum computing research has made big progress, which exploit quantum mechanical laws, such as interference, superposition and parallelism, to perform computing tasks. The most inducing thing is that the quantum computing can provide large rise to the speedup in quantum algorithm. Quantum computing can solve some problems, which are impossible or difficult for the classical computing. The problem of searching for a specific item in an unsorted database can be solved with certain quantum algorithm, for example, Grover quantum algorithm and Brueschweiler quantum algorithm. The former gives a quadratic speedup, and the latter gives an exponential speedup comparing with the corresponding classical algorithm. In Brueschweiler quantum searching algorithm, the data qubit and the read-out qubit (the ancilla qubit) are different qubits. The authors have studied Brueschweiler algorithm and proposed a modified version, in which no ancilla qubit is needed to reach exponential speedup in the searching, the data and the read-out qubit are the same qubits. The modified Brueschweiler algorithm can be easier to design and realize. The authors also demonstrate the modified Brueschweiler algorithm in a 3-qubit molecular system by Nuclear Magnetic Resonance (NMR) experiment

Quadratic grating apodized photon sieves for simultaneous multiplane microscopy

Science.gov (United States)

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.

Fundamental quadratic variational principle underlying general relativity

International Nuclear Information System (INIS)

Atkins, W.K.

1983-01-01

The fundamental result of Lanczos is used in a new type of quadratic variational principle whose field equations are the Einstein field equations together with the Yang-Mills type equations for the Riemann curvature. Additionally, a spin-2 theory of gravity for the special case of the Einstein vacuum is discussed

Investigating Students' Mathematical Difficulties with Quadratic Equations

Science.gov (United States)

O'Connor, Bronwyn Reid; Norton, Stephen

2016-01-01

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

Analytic Expression of Arbitrary Matrix Elements for Boson Exponential Quadratic Polynomial Operators

Institute of Scientific and Technical Information of China (English)

XU Xiu-Wei; REN Ting-Qi; LIU Shu-Yan; MA Qiu-Ming; LIU Sheng-Dian

2007-01-01

Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators (BEQPO's), we present the analytic expression of arbitrary matrix elements for BEQPO's. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO's.

Dynamic Programming and Graph Algorithms in Computer Vision*

Science.gov (United States)

Felzenszwalb, Pedro F.; Zabih, Ramin

2013-01-01

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

Design of variable-weight quadratic congruence code for optical CDMA

Science.gov (United States)

Feng, Gang; Cheng, Wen-Qing; Chen, Fu-Jun

2015-09-01

A variable-weight code family referred to as variable-weight quadratic congruence code (VWQCC) is constructed by algebraic transformation for incoherent synchronous optical code division multiple access (OCDMA) systems. Compared with quadratic congruence code (QCC), VWQCC doubles the code cardinality and provides the multiple code-sets with variable code-weight. Moreover, the bit-error rate (BER) performance of VWQCC is superior to those of conventional variable-weight codes by removing or padding pulses under the same chip power assumption. The experiment results show that VWQCC can be well applied to the OCDMA with quality of service (QoS) requirements.

Optimal reservoir operation policies using novel nested algorithms

Science.gov (United States)

Delipetrev, Blagoj; Jonoski, Andreja; Solomatine, Dimitri

2015-04-01

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

Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps

Directory of Open Access Journals (Sweden)

Minsong Zhang

2014-01-01

Full Text Available This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs and linear matrix inequalities (LMIs. Numerical examples are given to illustrate the effectiveness of the proposed methodology.

Mixmaster cosmological model in theories of gravity with a quadratic Lagrangian

International Nuclear Information System (INIS)

Barrow, J.D.; Sirousse-Zia, H.

1989-01-01

We use the method of matched asymptotic expansions to examine the behavior of the vacuum Bianchi type-IX mixmaster universe in a gravity theory derived from a purely quadratic gravitational Lagrangian. The chaotic behavior characteristic of the general-relativistic mixmaster model disappears and the asymptotic behavior is of the monotonic, nonchaotic form found in the exactly soluble Bianchi type-I models of the quadratic theory. The asymptotic behavior far from the singularity is also found to be of monotonic nonchaotic type

The generation algorithm of arbitrary polygon animation based on dynamic correction

Directory of Open Access Journals (Sweden)

Hou Ya Wei

2016-01-01

Full Text Available This paper, based on the key-frame polygon sequence, proposes a method that makes use of dynamic correction to develop continuous animation. Firstly we use quadratic Bezier curve to interpolate the corresponding sides vector of polygon sequence consecutive frame and realize the continuity of animation sequences. And then, according to Bezier curve characteristic, we conduct dynamic regulation to interpolation parameters and implement the changing smoothness. Meanwhile, we take use of Lagrange Multiplier Method to correct the polygon and close it. Finally, we provide the concrete algorithm flow and present numerical experiment results. The experiment results show that the algorithm acquires excellent effect.

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

Science.gov (United States)

Marusak, Piotr M.; Kuntanapreeda, Suwat

2018-01-01

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

Geometric Methods in the Algebraic Theory of Quadratic Forms : Summer School

CERN Document Server

2004-01-01

The geometric approach to the algebraic theory of quadratic forms is the study of projective quadrics over arbitrary fields. Function fields of quadrics have been central to the proofs of fundamental results since the renewal of the theory by Pfister in the 1960's. Recently, more refined geometric tools have been brought to bear on this topic, such as Chow groups and motives, and have produced remarkable advances on a number of outstanding problems. Several aspects of these new methods are addressed in this volume, which includes - an introduction to motives of quadrics by Alexander Vishik, with various applications, notably to the splitting patterns of quadratic forms under base field extensions; - papers by Oleg Izhboldin and Nikita Karpenko on Chow groups of quadrics and their stable birational equivalence, with application to the construction of fields which carry anisotropic quadratic forms of dimension 9, but none of higher dimension; - a contribution in French by Bruno Kahn which lays out a general fra...

A Homogeneous and Self-Dual Interior-Point Linear Programming Algorithm for Economic Model Predictive Control

DEFF Research Database (Denmark)

Sokoler, Leo Emil; Frison, Gianluca; Skajaa, Anders

2015-01-01

We develop an efficient homogeneous and self-dual interior-point method (IPM) for the linear programs arising in economic model predictive control of constrained linear systems with linear objective functions. The algorithm is based on a Riccati iteration procedure, which is adapted to the linear...... system of equations solved in homogeneous and self-dual IPMs. Fast convergence is further achieved using a warm-start strategy. We implement the algorithm in MATLAB and C. Its performance is tested using a conceptual power management case study. Closed loop simulations show that 1) the proposed algorithm...

Bonus algorithm for large scale stochastic nonlinear programming problems

CERN Document Server

Diwekar, Urmila

2015-01-01

This book presents the details of the BONUS algorithm and its real world applications in areas like sensor placement in large scale drinking water networks, sensor placement in advanced power systems, water management in power systems, and capacity expansion of energy systems. A generalized method for stochastic nonlinear programming based on a sampling based approach for uncertainty analysis and statistical reweighting to obtain probability information is demonstrated in this book. Stochastic optimization problems are difficult to solve since they involve dealing with optimization and uncertainty loops. There are two fundamental approaches used to solve such problems. The first being the decomposition techniques and the second method identifies problem specific structures and transforms the problem into a deterministic nonlinear programming problem. These techniques have significant limitations on either the objective function type or the underlying distributions for the uncertain variables. Moreover, these ...

Classification of the quantum two dimensional superintegrable systems with quadratic integrals and the Stackel transforms

International Nuclear Information System (INIS)

Dakaloyannis, C.

2006-01-01

Full text: (author)The two dimensional quantum superintegrable systems with quadratic integrals of motion on a manifold are classified by using the quadratic associative algebra of the integrals of motion. There are six general fundamental classes of quantum superintegrable systems corresponding to the classical ones. Analytic formulas for the involved integrals are calculated in all the cases. All the known quantum superintegrable systems with quadratic integrals are classified as special cases of these six general classes. The coefficients of the quadratic associative algebra of integrals are calculated and they are compared to the coefficients of the corresponding coefficients of the Poisson quadratic algebra of the classical systems. The quantum coefficients are similar as the classical ones multiplied by a quantum coefficient -n 2 plus a quantum deformation of order n 4 and n 6 . The systems inside the classes are transformed using Stackel transforms in the quantum case as in the classical case and general form is discussed. The idea of the Jacobi Hamiltonian corresponding to the Jacobi metric in the classical case is discussed

Quantum algorithm for association rules mining

Science.gov (United States)

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

2016-10-01

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

Algorithms and programs for evaluating fault trees with multi-state components

International Nuclear Information System (INIS)

Wickenhaeuser, A.

1989-07-01

Part 1 and 2 of the report contain a summary overview of methods and algorithms for the solution of fault tree analysis problems. The following points are treated in detail: Treatment of fault tree components with more than two states. Acceleration of the solution algorithms. Decomposition and modularization of extensive systems. Calculation of the structural function and the exact occurrence probability. Treatment of statistical dependencies. A flexible tool to be employed in solving these problems is the method of forming Boolean variables with restrictions. In this way, components with more than two states can be treated, the possibilities of forming modules expanded, and statistical dependencies treated. Part 3 contains descriptions of the MUSTAFA, MUSTAMO, PASPI, and SIMUST computer programs based on these methods. (orig./HP) [de

Phase space eigenfunctions of multidimensional quadratic Hamiltonians

International Nuclear Information System (INIS)

Dodonov, V.V.; Man'ko, V.I.

1986-01-01

We obtain the explicit expressions for phace space eigenfunctions (PSE),i.e. Weyl's symbols of dyadic operators like vertical stroken> ,vertical strokem>, being the solution of the Schroedinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian coordinates and conjugated to them momenta with time-dependent coefficients. It is shown that for an arbitrary quadratic Hamiltonian one can always construct the set of completely factorized PSE which are products of N factors, each factor being dependent only on two arguments for nnot=m and on a single argument for n=m. These arguments are nothing but constants of motion of the correspondent classical system. PSE are expressed in terms of the associated Laguerre polynomials in the case of a discrete spectrum and in terms of the Airy functions in the continuous spectrum case. Three examples are considered: a harmonic oscillator with a time-dependent frequency, a charged particle in a nonstationary uniform magnetic field, and a particle in a time-dependent uniform potential field. (orig.)

Quadratic Variation by Markov Chains

DEFF Research Database (Denmark)

Hansen, Peter Reinhard; Horel, Guillaume

We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...... microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the dis- crete Markov chain model that is well suited for the analysis of financial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analyti...

Coherent states for quadratic Hamiltonians

International Nuclear Information System (INIS)

Contreras-Astorga, Alonso; Fernandez C, David J; Velazquez, Mercedes

2011-01-01

The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows us to directly identify the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and will be compared with those attained through the displacement operator method. The corresponding wavefunction will be found, and a general procedure for obtaining several mean values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.

Optimal control linear quadratic methods

CERN Document Server

Anderson, Brian D O

2007-01-01

This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the

Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise

Directory of Open Access Journals (Sweden)

Huiying Sun

2014-01-01

Full Text Available We mainly consider the stability of discrete-time Markovian jump linear systems with state-dependent noise as well as its linear quadratic (LQ differential games. A necessary and sufficient condition involved with the connection between stochastic Tn-stability of Markovian jump linear systems with state-dependent noise and Lyapunov equation is proposed. And using the theory of stochastic Tn-stability, we give the optimal strategies and the optimal cost values for infinite horizon LQ stochastic differential games. It is demonstrated that the solutions of infinite horizon LQ stochastic differential games are concerned with four coupled generalized algebraic Riccati equations (GAREs. Finally, an iterative algorithm is presented to solve the four coupled GAREs and a simulation example is given to illustrate the effectiveness of it.

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

Science.gov (United States)

1990-09-01

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

Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations

DEFF Research Database (Denmark)

Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip

2016-01-01

We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...

Dynamic Programming Algorithms in Speech Recognition

Directory of Open Access Journals (Sweden)

Titus Felix FURTUNA

2008-01-01

Full Text Available In a system of speech recognition containing words, the recognition requires the comparison between the entry signal of the word and the various words of the dictionary. The problem can be solved efficiently by a dynamic comparison algorithm whose goal is to put in optimal correspondence the temporal scales of the two words. An algorithm of this type is Dynamic Time Warping. This paper presents two alternatives for implementation of the algorithm designed for recognition of the isolated words.

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

Science.gov (United States)

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

2015-01-01

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

Linear and Quadratic Interpolators Using Truncated-Matrix Multipliers and Squarers

Directory of Open Access Journals (Sweden)

E. George Walters III

2015-11-01

Full Text Available This paper presents a technique for designing linear and quadratic interpolators for function approximation using truncated multipliers and squarers. Initial coefficient values are found using a Chebyshev-series approximation and then adjusted through exhaustive simulation to minimize the maximum absolute error of the interpolator output. This technique is suitable for any function and any precision up to 24 bits (IEEE single precision. Designs for linear and quadratic interpolators that implement the 1/x, 1/ √ x, log2(1+2x, log2(x and 2x functions are presented and analyzed as examples. Results show that a proposed 24-bit interpolator computing 1/x with a design specification of ±1 unit in the last place of the product (ulp error uses 16.4% less area and 15.3% less power than a comparable standard interpolator with the same error specification. Sixteen-bit linear interpolators for other functions are shown to use up to 17.3% less area and 12.1% less power, and 16-bit quadratic interpolators are shown to use up to 25.8% less area and 24.7% less power.

Quadratic mass relations in topological bootstrap theory

International Nuclear Information System (INIS)

Jones, C.E.; Uschersohn, J.

1980-01-01

From the requirement of reality of discontinuities of scattering amplitudes at the spherical level of the topological bootstrap theory, a large number of mass relations for hadrons is derived. Quadratic mass formulas for the symmetry-breaking pattern of both mesons and baryon is obtained and their relation to conventional models of symmetry breaking is briefly discussed

Vacuum solutions of Bianchi cosmologies in quadratic gravity

International Nuclear Information System (INIS)