Configuring Airspace Sectors with Approximate Dynamic Programming
Bloem, Michael; Gupta, Pramod
2010-01-01
In response to changing traffic and staffing conditions, supervisors dynamically configure airspace sectors by assigning them to control positions. A finite horizon airspace sector configuration problem models this supervisor decision. The problem is to select an airspace configuration at each time step while considering a workload cost, a reconfiguration cost, and a constraint on the number of control positions at each time step. Three algorithms for this problem are proposed and evaluated: a myopic heuristic, an exact dynamic programming algorithm, and a rollouts approximate dynamic programming algorithm. On problem instances from current operations with only dozens of possible configurations, an exact dynamic programming solution gives the optimal cost value. The rollouts algorithm achieves costs within 2% of optimal for these instances, on average. For larger problem instances that are representative of future operations and have thousands of possible configurations, excessive computation time prohibits the use of exact dynamic programming. On such problem instances, the rollouts algorithm reduces the cost achieved by the heuristic by more than 15% on average with an acceptable computation time.
Approximate Dynamic Programming for Self-Learning Control
Derong Liu
2005-01-01
This paper introduces a self-learning control approach based on approximate dynamic programming. Dynamic programming was introduced by Bellman in the 1950's for solving optimal control problems of nonlinear dynamical systems. Due to its high computational complexity, the applications of dynamic programming have been limited to simple and small problems. The key step in finding approximate solutions to dynamic programming is to estimate the performance index in dynamic programming. The optimal control signal can then be determined by minimizing (or maximizing) the performance index. Artificial neural networks are very efficient tools in representing the performance index in dynamic programming. This paper assumes the use of neural networks for estimating the performance index in dynamic programming and for generating optimal control signals, thus to achieve optimal control through self-learning.
Approximate Dynamic Programming Solving the Curses of Dimensionality
Powell, Warren B
2011-01-01
Praise for the First Edition "Finally, a book devoted to dynamic programming and written using the language of operations research (OR)! This beautiful book fills a gap in the libraries of OR specialists and practitioners."-Computing Reviews This new edition showcases a focus on modeling and computation for complex classes of approximate dynamic programming problems Understanding approximate dynamic programming (ADP) is vital in order to develop practical and high-quality solutions to complex industrial problems, particularly when those problems involve making decisions in the presence of unce
Chen, Wei; Huang, Dayu; Kulkarni, Ankur A.; Unnikrishnan, Jayakrishnan; Zhu, Quanyan; Mehta, Prashant; Meyn, Sean; Wierman, Adam
2013-01-01
Neuro-dynamic programming is a class of powerful techniques for approximating the solution to dynamic programming equations. In their most computationally attractive formulations, these techniques provide the approximate solution only within a prescribed finite-dimensional function class. Thus, the question that always arises is how should the function class be chosen? The goal of this paper is to propose an approach using the solutions to associated fluid and diffusion approximations. In ord...
Approximate Dynamic Programming By Minimizing Distributionally Robust Bounds
Petrik, Marek
2012-01-01
Approximate dynamic programming is a popular method for solving large Markov decision processes. This paper describes a new class of approximate dynamic programming (ADP) methods- distributionally robust ADP-that address the curse of dimensionality by minimizing a pessimistic bound on the policy loss. This approach turns ADP into an optimization problem, for which we derive new mathematical program formulations and analyze its properties. DRADP improves on the theoretical guarantees of existing ADP methods-it guarantees convergence and L1 norm based error bounds. The empirical evaluation of DRADP shows that the theoretical guarantees translate well into good performance on benchmark problems.
An Approximate Dynamic Programming Approach to Multidimensional Knapsack Problems
Dimitris Bertsimas; Ramazan Demir
2002-01-01
We present an Approximate Dynamic Programming (ADP) approach for the multidimensional knapsack problem (MKP). We approximate the value function (a) using parametric and nonparametric methods and (b)using a base-heuristic. We propose a new heuristic which adaptively rounds the solution of the linear programming relaxation. Our computational study suggests: (a)the new heuristic produces high quality solutions fast and robustly, (b)state of the art commercial packages like CPLEX require signific...
Approximate Dynamic Programming Based on High Dimensional Model Representation
Pištěk, Miroslav
2013-01-01
Roč. 49, č. 5 (2013), s. 720-737. ISSN 0023-5954 R&D Projects: GA ČR(CZ) GAP102/11/0437 Institutional support: RVO:67985556 Keywords : approximate dynamic programming * Bellman equation * approximate HDMR minimization * trust region problem Subject RIV: BC - Control Systems Theory Impact factor: 0.563, year: 2013 http://library.utia.cas.cz/separaty/2013/AS/pistek-0399560.pdf
Approximate dynamic programming solving the curses of dimensionality
Powell, Warren B
2007-01-01
Warren B. Powell, PhD, is Professor of Operations Research and Financial Engineering at Princeton University, where he is founder and Director of CASTLE Laboratory, a research unit that works with industrial partners to test new ideas found in operations research. The recipient of the 2004 INFORMS Fellow Award, Dr. Powell has authored over 100 refereed publications on stochastic optimization, approximate dynamic programming, and dynamic resource management.
Editorial Special issue on approximate dynamic programming and reinforcement learning
Silvia Ferrari; Jagannathan Sarangapani; Frank L. Lewis
2011-01-01
We are extremely pleased to present this special issue of the Journal of Control Theory and Applications.Approximate dynamic programming (ADP) is a general and effective approach for solving optimal control and estimation problems by adapting to uncertain environments over time.ADP optimizes the sensing objectives accrued over a future time interval with respect to an adaptive control law,conditioned on prior knowledge of the system,its state,and uncertainties.A numerical search over the present value of the control minimizes a Hamilton-Jacobi-Bellman (HJB) equation providing a basis for real-time,approximate optimal control.
Approximate Dynamic Programming in Tracking Control of a Robotic Manipulator
Marcin Szuster
2016-02-01
Full Text Available This article focuses on the implementation of an approximate dynamic programming algorithm in the discrete tracking control system of the three-degrees of freedom Scorbot-ER 4pc robotic manipulator. The controlled system is included in an articulated robots group which uses rotary joints to access their work space. The main part of the control system is a dual heuristic dynamic programming algorithm that consists of two structures designed in the form of neural networks: an actor and a critic. The actor generates the suboptimal control law while the critic approximates the difference of the value function from Bellman’s equation with respect to the state. The residual elements of the control system are the PD controller, the supervisory term and an additional control signal. The structure of the supervisory term derives from the stability analysis performed using the Lyapunov stability theorem. The control system works online, the neural networks’ weights-adaptation procedure is performed in every iteration step, and the neural networks’ preliminary learning process is not required. The performance of the control system was verified by a series of computer simulations and experiments performed using the Scorbot-ER 4pc robotic manipulator.
F -Discrepancy for Efficient Sampling in Approximate Dynamic Programming.
Cervellera, Cristiano; Maccio, Danilo
2016-07-01
In this paper, we address the problem of generating efficient state sample points for the solution of continuous-state finite-horizon Markovian decision problems through approximate dynamic programming. It is known that the selection of sampling points at which the value function is observed is a key factor when such function is approximated by a model based on a finite number of evaluations. A standard approach consists in generating these points through a random or deterministic procedure, aiming at a balanced covering of the state space. Yet, this solution may not be efficient if the state trajectories are not uniformly distributed. Here, we propose to exploit F -discrepancy, a quantity that measures how closely a set of random points represents a probability distribution, and introduce an example of an algorithm based on such concept to automatically select point sets that are efficient with respect to the underlying Markovian process. An error analysis of the approximate solution is provided, showing how the proposed algorithm enables convergence under suitable regularity hypotheses. Then, simulation results are provided concerning an inventory forecasting test problem. The tests confirm in general the important role of F -discrepancy, and show how the proposed algorithm is able to yield better results than uniform sampling, using sets even 50 times smaller. PMID:26241987
Dynamic programming approach to optimization of approximate decision rules
Amin, Talha
2013-02-01
This paper is devoted to the study of an extension of dynamic programming approach which allows sequential optimization of approximate decision rules relative to the length and coverage. We introduce an uncertainty measure R(T) which is the number of unordered pairs of rows with different decisions in the decision table T. For a nonnegative real number β, we consider β-decision rules that localize rows in subtables of T with uncertainty at most β. Our algorithm constructs a directed acyclic graph Δβ(T) which nodes are subtables of the decision table T given by systems of equations of the kind "attribute = value". This algorithm finishes the partitioning of a subtable when its uncertainty is at most β. The graph Δβ(T) allows us to describe the whole set of so-called irredundant β-decision rules. We can describe all irredundant β-decision rules with minimum length, and after that among these rules describe all rules with maximum coverage. We can also change the order of optimization. The consideration of irredundant rules only does not change the results of optimization. This paper contains also results of experiments with decision tables from UCI Machine Learning Repository. © 2012 Elsevier Inc. All rights reserved.
Jooyoung Park; Gyo-Bum Chung; Jungdong Lim; Dongsu Yang
2015-01-01
Recently, the optimization of power flows in portable hybrid power-supply systems (HPSSs) has become an important issue with the advent of a variety of mobile systems and hybrid energy technologies. In this paper, a control strategy is considered for dynamically managing power flows in portable HPSSs employing batteries and supercapacitors. Our dynamic power management strategy utilizes the concept of approximate dynamic programming (ADP). ADP methods are important tools in the fields of stoc...
Jooyoung Park
2015-05-01
Full Text Available Recently, the optimization of power flows in portable hybrid power-supply systems (HPSSs has become an important issue with the advent of a variety of mobile systems and hybrid energy technologies. In this paper, a control strategy is considered for dynamically managing power flows in portable HPSSs employing batteries and supercapacitors. Our dynamic power management strategy utilizes the concept of approximate dynamic programming (ADP. ADP methods are important tools in the fields of stochastic control and machine learning, and the utilization of these tools for practical engineering problems is now an active and promising research field. We propose an ADP-based procedure based on optimization under constraints including the iterated Bellman inequalities, which can be solved by convex optimization carried out offline, to find the optimal power management rules for portable HPSSs. The effectiveness of the proposed procedure is tested through dynamic simulations for smartphone workload scenarios, and simulation results show that the proposed strategy can successfully cope with uncertain workload demands.
Hamilton-Jacobi-Bellman equations and approximate dynamic programming on time scales.
Seiffertt, John; Sanyal, Suman; Wunsch, Donald C
2008-08-01
The time scales calculus is a key emerging area of mathematics due to its potential use in a wide variety of multidisciplinary applications. We extend this calculus to approximate dynamic programming (ADP). The core backward induction algorithm of dynamic programming is extended from its traditional discrete case to all isolated time scales. Hamilton-Jacobi-Bellman equations, the solution of which is the fundamental problem in the field of dynamic programming, are motivated and proven on time scales. By drawing together the calculus of time scales and the applied area of stochastic control via ADP, we have connected two major fields of research. PMID:18632378
Approximate group context tree: applications to dynamic programming and dynamic choice models
Belloni, Alexandre
2011-01-01
The paper considers a variable length Markov chain model associated with a group of stationary processes that share the same context tree but potentially different conditional probabilities. We propose a new model selection and estimation method, develop oracle inequalities and model selection properties for the estimator. These results also provide conditions under which the use of the group structure can lead to improvements in the overall estimation. Our work is also motivated by two methodological applications: discrete stochastic dynamic programming and dynamic discrete choice models. We analyze the uniform estimation of the value function for dynamic programming and the uniform estimation of average dynamic marginal effects for dynamic discrete choice models accounting for possible imperfect model selection. We also derive the typical behavior of our estimator when applied to polynomially $\\beta$-mixing stochastic processes. For parametric models, we derive uniform rate of convergence for the estimation...
A Case Study on Air Combat Decision Using Approximated Dynamic Programming
Yaofei Ma
2014-01-01
Full Text Available As a continuous state space problem, air combat is difficult to be resolved by traditional dynamic programming (DP with discretized state space. The approximated dynamic programming (ADP approach is studied in this paper to build a high performance decision model for air combat in 1 versus 1 scenario, in which the iterative process for policy improvement is replaced by mass sampling from history trajectories and utility function approximating, leading to high efficiency on policy improvement eventually. A continuous reward function is also constructed to better guide the plane to find its way to “winner” state from any initial situation. According to our experiments, the plane is more offensive when following policy derived from ADP approach other than the baseline Min-Max policy, in which the “time to win” is reduced greatly but the cumulated probability of being killed by enemy is higher. The reason is analyzed in this paper.
The Smoothed Approximate Linear Program
Desai, V V; Moallemi, C C
2009-01-01
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural `projection' of a well studied linear program for exact dynamic programming. Such programs restrict attention to approximations that are lower bounds to the optimal cost-to-go function. Our program--the `smoothed approximate linear program'--is distinct from such approaches and relaxes the restriction to lower bounding approximations in an appropriate fashion while remaining computationally tractable. Doing so appears to have several advantages: First, we demonstrate substantially superior bounds on the quality of approximation to the optimal cost-to-go function afforded by our approach. Second, experiments with our approach on a challenging problem (the game of Tetris) show that the approach outperforms the existing LP approach (which has previously been shown to be competitive with several AD...
Approximating high-dimensional dynamics by barycentric coordinates with linear programming
Hirata, Yoshito, E-mail: yoshito@sat.t.u-tokyo.ac.jp; Aihara, Kazuyuki; Suzuki, Hideyuki [Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505 (Japan); Department of Mathematical Informatics, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656 (Japan); CREST, JST, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan); Shiro, Masanori [Department of Mathematical Informatics, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656 (Japan); Mathematical Neuroinformatics Group, Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568 (Japan); Takahashi, Nozomu; Mas, Paloma [Center for Research in Agricultural Genomics (CRAG), Consorci CSIC-IRTA-UAB-UB, Barcelona 08193 (Spain)
2015-01-15
The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.
Approximating high-dimensional dynamics by barycentric coordinates with linear programming
The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data
Dynamic Analyses of Result Quality in Energy-Aware Approximate Programs
RIngenburg, Michael F.
Energy efficiency is a key concern in the design of modern computer systems. One promising approach to energy-efficient computation, approximate computing, trades off output precision for energy efficiency. However, this tradeoff can have unexpected effects on computation quality. This thesis presents dynamic analysis tools to study, debug, and monitor the quality and energy efficiency of approximate computations. We propose three styles of tools: prototyping tools that allow developers to experiment with approximation in their applications, online tools that instrument code to determine the key sources of error, and online tools that monitor the quality of deployed applications in real time. Our prototyping tool is based on an extension to the functional language OCaml. We add approximation constructs to the language, an approximation simulator to the runtime, and profiling and auto-tuning tools for studying and experimenting with energy-quality tradeoffs. We also present two online debugging tools and three online monitoring tools. The first online tool identifies correlations between output quality and the total number of executions of, and errors in, individual approximate operations. The second tracks the number of approximate operations that flow into a particular value. Our online tools comprise three low-cost approaches to dynamic quality monitoring. They are designed to monitor quality in deployed applications without spending more energy than is saved by approximation. Online monitors can be used to perform real time adjustments to energy usage in order to meet specific quality goals. We present prototype implementations of all of these tools and describe their usage with several applications. Our prototyping, profiling, and autotuning tools allow us to experiment with approximation strategies and identify new strategies, our online tools succeed in providing new insights into the effects of approximation on output quality, and our monitors succeed in
Bottacin-Busolin, Andrea; Wörman, Anders; Zmijewski, Nicholas
2013-04-01
A main challenge for the planning and management of water resources is the development of strategies for regulation of multireservoir systems under a complex stochastic environment. The sequential decision problem involving the release of water from multiple reservoirs depends on the stochastic variability of the hydrologic inflows over a spectrum of time scales. An important distinction is made between short-term and mid-term planning: the first is associated with regulation on the hourly scale within the one-week time horizon, whilst the second is associated with the weekly scale within the one-year horizon. Although a variety of optimization methods have been suggested, the achievement of a global optimum in the operation of large-scale systems is hindered by their high dimensional state space and by the stochastic nature of the hydrologic inflows. In this work, operational plans for multireservoir systems are derived via an approximate dynamic programming approach using a policy iteration algorithm. The algorithm is based on an off-line learning process in which policies are evaluated for a number of stochastic inflow scenarios by constructing approximations of their value functions, and the resulting value functions are used iteratively to design new, improved policies. In the mid-term planning phase, inflow scenarios are generated with a periodic autoregressive model that is calibrated against historical inflow data, and the policy iteration algorithm leads to a cyclostationary operating policy. In the short-term planning phase, the mid-term value function is used to calculate the value of a policy at the end of the short-term operating horizon, and synthetic inflow scenarios are generated by perturbing streamflow forecasts with Gaussian noise, following Zhao et al. (Water Resour. Res., 48, W01540, 2012). The variance of the noise is assumed to increase linearly over time and converges to the local variance of the historical time series. A case study is
Amin, Talha
2013-01-01
In the paper, we present a comparison of dynamic programming and greedy approaches for construction and optimization of approximate decision rules relative to the number of misclassifications. We use an uncertainty measure that is a difference between the number of rows in a decision table T and the number of rows with the most common decision for T. For a nonnegative real number γ, we consider γ-decision rules that localize rows in subtables of T with uncertainty at most γ. Experimental results with decision tables from the UCI Machine Learning Repository are also presented. © 2013 Springer-Verlag.
Approximate Dynamic Programming for Fast Denoising of aCGH Data
Miller, Gary L; Schwartz, Russell; Tsourakakis, Charalampos E
2010-01-01
DNA sequence copy number is the number of copies of DNA at a region of a genome. Identifying genomic regions whose DNA copy number deviates from the normal is a crucial task in understanding cancer evolution. Array-based comparative genomic hybridization (aCGH) is a high-throughput technique for identifying DNA gain or loss. Due to the high level of noise in microarray data, however, interpretation of aCGH output is a difficult and error-prone task. In this paper, we adopt a recent formulation of the denoising aCGH data problem as a regularized least squares problem and propose an approximation algorithm within $\\epsilon$ additive error, where \\epsilon is an arbitrarily small positive constant. Specifically, we show that for n probes, we can approximate the optimal value of our function within additive \\epsilon with an algorithm that runs in $\\tilde{O}(n^{1.5} \\log{(\\frac{U}{\\epsilon}))}$ time, where U is the maximum value over the regularization term and the probes. The basis of our algorithm is the definiti...
Xiao, Jingjie
A key hurdle for implementing real-time pricing of electricity is a lack of consumers' responses. Solutions to overcome the hurdle include the energy management system that automatically optimizes household appliance usage such as plug-in hybrid electric vehicle charging (and discharging with vehicle-to-grid) via a two-way communication with the grid. Real-time pricing, combined with household automation devices, has a potential to accommodate an increasing penetration of plug-in hybrid electric vehicles. In addition, the intelligent energy controller on the consumer-side can help increase the utilization rate of the intermittent renewable resource, as the demand can be managed to match the output profile of renewables, thus making the intermittent resource such as wind and solar more economically competitive in the long run. One of the main goals of this dissertation is to present how real-time retail pricing, aided by control automation devices, can be integrated into the wholesale electricity market under various uncertainties through approximate dynamic programming. What distinguishes this study from the existing work in the literature is that whole- sale electricity prices are endogenously determined as we solve a system operator's economic dispatch problem on an hourly basis over the entire optimization horizon. This modeling and algorithm framework will allow a feedback loop between electricity prices and electricity consumption to be fully captured. While we are interested in a near-optimal solution using approximate dynamic programming; deterministic linear programming benchmarks are use to demonstrate the quality of our solutions. The other goal of the dissertation is to use this framework to provide numerical evidence to the debate on whether real-time pricing is superior than the current flat rate structure in terms of both economic and environmental impacts. For this purpose, the modeling and algorithm framework is tested on a large-scale test case
Jou, Jonathan D; Jain, Swati; Georgiev, Ivelin S; Donald, Bruce R
2016-06-01
Sparse energy functions that ignore long range interactions between residue pairs are frequently used by protein design algorithms to reduce computational cost. Current dynamic programming algorithms that fully exploit the optimal substructure produced by these energy functions only compute the GMEC. This disproportionately favors the sequence of a single, static conformation and overlooks better binding sequences with multiple low-energy conformations. Provable, ensemble-based algorithms such as A* avoid this problem, but A* cannot guarantee better performance than exhaustive enumeration. We propose a novel, provable, dynamic programming algorithm called Branch-Width Minimization* (BWM*) to enumerate a gap-free ensemble of conformations in order of increasing energy. Given a branch-decomposition of branch-width w for an n-residue protein design with at most q discrete side-chain conformations per residue, BWM* returns the sparse GMEC in O([Formula: see text]) time and enumerates each additional conformation in merely O([Formula: see text]) time. We define a new measure, Total Effective Search Space (TESS), which can be computed efficiently a priori before BWM* or A* is run. We ran BWM* on 67 protein design problems and found that TESS discriminated between BWM*-efficient and A*-efficient cases with 100% accuracy. As predicted by TESS and validated experimentally, BWM* outperforms A* in 73% of the cases and computes the full ensemble or a close approximation faster than A*, enumerating each additional conformation in milliseconds. Unlike A*, the performance of BWM* can be predicted in polynomial time before running the algorithm, which gives protein designers the power to choose the most efficient algorithm for their particular design problem. PMID:26744898
François-Lavet, Vincent; Fonteneau, Raphaël; Ernst, Damien
2014-01-01
This paper proposes a methodology to estimate the maximum revenue that can be generated by a company that operates a high-capacity storage device to buy or sell electricity on the day-ahead electricity market. The methodology exploits the Dynamic Programming (DP) principle and is specified for hydrogen-based storage devices that use electrolysis to produce hydrogen and fuel cells to generate electricity from hydrogen. Experimental results are generated using historical data of energy prices o...
Reduction of Linear Programming to Linear Approximation
Vaserstein, Leonid N.
2006-01-01
It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.
Moraes Rêgo, Patrícia Helena; Viana da Fonseca Neto, João; Ferreira, Ernesto M.
2015-08-01
The main focus of this article is to present a proposal to solve, via UDUT factorisation, the convergence and numerical stability problems that are related to the covariance matrix ill-conditioning of the recursive least squares (RLS) approach for online approximations of the algebraic Riccati equation (ARE) solution associated with the discrete linear quadratic regulator (DLQR) problem formulated in the actor-critic reinforcement learning and approximate dynamic programming context. The parameterisations of the Bellman equation, utility function and dynamic system as well as the algebra of Kronecker product assemble a framework for the solution of the DLQR problem. The condition number and the positivity parameter of the covariance matrix are associated with statistical metrics for evaluating the approximation performance of the ARE solution via RLS-based estimators. The performance of RLS approximators is also evaluated in terms of consistence and polarisation when associated with reinforcement learning methods. The used methodology contemplates realisations of online designs for DLQR controllers that is evaluated in a multivariable dynamic system model.
Proving acceptability properties of relaxed nondeterministic approximate programs
Carbin, Michael James; Kim, Deokhwan; Misailovic, Sasa; Rinard, Martin C
2012-01-01
Approximate program transformations such as skipping tasks [29, 30], loop perforation [21, 22, 35], reduction sampling [38], multiple selectable implementations [3, 4, 16, 38], dynamic knobs [16], synchronization elimination [20, 32], approximate function memoization [11],and approximate data types [34] produce programs that can execute at a variety of points in an underlying performance versus accuracy tradeoff space. These transformed programs have the ability to trade accuracy of their res...
Dynamical equations and approximation methods
The integral equations approach to the three-body problem, decisively stimulated by Faddeev's formulation, provides the most powerful tool for studying the internal structure of this system. An essential step towards a detailed understanding of composite particle dynamics has been done in this way. The search for adequate extensions to the general N-body situation therefore represented, and still represents a natural challenge. For various reasons this transition is non-trivial and non-unique. Emphasizing different aspects of the three-body theory, different generalizations have been found. In particular, it was the concept of connectedness of the (iterated) integral kernel which allows for an arbitrary number of formulations, many of them being presumably only mathematically correct, but physically rather unsatisfactory. Therefore, the present status of the N-body theory is reviewed in a less technical way. Starting from the basic, physically convincing definitions of scattering states, the defining equations are replaced by more appropriate matrix relations. This is done in a reversible way, thus preserving in every step the original structure and information. In order to be as close as possible to the basic definitions, all relations are first derived for scattering states or half-on-shell transition amplitudes. The ambiguity in going over to corresponding operator identities (fully off-shell equations) is demonstrated. (Auth.)
Dynamical Vertex Approximation for Nanoscopic Systems
Full text: We present model calculations for nanoscopic systems including Hubbard-like Coulomb repulsion and double exchange interactions with localized, classical spins. We compare the results of the recently introduced nanoscopic version of the dynamical vertex approximation at dynamical mean field level against exact diagonalization for a Benzene-like ring, where the latter is doable. This comparison allows us to investigate the reliability of the approximation. It shows that, already at the simplest approximation level (i.e. including only local correlations) the results are very accurate in a rather wide range of parameters. Since the computational effort is highly reduced, it is suitable for studying more complex systems. (author)
Nonlinear Programming Method for Dynamic Programming
Yongyang Cai; Judd, Kenneth L; Lontzek, Thomas S.; Valentina Michelangeli; Che-Lin Su
2013-01-01
A nonlinear programming formulation is introduced to solve infinite horizon dynamic programming problems. This extends the linear approach to dynamic programming by using ideas from approximation theory to avoid inefficient discretization. Our numerical results show that this nonlinear programming method is efficient and accurate.
Dynamic Approximate Vertex Cover and Maximum Matching
Onak, Krzysztof; Rubinfeld, Ronitt
2010-01-01
We consider the problem of maintaining a large matching or a small vertex cover in a dynamically changing graph. Each update to the graph is either an edge deletion or an edge insertion. We give the first randomized data structure that simultaneously achieves a constant approximation factor and handles a sequence of k updates in k. polylog(n) time. Previous data structures require a polynomial amount of computation per update. The starting point of our construction is a distributed algorit...
李雪; 聂兰顺; 齐文艳; 战德臣
2015-01-01
针对物流配送服务业中，车辆调度问题日渐呈现任务规模大，车辆类型多、属性多，调度实时性要求越来越高等特点，提出了基于近似动态规划的动态车辆调度算法。根据当前的任务需求与车辆状态以及相应的约束条件作出相应的调度，并且对一些样本进行训练，得到了一个近似价值函数。通过该价值函数，即可对任务迅速作出相应的决策。仿真模拟实验证明了该算法的有效性和优越性。%Vehicle scheduling in service industry of logistics distribution was presenting features including the tasks tended to be of large scale,vehicles were multi-type and had multiple attributes as well as high demands for real-time scheduling.To solve these problems,this paper proposed a dy-namic vehicle scheduling algorithm based on the approximate dynamic programming.An approximate value function was obtained through training of some samples,and according to mission require-ments,vehicle state and conditions,and quick scheduling decisions could be made with the value func-tion.The simulation test has proved the correctness and effectiveness of the algorithm.
Escape dynamics: a continuous-time approximation
Kolyuzhnov, D.; Bogomolova, A.; Slobodyan, Sergey
2014-01-01
Roč. 38, January (2014), s. 161-183. ISSN 0165-1889 Institutional support: RVO:67985998 Keywords : constant gain adaptive learning * escape dynamics * recursive least squares Subject RIV: AH - Economics Impact factor: 1.018, year: 2014
Escape dynamics: a continuous-time approximation
Kolyuzhnov, Dmitri; Bogomolova, Anna; Slobodyan, S.
2014-01-01
Roč. 38, January (2014), s. 161-183. ISSN 0165-1889 R&D Projects: GA ČR(CZ) GBP402/12/G097 Institutional support: PRVOUK-P23 Keywords : constant gain adaptive learning * escape dynamics * recursive least squares Subject RIV: AH - Economics Impact factor: 1.018, year: 2014
STOVL propulsion system volume dynamics approximations
Drummond, Colin K.
1989-01-01
Two approaches to modeling turbofan engine component volume dynamics are explored and compared with a view toward application to real-time simulation of short take-off vertical landing (STOVL) aircraft propulsion systems. The first (and most popular) approach considers only heat and mass balances; the second approach includes a momentum balance and substitutes the heat equation with a complete energy balance. Results for a practical test case are presented and discussed.
Phase field approximation of dynamic brittle fracture
Schlüter, Alexander; Willenbücher, Adrian; Kuhn, Charlotte; Müller, Ralf
2014-11-01
Numerical methods that are able to predict the failure of technical structures due to fracture are important in many engineering applications. One of these approaches, the so-called phase field method, represents cracks by means of an additional continuous field variable. This strategy avoids some of the main drawbacks of a sharp interface description of cracks. For example, it is not necessary to track or model crack faces explicitly, which allows a simple algorithmic treatment. The phase field model for brittle fracture presented in Kuhn and Müller (Eng Fract Mech 77(18):3625-3634, 2010) assumes quasi-static loading conditions. However dynamic effects have a great impact on the crack growth in many practical applications. Therefore this investigation presents an extension of the quasi-static phase field model for fracture from Kuhn and Müller (Eng Fract Mech 77(18):3625-3634, 2010) to the dynamic case. First of all Hamilton's principle is applied to derive a coupled set of Euler-Lagrange equations that govern the mechanical behaviour of the body as well as the crack growth. Subsequently the model is implemented in a finite element scheme which allows to solve several test problems numerically. The numerical examples illustrate the capabilities of the developed approach to dynamic fracture in brittle materials.
Approximating Sparse Covering Integer Programs Online
Gupta, Anupam
2012-01-01
A covering integer program (CIP) is a mathematical program of the form: min {c^T x : Ax >= 1, 0 <= x <= u, x integer}, where A is an m x n matrix, and c and u are n-dimensional vectors, all having non-negative entries. In the online setting, the constraints (i.e., the rows of the constraint matrix A) arrive over time, and the algorithm can only increase the coordinates of vector x to maintain feasibility. As an intermediate step, we consider solving the covering linear program (CLP) online, where the integrality requirement on x is dropped. Our main results are (a) an O(log k)-competitive online algorithm for solving the CLP, and (b) an O(log k log L)-competitive randomized online algorithm for solving the CIP. Here k<=n and L<=m respectively denote the maximum number of non-zero entries in any row and column of the constraint matrix A. By a result of Feige and Korman, this is the best possible for polynomial-time online algorithms, even in the special case of set cover.
Real space Dynamical Super Cell Approximation for interacting disordered systems
Moradian, Rostam
2004-01-01
Effective medium super-cell approximation method which is introduced for disordered systems is extended to a general case of interacting disordered systems. We found that the dynamical cluster approximation (DCA) and also the non local coherent potential approximation (NLCPA) are two simple case of this technique. Whole equations of this formalism derived by using the effective medium theory in real space.
Approximate Augmented Lagrangian Functions and Nonlinear Semidefinite Programs
X. X. HUANG; K. L. TEO; X. Q. YANG
2006-01-01
In this paper, an approximate augmented Lagrangian function for nonlinear semidefinite programs is introduced. Some basic properties of the approximate augmented Lagrange function such as monotonicity and convexity are discussed. Necessary and sufficient conditions for approximate strong duality results are derived. Conditions for an approximate exact penalty representation in the framework of augmented Lagrangian are given. Under certain conditions, it is shown that any limit point of a sequence of stationary points of approximate augmented Lagrangian problems is a KKT point of the original semidefinite program and that a sequence of optimal solutions to augmented Lagrangian problems converges to a solution of the original semidefinite program.
Multistage Stochastic Programming Problems; Stability and Approximation
Kaňková, Vlasta
Berlin: Springer, 2007 - (Waldmann, K.; Stocker, U.), s. 595-600 ISBN 978-3-540-69994-1. [Annual International Conference of the German Operations Research Society (GOR). Karlsruhe (DE), 06.09.2006-08.09.2006] R&D Projects: GA ČR GA402/04/1294; GA ČR GA402/05/0115; GA ČR(CZ) GA402/06/1417 Institutional research plan: CEZ:AV0Z10750506 Keywords : Multistage Sstochastic programming problems * individal probability constraints * autoregressive (generally) nonlinear sequence Subject RIV: BB - Applied Statistics, Operational Research
Optimal Piecewise-Linear Approximation of the Quadratic Chaotic Dynamics
J. Petrzela
2012-04-01
Full Text Available This paper shows the influence of piecewise-linear approximation on the global dynamics associated with autonomous third-order dynamical systems with the quadratic vector fields. The novel method for optimal nonlinear function approximation preserving the system behavior is proposed and experimentally verified. This approach is based on the calculation of the state attractor metric dimension inside a stochastic optimization routine. The approximated systems are compared to the original by means of the numerical integration. Real electronic circuits representing individual dynamical systems are derived using classical as well as integrator-based synthesis and verified by time-domain analysis in Orcad Pspice simulator. The universality of the proposed method is briefly discussed, especially from the viewpoint of the higher-order dynamical systems. Future topics and perspectives are also provided
A Linear-Programming Approximation of AC Power Flows
Coffrin, Carleton; Van Hentenryck, Pascal
2012-01-01
Linear active-power-only DC power flow approximations are pervasive in the planning and control of power systems. However, these approximations fail to capture reactive power and voltage magnitudes, both of which are necessary in many applications to ensure voltage stability and AC power flow feasibility. This paper proposes linear-programming models (the LPAC models) that incorporate reactive power and voltage magnitudes in a linear power flow approximation. The LPAC models are built on a co...
Approximate dynamic programming and aerial refueling
Panos, Dennis C.
2007-01-01
Aerial refueling is an integral part of the United States military's ability to strike targets around the world with an overwhelming and continuous projection of force. However, with an aging fleet of refueling tankers and an indefinite replacement schedule the optimization of tanker usage is vital to national security. Optimizing tanker and receiver refueling operations is a complicated endeavor as it can involve over a thousand of missions during a 24 hour period, as in Operation Iraqi Free...
Approximating the maximum weight clique using replicator dynamics.
Bomze, I R; Pelillo, M; Stix, V
2000-01-01
Given an undirected graph with weights on the vertices, the maximum weight clique problem (MWCP) is to find a subset of mutually adjacent vertices (i.e., a clique) having the largest total weight. This is a generalization of the classical problem of finding the maximum cardinality clique of an unweighted graph, which arises as a special case of the MWCP when all the weights associated to the vertices are equal. The problem is known to be NP-hard for arbitrary graphs and, according to recent theoretical results, so is the problem of approximating it within a constant factor. Although there has recently been much interest around neural-network algorithms for the unweighted maximum clique problem, no effort has been directed so far toward its weighted counterpart. In this paper, we present a parallel, distributed heuristic for approximating the MWCP based on dynamics principles developed and studied in various branches of mathematical biology. The proposed framework centers around a recently introduced continuous characterization of the MWCP which generalizes an earlier remarkable result by Motzkin and Straus. This allows us to formulate the MWCP (a purely combinatorial problem) in terms of a continuous quadratic programming problem. One drawback associated with this formulation, however, is the presence of "spurious" solutions, and we present characterizations of these solutions. To avoid them we introduce a new regularized continuous formulation of the MWCP inspired by previous works on the unweighted problem, and show how this approach completely solves the problem. The continuous formulation of the MWCP naturally maps onto a parallel, distributed computational network whose dynamical behavior is governed by the so-called replicator equations. These are dynamical systems introduced in evolutionary game theory and population genetics to model evolutionary processes on a macroscopic scale.We present theoretical results which guarantee that the solutions provided by
Approximate Separability for Weak Interaction in Dynamic Systems
Pfeffer, Avi
2012-01-01
One approach to monitoring a dynamic system relies on decomposition of the system into weakly interacting subsystems. An earlier paper introduced a notion of weak interaction called separability, and showed that it leads to exact propagation of marginals for prediction. This paper addresses two questions left open by the earlier paper: can we define a notion of approximate separability that occurs naturally in practice, and do separability and approximate separability lead to accurate monitor...
Some approximations in the linear dynamic equations of thin cylinders
El-Raheb, M.; Babcock, C. D., Jr.
1981-01-01
Theoretical analysis is performed on the linear dynamic equations of thin cylindrical shells to find the error committed by making the Donnell assumption and the neglect of in-plane inertia. At first, the effect of these approximations is studied on a shell with classical simply supported boundary condition. The same approximations are then investigated for other boundary conditions from a consistent approximate solution of the eigenvalue problem. The Donnell assumption is valid at frequencies high compared with the ring frequencies, for finite length thin shells. The error in the eigenfrequencies from omitting tangential inertia is appreciable for modes with large circumferential and axial wavelengths, independent of shell thickness and boundary conditions.
The most important constituents and capacities of the practice-oriented program package DYNAMIC are explained. The versatility of the package in dealing with problems of structural dynamics is shown by examples (seismic qualification of SF6 switchgear equipment, turbine building of a BWR). The examples explain applications in the fields of construction engineering and electromechanics. (orig./HP)
Approximate bayesian parameter inference for dynamical systems in systems biology
This paper proposes to use approximate instead of exact stochastic simulation algorithms for approximate Bayesian parameter inference of dynamical systems in systems biology. It first presents the mathematical framework for the description of systems biology models, especially from the aspect of a stochastic formulation as opposed to deterministic model formulations based on the law of mass action. In contrast to maximum likelihood methods for parameter inference, approximate inference method- share presented which are based on sampling parameters from a known prior probability distribution, which gradually evolves toward a posterior distribution, through the comparison of simulated data from the model to a given data set of measurements. The paper then discusses the simulation process, where an over- view is given of the different exact and approximate methods for stochastic simulation and their improvements that we propose. The exact and approximate simulators are implemented and used within approximate Bayesian parameter inference methods. Our evaluation of these methods on two tasks of parameter estimation in two different models shows that equally good results are obtained much faster when using approximate simulation as compared to using exact simulation. (Author)
Efficient Optimization of Dynamic Systems Using Pade Approximants
Jensen, Jakob Søndergaard
2006-01-01
A numerical procedure is suggested for efficient optimization of large dynamic systems. The method is based on Pad´e approximants that give a remarkably accurate approximation of the vibration response for large ranges of frequencies at low computational cost. Analytical expressions for the design...... sensitivities are derived by an adjoint method making the method well suited for large number of design variables. The method is illustrated by a topology optimization example for an elastic body subjected to a time-harmonic load. The distribution of two material phases is optimized in order to reduce the...
Dynamic programming using radial basis functions
Junge, Oliver; Schreiber, Alex
2014-01-01
We propose a discretization of the optimality principle in dynamic programming based on radial basis functions and Shepard's moving least squares approximation method. We prove convergence of the approximate optimal value function to the true one and present several numerical experiments.
Wave packet dynamics in the optimal superadiabatic approximation
Betz, Volker; Manthe, Uwe
2016-01-01
We explain the concept of superadiabatic approximations and show how in the context of the Born- Oppenheimer approximation they lead to an explicit formula that can be used to predict transitions at avoided crossings. Based on this formula, we present a simple method for computing wave packet dynamics across avoided crossings. Only knowledge of the adiabatic electronic energy levels near the avoided crossing is required for the computation. In particular, this means that no diabatization procedure is necessary, the adiabatic energy levels can be computed on the fly, and they only need to be computed to higher accuracy when an avoided crossing is detected. We test the quality of our method on the paradigmatic example of photo-dissociation of NaI, finding very good agreement with results of exact wave packet calculations.
Dynamical Mean Field Approximation Applied to Quantum Field Theory
Akerlund, Oscar; Georges, Antoine; Werner, Philipp
2013-01-01
We apply the Dynamical Mean Field (DMFT) approximation to the real, scalar phi^4 quantum field theory. By comparing to lattice Monte Carlo calculations, perturbation theory and standard mean field theory, we test the quality of the approximation in two, three, four and five dimensions. The quantities considered in these tests are the critical coupling for the transition to the ordered phase and the associated critical exponents nu and beta. We also map out the phase diagram in four dimensions. In two and three dimensions, DMFT incorrectly predicts a first order phase transition for all bare quartic couplings, which is problematic, because the second order nature of the phase transition of lattice phi^4-theory is crucial for taking the continuum limit. Nevertheless, by extrapolating the behaviour away from the phase transition, one can obtain critical couplings and critical exponents. They differ from those of mean field theory and are much closer to the correct values. In four dimensions the transition is sec...
Approximate dynamic fault tree calculations for modelling water supply risks
Traditional fault tree analysis is not always sufficient when analysing complex systems. To overcome the limitations dynamic fault tree (DFT) analysis is suggested in the literature as well as different approaches for how to solve DFTs. For added value in fault tree analysis, approximate DFT calculations based on a Markovian approach are presented and evaluated here. The approximate DFT calculations are performed using standard Monte Carlo simulations and do not require simulations of the full Markov models, which simplifies model building and in particular calculations. It is shown how to extend the calculations of the traditional OR- and AND-gates, so that information is available on the failure probability, the failure rate and the mean downtime at all levels in the fault tree. Two additional logic gates are presented that make it possible to model a system's ability to compensate for failures. This work was initiated to enable correct analyses of water supply risks. Drinking water systems are typically complex with an inherent ability to compensate for failures that is not easily modelled using traditional logic gates. The approximate DFT calculations are compared to results from simulations of the corresponding Markov models for three water supply examples. For the traditional OR- and AND-gates, and one gate modelling compensation, the errors in the results are small. For the other gate modelling compensation, the error increases with the number of compensating components. The errors are, however, in most cases acceptable with respect to uncertainties in input data. The approximate DFT calculations improve the capabilities of fault tree analysis of drinking water systems since they provide additional and important information and are simple and practically applicable.
Dynamic Programming Strikes Back
Moerkotte, Guido; Neumann, Thomas
2008-01-01
Two highly efficient algorithms are known for optimally ordering joins while avoiding cross products: DPccp, which is based on dynamic programming, and Top-Down Partition Search, based on memoization. Both have two severe limitations: They handle only (1) simple (binary) join predicates and (2) inner joins. However, real queries may contain complex join predicates, involving more than two relations, and outer joins as well as other non-inner joins. Taking the mos...
Approximations for inclusion of rotor lag dynamics in helicopter flight dynamics models
Mckillip, Robert, Jr.; Curtiss, Howard C., Jr.
1991-01-01
Approximate forms are suggested for augmenting linear rotor/body response models to include rotor lag dynamics. Use of an analytically linearized rotor/body model has shown that the primary effect comes from the additional angular rate contributions of the lag inertial response. Addition of lag dynamics may be made assuming these dynamics are represented by an isolated rotor with no shaft motion. Implications of such an approximation are indicated through comparison with flight test data and sensitivity of stability levels with body rate feedback.
Exact and approximate probabilistic symbolic execution for nondeterministic programs
Luckow, Kasper Søe; Păsăreanu, Corina S.; Dwyer, Matthew B.; Filieri, Antonio; Visser, Willem
Probabilistic software analysis seeks to quantify the likelihood of reaching a target event under uncertain environments. Recent approaches compute probabilities of execution paths using symbolic execution, but do not support nondeterminism. Nondeterminism arises naturally when no suitable...... probabilistic model can capture a program behavior, e.g., for multithreading or distributed systems. In this work, we propose a technique, based on symbolic execution, to synthesize schedulers that resolve nondeterminism to maximize the probability of reaching a target event. To scale to large systems, we also...... introduce approximate algorithms to search for good schedulers, speeding up established random sampling and reinforcement learning results through the quantification of path probabilities based on symbolic execution. We implemented the techniques in Symbolic PathFinder and evaluated them on nondeterministic...
Approximate labeling via graph cuts based on linear programming.
Komodakis, Nikos; Tziritas, Georgios
2007-08-01
A new framework is presented for both understanding and developing graph-cut-based combinatorial algorithms suitable for the approximate optimization of a very wide class of Markov Random Fields (MRFs) that are frequently encountered in computer vision. The proposed framework utilizes tools from the duality theory of linear programming in order to provide an alternative and more general view of state-of-the-art techniques like the \\alpha-expansion algorithm, which is included merely as a special case. Moreover, contrary to \\alpha-expansion, the derived algorithms generate solutions with guaranteed optimality properties for a much wider class of problems, for example, even for MRFs with nonmetric potentials. In addition, they are capable of providing per-instance suboptimality bounds in all occasions, including discrete MRFs with an arbitrary potential function. These bounds prove to be very tight in practice (that is, very close to 1), which means that the resulting solutions are almost optimal. Our algorithms' effectiveness is demonstrated by presenting experimental results on a variety of low-level vision tasks, such as stereo matching, image restoration, image completion, and optical flow estimation, as well as on synthetic problems. PMID:17568146
Envelope induced ionization dynamics beyond the dipole approximation
Simonsen, Aleksander Skjerlie; Førre, Morten; Lindroth, Eva; Selstø, Sølve
2015-01-01
When atoms and molecules are ionized by laser pulses of finite duration and increasingly high intensities, the validity of the much used dipole approximation, in which the spatial dependence and magnetic component of the external field are neglected, eventually breaks down. We report that when going beyond the dipole approximation for the description of atoms exposed to ultraviolet light, the spatial dependence of the pulse shape, the envelope, provides the dominant correction, while the spatial dependence of the carrier may safely be neglected in the general case. We present a first order beyond-dipole correction to the Hamiltonian which accounts exclusively for effects stemming from the carrier-envelope of the pulse. This much simpler form of the correction is further discussed in connection with various descriptions of the light-matter interaction. We demonstrate by ab initio calculations that this approximation, which we will refer to as the envelope approximation, reproduces the full interaction beyond t...
Approximate supernova remnant dynamics with cosmic ray production
Supernova explosions are the most violent and energetic events in the galaxy and have long been considered probable sources of cosmic rays. Recent shock acceleration models treating the cosmic rays (CR's) as test particles nb a prescribed supernova remnant (SNR) evolution, indeed indicate an approximate power law momentum distribution f sub source (p) approximation p(-a) for the particles ultimately injected into the interstellar medium (ISM). This spectrum extends almost to the momentum p = 1 million GeV/c, where the break in the observed spectrum occurs. The calculated power law index approximately less than 4.2 agrees with that inferred for the galactic CR sources. The absolute CR intensity can however not be well determined in such a test particle approximation
Dynamic Spatial Approximation Trees with clusters for secondary memory
Britos, Luís; Printista, Alicia Marcela; Reyes, Nora Susana
2010-01-01
Metric space searching is an emerging technique to address the problem of e cient similarity searching in many applications, including multimedia databases and other repositories handling complex objects. Although promising, the metric space approach is still immature in several aspects that are well established in traditional databases. In particular, most indexing schemes are not dynamic. From the few dynamic indexes, even fewer work well in secondary memory. That is, most of them need the ...
Taylor Series Approximation to Solve Neutrosophic Multiobjective Programming Problem
Ibrahim M. Hezam
2015-12-01
Full Text Available In this paper, Taylor series is used to solve neutrosophic multi-objective programming problem (NMOPP. In the proposed approach, the truth membership, Indeterminacy membership, falsity membership functions associated with each objective of multi-objective programming problems are transformed into a single objective linear programming problem by using a first order Taylor polynomial series. Finally, to illustrate the efficiency of the proposed method, a numerical experiment for supplier selection is given as an application of Taylor series method for solving neutrosophic multi-objective programming problem at end of this paper.
Dynamic Programming Foundations and Principles
Sniedovich, Moshe
2010-01-01
Focusing on the modeling and solution of deterministic multistage decision problems, this book looks at dynamic programming as a problem-solving optimization method. With over 400 useful references, this edition discusses the dynamic programming analysis of a problem, illustrates the rationale behind this analysis, and clarifies the theoretical grounds that justify the rationale. It also explains the meaning and role of the concept of state in dynamic programming, examines the purpose and function of the principle of optimality, and outlines solution strategies for problems defiant of conventi
Introduction to stochastic dynamic programming
Ross, Sheldon M; Lukacs, E
1983-01-01
Introduction to Stochastic Dynamic Programming presents the basic theory and examines the scope of applications of stochastic dynamic programming. The book begins with a chapter on various finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Subsequent chapters study infinite-stage models: discounting future returns, minimizing nonnegative costs, maximizing nonnegative returns, and maximizing the long-run average return. Each of these chapters first considers whether an optimal policy need exist-providing counterexamples where appropriate-and the
Strong semiclassical approximation of Wigner functions for the Hartree dynamics
Athanassoulis, Agissilaos
2011-01-01
We consider the Wigner equation corresponding to a nonlinear Schrödinger evolution of the Hartree type in the semiclassical limit h → 0. Under appropriate assumptions on the initial data and the interaction potential, we show that the Wigner function is close in L 2 to its weak limit, the solution of the corresponding Vlasov equation. The strong approximation allows the construction of semiclassical operator-valued observables, approximating their quantum counterparts in Hilbert-Schmidt topology. The proof makes use of a pointwise-positivity manipulation, which seems necessary in working with the L 2 norm and the precise form of the nonlinearity. We employ the Husimi function as a pivot between the classical probability density and the Wigner function, which - as it is well known - is not pointwise positive in general.
Approximate analysis of dynamic soil-structure interaction
Lanzi, Armando
2011-01-01
This study focuses on the approximate analysis of soil- structure interaction problems, specifically on the application of classical modal analysis for coupled horizontal-rocking vibrations of plane structures resting on a linear elastic soil. Although the classical modal approach provides a non-rigorous solution, it is particularly meaningful as it offers physical insight into the nature of soil-structure interaction effects. After validating the numerical algorithm by comparison with earlie...
Approximate Solutions of Interactive Dynamic Influence Diagrams Using Model Clustering
Zeng, Yifeng; Doshi, Prashant; Qiongyu, Cheng
2007-01-01
Interactive dynamic influence diagrams (I-DIDs) offer a transparent and semantically clear representation for the sequential decision-making problem over multiple time steps in the presence of other interacting agents. Solving I-DIDs exactly involves knowing the solutions of possible models of the...
Secure Dynamic Program Repartitioning
Hansen, Rene Rydhoff; Probst, Christian
2005-01-01
Secure program partitioning has been introduced as a language-based technique to allow the distribution of data and computation across mutualy untrusted hosts, while at the same time guaranteeing the protection of confidential data. Programs that have been annotated with security types are...
Approximate Bayesian Image Interpretation using Generative Probabilistic Graphics Programs
Mansinghka, Vikash K.; Kulkarni, Tejas D.; Perov, Yura N.; Tenenbaum, Joshua B.
2013-01-01
The idea of computer vision as the Bayesian inverse problem to computer graphics has a long history and an appealing elegance, but it has proved difficult to directly implement. Instead, most vision tasks are approached via complex bottom-up processing pipelines. Here we show that it is possible to write short, simple probabilistic graphics programs that define flexible generative models and to automatically invert them to interpret real-world images. Generative probabilistic graphics program...
Dynamic Textures Modelling with Temporal Mixing Coefficients Approximation
Havlíček, Michal
Praha : ČVUT, 2013, s. 41-48. ISBN 978-80-01-05379-9. [Doktorandské dny 2013 FJFI oboru Matematické inženýrství. Praha (CZ), 15.11.2013] Institutional support: RVO:67985556 Keywords : dynamic texture * texture synthesis Subject RIV: BD - Theory of Information http://kmwww.fjfi.cvut.cz/ddny/historie/13-sbornik.pdf
Lattice dynamics of rhenium trioxide from the quasiharmonic approximation
Wdowik, U.D.; Parlinski, K.; Chatterji, T.; Rols, S.; Schober, H.
2010-01-01
The quasiharmonic theory is applied to study the lattice dynamics and thermal properties of rhenium trioxide, a material exhibiting the negative thermal-expansion phenomenon. Phonons are calculated at several external pressures. The pressure dependence of the M, R, and zone-center phonon modes is analyzed. Relying on the Gruneisen formalism an influence of temperature on the M phonon mode is investigated. The calculated free energy of the system provides predictions for the temperature depend...
Evolutionary Algorithms and Dynamic Programming
Doerr, Benjamin; Eremeev, Anton; Neumann, Frank; Theile, Madeleine; Thyssen, Christian
2013-01-01
Recently, it has been proven that evolutionary algorithms produce good results for a wide range of combinatorial optimization problems. Some of the considered problems are tackled by evolutionary algorithms that use a representation which enables them to construct solutions in a dynamic programming fashion. We take a general approach and relate the construction of such algorithms to the development of algorithms using dynamic programming techniques. Thereby, we give general guidelines on how ...
Modelling Opinion Dynamics: Theoretical analysis and continuous approximation
Pinasco, Juan Pablo; Balenzuela, Pablo
2016-01-01
Frequently we revise our first opinions after talking over with other individuals because we get convinced. Argumentation is a verbal and social process aimed at convincing. It includes conversation and persuasion. In this case, the agreement is reached because the new arguments are incorporated. In this paper we deal with a simple model of opinion formation with such persuasion dynamics, and we find the exact analytical solutions for both, long and short range interactions. A novel theoretical approach has been used in order to solve the master equations of the model with non-local kernels. Simulation results demonstrate an excellent agreement with results obtained by the theoretical estimation.
On the point-source approximation of earthquake dynamics
Andrea Bizzarri
2014-06-01
Full Text Available The focus on the present study is on the point-source approximation of a seismic source. First, we compare the synthetic motions on the free surface resulting from different analytical evolutions of the seismic source (the Gabor signal (G, the Bouchon ramp (B, the Cotton and Campillo ramp (CC, the Yoffe function (Y and the Liu and Archuleta function (LA. Our numerical experiments indicate that the CC and the Y functions produce synthetics with larger oscillations and correspondingly they have a higher frequency content. Moreover, the CC and the Y functions tend to produce higher peaks in the ground velocity (roughly of a factor of two. We have also found that the falloff at high frequencies is quite different: it roughly follows ω−2 in the case of G and LA functions, it decays more faster than ω−2 for the B function, while it is slow than ω−1 for both the CC and the Y solutions. Then we perform a comparison of seismic waves resulting from 3-D extended ruptures (both supershear and subshear obeying to different governing laws against those from a single point-source having the same features. It is shown that the point-source models tend to overestimate the ground motions and that they completely miss the Mach fronts emerging from the supershear transition process. When we compare the extended fault solutions against a multiple point-sources model the agreement becomes more significant, although relevant discrepancies still persist. Our results confirm that, and more importantly quantify how, the point-source approximation is unable to adequately describe the radiation emitted during a real world earthquake, even in the most idealized case of planar fault with homogeneous properties and embedded in a homogeneous, perfectly elastic medium.
Wave packet dynamics in the optimal superadiabatic approximation
Betz, V.; Goddard, B. D.; Manthe, U.
2016-06-01
We explain the concept of superadiabatic representations and show how in the context of electronically non-adiabatic transitions they lead to an explicit formula that can be used to predict transitions at avoided crossings. Based on this formula, we present a simple method for computing wave packet dynamics across avoided crossings. Only knowledge of the adiabatic potential energy surfaces near the avoided crossing is required for the computation. In particular, this means that no diabatization procedure is necessary, the adiabatic electronic energies can be computed on the fly, and they only need to be computed to higher accuracy when an avoided crossing is detected. We test the quality of our method on the paradigmatic example of photo-dissociation of NaI, finding very good agreement with results of exact wave packet calculations.
Dynamic-local-field approximation for the quantum solids
Etters, R. D.; Danilowicz, R. L.
1974-01-01
A local-molecular-field description for the ground-state properties of the quantum solids is presented. The dynamical behavior of atoms contributing to the local field, which acts on an arbitrary pair of test particles, is incorporated by decoupling the pair correlations between these field atoms. The energy, pressure, compressibility, single-particle-distribution function, and the rms atomic deviations about the equilibrium lattice sites are calculated for H2, He-3, and He-4 over the volume range from 5 to 24.5 cu cm/mole. The results are in close agreement with existing Monte Carlo calculations wherever comparisons are possible. At very high pressure, the results agree with simplified descriptions which depend on negligible overlap of the system wave function between neighboring lattice sites.
Trojan dynamics well approximated by a new Hamiltonian normal form
Paez, Rocio Isabel
2015-01-01
We revisit a classical perturbative approach to the Hamiltonian related to the motions of Trojan bodies, in the framework of the Planar Circular Restricted Three-Body Problem (PCRTBP), by introducing a number of key new ideas in the formulation. In some sense, we adapt the approach of Garfinkel (1977) to the context of the normal form theory and its modern techniques. First, we make use of Delaunay variables for a physically accurate representation of the system. Therefore, we introduce a novel manipulation of the variables so as to respect the natural behavior of the model. We develop a normalization procedure over the fast angle which exploits the fact that singularities in this model are essentially related to the slow angle. Thus, we produce a new normal form, i.e. an integrable approximation to the Hamiltonian. We emphasize some practical examples of the applicability of our normalizing scheme, e.g. the estimation of the stable libration region. Finally, we compare the level curves produced by our normal...
Trojan dynamics well approximated by a new Hamiltonian normal form
Páez, Rocío Isabel; Locatelli, Ugo
2015-10-01
We revisit a classical perturbative approach to the Hamiltonian related to the motions of Trojan bodies, in the framework of the planar circular restricted three-body problem, by introducing a number of key new ideas in the formulation. In some sense, we adapt the approach of Garfinkel to the context of the normal form theory and its modern techniques. First, we make use of Delaunay variables for a physically accurate representation of the system. Therefore, we introduce a novel manipulation of the variables so as to respect the natural behaviour of the model. We develop a normalization procedure over the fast angle which exploits the fact that singularities in this model are essentially related to the slow angle. Thus, we produce a new normal form, i.e. an integrable approximation to the Hamiltonian. We emphasize some practical examples of the applicability of our normalizing scheme, e.g. the estimation of the stable libration region. Finally, we compare the level curves produced by our normal form with surfaces of section provided by the integration of the non-normalized Hamiltonian, with very good agreement. Further precision tests are also provided. In addition, we give a step-by-step description of the algorithm, allowing for extensions to more complicated models.
Stress stiffening and approximate equations in flexible multibody dynamics
Padilla, Carlos E.; Vonflotow, Andreas H.
1993-01-01
A useful model for open chains of flexible bodies undergoing large rigid body motions, but small elastic deformations, is one in which the equations of motion are linearized in the small elastic deformations and deformation rates. For slow rigid body motions, the correctly linearized, or consistent, set of equations can be compared to prematurely linearized, or inconsistent, equations and to 'oversimplified,' or ruthless, equations through the use of open loop dynamic simulations. It has been shown that the inconsistent model should never be used, while the ruthless model should be used whenever possible. The consistent and inconsistent models differ by stress stiffening terms. These are due to zeroth-order stresses effecting virtual work via nonlinear strain-displacement terms. In this paper we examine in detail the nature of these stress stiffening terms and conclude that they are significant only when the associated zeroth-order stresses approach 'buckling' stresses. Finally it is emphasized that when the stress stiffening terms are negligible the ruthlessly linearized equations should be used.
Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics
Montoya-Castillo, Andrés; Reichman, David R.
2016-05-01
We present a formalism that explicitly unifies the commonly used Nakajima-Zwanzig approach for reduced density matrix dynamics with the more versatile Mori theory in the context of nonequilibrium dynamics. Employing a Dyson-type expansion to circumvent the difficulty of projected dynamics, we obtain a self-consistent equation for the memory kernel which requires only knowledge of normally evolved auxiliary kernels. To illustrate the properties of the current approach, we focus on the spin-boson model and limit our attention to the use of a simple and inexpensive quasi-classical dynamics, given by the Ehrenfest method, for the calculation of the auxiliary kernels. For the first time, we provide a detailed analysis of the dependence of the properties of the memory kernels obtained via different projection operators, namely, the thermal (Redfield-type) and population based (NIBA-type) projection operators. We further elucidate the conditions that lead to short-lived memory kernels and the regions of parameter space to which this program is best suited. Via a thorough analysis of the different closures available for the auxiliary kernels and the convergence properties of the self-consistently extracted memory kernel, we identify the mechanisms whereby the current approach leads to a significant improvement over the direct usage of standard semi- and quasi-classical dynamics.
Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics.
Montoya-Castillo, Andrés; Reichman, David R
2016-05-14
We present a formalism that explicitly unifies the commonly used Nakajima-Zwanzig approach for reduced density matrix dynamics with the more versatile Mori theory in the context of nonequilibrium dynamics. Employing a Dyson-type expansion to circumvent the difficulty of projected dynamics, we obtain a self-consistent equation for the memory kernel which requires only knowledge of normally evolved auxiliary kernels. To illustrate the properties of the current approach, we focus on the spin-boson model and limit our attention to the use of a simple and inexpensive quasi-classical dynamics, given by the Ehrenfest method, for the calculation of the auxiliary kernels. For the first time, we provide a detailed analysis of the dependence of the properties of the memory kernels obtained via different projection operators, namely, the thermal (Redfield-type) and population based (NIBA-type) projection operators. We further elucidate the conditions that lead to short-lived memory kernels and the regions of parameter space to which this program is best suited. Via a thorough analysis of the different closures available for the auxiliary kernels and the convergence properties of the self-consistently extracted memory kernel, we identify the mechanisms whereby the current approach leads to a significant improvement over the direct usage of standard semi- and quasi-classical dynamics. PMID:27179468
Reinforcement learning control with approximation of time-dependent agent dynamics
Kirkpatrick, Kenton Conrad
Reinforcement Learning has received a lot of attention over the years for systems ranging from static game playing to dynamic system control. Using Reinforcement Learning for control of dynamical systems provides the benefit of learning a control policy without needing a model of the dynamics. This opens the possibility of controlling systems for which the dynamics are unknown, but Reinforcement Learning methods like Q-learning do not explicitly account for time. In dynamical systems, time-dependent characteristics can have a significant effect on the control of the system, so it is necessary to account for system time dynamics while not having to rely on a predetermined model for the system. In this dissertation, algorithms are investigated for expanding the Q-learning algorithm to account for the learning of sampling rates and dynamics approximations. For determining a proper sampling rate, it is desired to find the largest sample time that still allows the learning agent to control the system to goal achievement. An algorithm called Sampled-Data Q-learning is introduced for determining both this sample time and the control policy associated with that sampling rate. Results show that the algorithm is capable of achieving a desired sampling rate that allows for system control while not sampling "as fast as possible". Determining an approximation of an agent's dynamics can be beneficial for the control of hierarchical multiagent systems by allowing a high-level supervisor to use the dynamics approximations for task allocation decisions. To this end, algorithms are investigated for learning first- and second-order dynamics approximations. These algorithms are respectively called First-Order Dynamics Learning and Second-Order Dynamics Learning. The dynamics learning algorithms are evaluated on several examples that show their capability to learn accurate approximations of state dynamics. All of these algorithms are then evaluated on hierarchical multiagent systems
侯进军
2007-01-01
@@ 1 Seed Selection Genetic Programming In Genetic Programming, each tree in population shows an algebraic or surmounting expression, and each algebraic or surmounting expression shows an approximate analytic solution to differential equations.
Miura, H.; Schmit, L. A., Jr.
1976-01-01
The program documentation and user's guide for the ACCESS-1 computer program is presented. ACCESS-1 is a research oriented program which implements a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and general mathematical programming algorithms are applied in the design optimization procedure. Implementation of the computer program, preparation of input data and basic program structure are described, and three illustrative examples are given.
Approximate models of dynamic thermoviscoelasticity describing shape-memory-alloy phase transitions
Melnik, R. V. N.; Roberts, A. J.
1999-01-01
We consider problems of dynamic viscoelasticity taking into account the coupling of elastic and thermal fields. Efficient approximate models are developed and computational results on thermomechanical behaviour of shape-memory-alloy structures are presented.
A dynamic inequality generation scheme for polynomial programming
Ghaddar, B.; Vera Lizcano, J.C.; Anjos, M.F.
2016-01-01
Hierarchies of semidefinite programs have been used to approximate or even solve polynomial programs. This approach rapidly becomes computationally expensive and is often tractable only for problems of small size. In this paper, we propose a dynamic inequality generation scheme to generate valid pol
Dynamics of multilevel molecules and pulse propagation is studied near the two-photon resonance. We have found a strict solution of this problem beyond the rotating wave approximation. Our analytical solution is in close agreement with the strict numerical solution for the 4,4'-bis(dimethylamino) stilbene molecule. The compensation of the dynamical Stark shift is studied for fixed-in-space molecules. It is shown that the orientational disorder does not allow complete compensation of the dynamical Stark shift
Gate complexity using Dynamic Programming
Sridharan, Srinivas; Gu, Mile; James, Matthew R.
2008-01-01
The relationship between efficient quantum gate synthesis and control theory has been a topic of interest in the quantum control literature. Motivated by this work, we describe in the present article how the dynamic programming technique from optimal control may be used for the optimal synthesis of quantum circuits. We demonstrate simulation results on an example system on SU(2), to obtain plots related to the gate complexity and sample paths for different logic gates.
We develop two classes of quasi-classical dynamics that are shown to conserve the initial quantum ensemble when used in combination with the Feynman-Kleinert approximation of the density operator. These dynamics are used to improve the Feynman-Kleinert implementation of the classical Wigner approximation for the evaluation of quantum time correlation functions known as Feynman-Kleinert linearized path-integral. As shown, both classes of dynamics are able to recover the exact classical and high temperature limits of the quantum time correlation function, while a subset is able to recover the exact harmonic limit. A comparison of the approximate quantum time correlation functions obtained from both classes of dynamics is made with the exact results for the challenging model problems of the quartic and double-well potentials. It is found that these dynamics provide a great improvement over the classical Wigner approximation, in which purely classical dynamics are used. In a special case, our first method becomes identical to centroid molecular dynamics
Application of approximate entropy on dynamic characteristics of epileptic absence seizure
Yi Zhou; Ruimei Huang; Ziyi Chen; Xin Chang; Jialong Chen; Lingli Xie
2012-01-01
Electroencephalogram signals are time-varying complex electrophysiological signals. Existing studies show that approximate entropy, which is a nonlinear dynamics index, is not an ideal method for electroencephalogram analysis. Clinical electroencephalogram measurements usually contain electrical interference signals, creating additional challenges in terms of maintaining robustness of the analytic methods. There is an urgent need for a novel method of nonlinear dynamical analysis of the electroencephalogram that can characterize seizure-related changes in cerebral dynamics. The aim of this paper was to study the fluctuations of approximate entropy in preictal, ictal, and postictal electroencephalogram signals from a patient with absence seizures, and to improve the algorithm used to calculate the approximate entropy. The approximate entropy algorithm, especially our modified version, could accurately describe the dynamical changes of the brain during absence seizures. We could also demonstrate that the complexity of the brain was greater in the normal state than in the ictal state. The fluctuations of the approximate entropy before epileptic seizures observed in this study can form a goodbasis for further study on the prediction of seizures with nonlinear dynamics.
Tuncay Bayram
2012-04-01
Full Text Available Objective: In this study, we aimed to make a computer program that calculates approximate radiation dose received by embryo/fetus in nuclear medicine applications. Material and Methods: Radiation dose values per MBq-1 received by embryo/fetus in nuclear medicine applications were gathered from literature for various stages of pregnancy. These values were embedded in the computer code, which was written in Fortran 90 program language. Results: The computer program called nmfdose covers almost all radiopharmaceuticals used in nuclear medicine applications. Approximate radiation dose received by embryo/fetus can be calculated easily at a few steps using this computer program. Conclusion: Although there are some constraints on using the program for some special cases, nmfdose is useful and it provides practical solution for calculation of approximate dose to embryo/fetus in nuclear medicine applications. (MIRT 2012;21:19-22
Dynamical response of a disordered ferromagnetic chain: alloy transfer matrix approximation
The alloy transfer matrix approximation is used to study the uniform dynamic susceptibility of a disordered ferromagnetic chain. The approximation allows for a consistent treatment of diagonal and off- diagonal disorder. The results, in the limit of low concentrations, are in agreement with the exact single impurity ones. Intensities and lineshapes for infrared absorption are calculated for finite impurity concentrations and different values of the relative anisotropy parameter of a model alloy. (Author)
Dynamics of Rabi model under second-order Born—Oppenheimer approximation
We apply the second-order Born—Oppenheimer (BO) approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating wave approximation. By comparing with the numerical results, we find that our approach works well when the frequency of the two-level system is much smaller than that of the bosonic mode
λ-PDF AND GEGENBAUER POLYNOMIAL APPROXIMATION FOR DYNAMIC RESPONSE PROBLEMS OF RANDOM STRUCTURES
FANG Tong; LENG Xiaolei; MA Xiaoping; MENG Guang
2004-01-01
A bounded, mono-peak, and symmetrically distributed probability density function,called λ-PDF, together with the Gegenbauer polynomial approximation, is used in dynamic response problems of random structures. The λ-PDF can reasonably model a variety of random parameters in engineering random structures. The Gegenbauer polynomial approximation can be viewed as a new extension of the weighted residual method into the random space. Both of them can be easily used by scientists and engineers, and applied to a variety of response problems of random structures. The numerical example shows the effectiveness of the proposed method to study dynamic phenomena in random structures.
Improved Approximation of Interactive Dynamic Influence DiagramsUsing Discriminative Model Updates
Prashant, Doshi; Zeng, Yifeng
2009-01-01
the concept of a minimal model set, which facilitates qualitative comparisons between different approximation techniques. We then present a new approximation technique that minimizes the space of candidate models by discriminating between model updates. We empirically demonstrate that our approach improves......Interactive dynamic influence diagrams (I-DIDs) are graphical models for sequential decision making in uncertain settings shared by other agents. Algorithms for solving I-DIDs face the challenge of an exponentially growing space of candidate models ascribed to other agents, over time. We formalize...... significantly in performance on the previous clustering based approximation technique....
An Approximate Algorithm for a Class of Nonlinear Bilevel Integer Programming
LI Lei; TENG Chun-xian; TIAN Guang-yue
2002-01-01
The algorithm for a class of nonlinear bilevel integer programming is discussed in this paper. It is based on the theory and algorithm for nonlinear integer programming. The continuity methods for integer programming are studied in this paper. After simulated annealing algorithm is applied to the upper-level programming problem and the thought of filled function method for continuous global optimization is applied to the corresponding lower-level programming, an approximate algorithm is established. The satisfactory algorithm is elaborated in the following example.
Lu, Jianfeng
2016-01-01
In the spirit of the fewest switches surface hopping, the frozen Gaussian approximation with surface hopping (FGA-SH) method samples a path integral representation of the non-adiabatic dynamics in the semiclassical regime. An improved sampling scheme is developed in this work for FGA-SH based on birth and death branching processes. The algorithm is validated for the standard test examples of non-adiabatic dynamics.
Verschl, M
2005-01-01
An analytical approach to quantum mechanical wave packet dynamics of laser-driven particles is presented. The time-dependent Schroedinger equation is solved for an electron exposed to a linearly polarized plane wave of arbitrary shape. The calculation goes beyond the dipole approximation, such that magnetic field effects like wave packet shearing are included. Analytical expressions for the time-dependent widths of the wave packet and its orientation are established. These allow for a simple understanding of the wave packet dynamics.
Potential function methods for approximately solving linear programming problems theory and practice
Bienstock, Daniel
2002-01-01
Potential Function Methods For Approximately Solving Linear Programming Problems breaks new ground in linear programming theory. The book draws on the research developments in three broad areas: linear and integer programming, numerical analysis, and the computational architectures which enable speedy, high-level algorithm design. During the last ten years, a new body of research within the field of optimization research has emerged, which seeks to develop good approximation algorithms for classes of linear programming problems. This work both has roots in fundamental areas of mathematical programming and is also framed in the context of the modern theory of algorithms. The result of this work, in which Daniel Bienstock has been very much involved, has been a family of algorithms with solid theoretical foundations and with growing experimental success. This book will examine these algorithms, starting with some of the very earliest examples, and through the latest theoretical and computational developments.
Approximate-model Based Estimation Method for Dynamic Response of Forging Processes
LEI Jie; LU Xinjiang; LI Yibo; HUANG Minghui; ZOU Wei
2015-01-01
Many high-quality forging productions require the large-sized hydraulic press machine (HPM) to have a desirable dynamic response. Since the forging process is complex under the low velocity, its response is difficult to estimate. And this often causes the desirable low-velocity forging condition difficult to obtaln. So far little work has been found to estimate the dynamic response of the forging process under low velocity. In this paper, an approximate-model based estimation method is proposed to estimate the dynamic response of the forging process under low velocity. First, an approximate model is developed to represent the forging process of this complex HPM around the low-velocity working point. Under guaranteeing the modeling performance, the model may greatly ease the complexity of the subsequent estimation of the dynamic response because it has a good linear structure. On this basis, the dynamic response is estimated and the conditions for stability, vibration, and creep are derived according to the solution of the velocity. All these analytical results are further verified by both simulations and experiment. In the simulation verification for modeling, the original movement model and the derived approximate model always have the same dynamic responses with very small approximate error. The simulations and experiment finally demonstrate and test the effectiveness of the derived conditions for stability, vibration, and creep, and these conditions will benefit both the prediction of the dynamic response of the forging process and the design of the controller for the high-quality forging. The proposed method is an effective solution to achieve the desirable low-velocity forging condition.
The time-dependent variational principle of Balian and Veneroni was applied to the Φ4 theory. An appropriate parametrization for the variational objects allows the derivation of coupled dynamical equations from which yield approximations for the two-time correlation functions involving two, three or four field operators. (author) 7 refs
Neuro-dynamic programming for the efficient management of reservoir networks
de Rigo, Daniele; Rizzoli, Andrea Emilio; Soncini-Sessa, Rodolfo; Weber, Enrico; Zenesi, Pietro
2001-01-01
Significance This article introduced in 2001 one of the very first successful applications of advanced machine learning techniques to solve complex, multicriteria management problems in water resources dealing with networks of water reservoirs. It applied approximate dynamic programming (here, neuro-dynamic programming - whose approximation of stochastic dynamic programming relies on artificial neural networks) to the integrated water resources management. The methodology is general enoug...
Gravitational-wave dynamics and black-hole dynamics: second quasi-spherical approximation
Hayward, Sean A.
2001-01-01
Gravitational radiation with roughly spherical wavefronts, produced by roughly spherical black holes or other astrophysical objects, is described by an approximation scheme. The first quasi-spherical approximation, describing radiation propagation on a background, is generalized to include additional non-linear effects, due to the radiation itself. The gravitational radiation is locally defined and admits an energy tensor, satisfying all standard local energy conditions and entering the trunc...
Based on ballistic-diffusive approximation, a method is presented to model heat transfer in nanocomposites containing metal nanoparticles. This method provides analytical expression for the temperature dynamics of metallic nanoparticles embedded in a dielectric medium. In this study, nanoparticles are considered as spherical shells, so that Boltzmann equation is solved using ballistic-diffusive approximation to calculate the electron and lattice thermal dynamics in gold nanoparticles, while thermal exchange between the particles is taken into account. The model was used to investigate the influence of particle size and metal concentration of the medium on the electron and lattice thermal dynamics. It is shown that these two parameters are crucial in determining the nanocomposite thermal behavior. Our results showed that the heat transfer rate from nanoparticles to the matrix decreases as the nanoparticle size increases. On the other hand, increasing the metal concentration of the medium can also decrease the heat transfer rate
BUILDING MATHEMATICAL MODELS IN DYNAMIC PROGRAMMING
LIANA RODICA PATER
2012-05-01
Full Text Available In short, we can say that dynamic programming is a method of optimization of systems, using their mathematical representation in phases or sequences or as we say, periods. Such systems are common in economic studies at the implementation of programs on the most advanced techniques, such as for example that involving cosmic navigation. Another concept that is involved in the study of dynamic programs is the economic horizon (number of periods or phases that a dynamic program needs. This concept often leads to the examination of the convergence of certain variables on infinite horizon. In many cases from the real economy by introducing updating, dynamic programs can be made convergent.
Gravitational-wave dynamics and black-hole dynamics second quasi-spherical approximation
Hayward, S A
2001-01-01
Gravitational radiation with roughly spherical wavefronts, produced by roughly spherical black holes or other astrophysical objects, is described by an approximation scheme. The first quasi-spherical approximation, describing radiation propagation on a background, is generalized to include additional non-linear effects, due to the radiation itself. The gravitational radiation is locally defined and admits an energy tensor, satisfying all standard local energy conditions and entering the truncated Einstein equations as an effective energy tensor. This second quasi-spherical approximation thereby includes gravitational radiation reaction, such as the back-reaction on the black hole. With respect to a canonical flow of time, the combined energy-momentum of the matter and gravitational radiation is covariantly conserved. The corresponding Noether charge is a local gravitational mass-energy. Energy conservation is formulated as a local first law relating the gradient of the gravitational mass to work and energy-su...
Dynamic Programming Applications in Water Resources
Yakowitz, Sidney
1982-08-01
The central intention of this survey is to review dynamic programming models for water resource problems and to examine computational techniques which have been used to obtain solutions to these problems. Problem areas surveyed here include aqueduct design, irrigation system control, project development, water quality maintenance, and reservoir operations analysis. Computational considerations impose severe limitation on the scale of dynamic programming problems which can be solved. Inventive numerical techniques for implementing dynamic programming have been applied to water resource problems. Discrete dynamic programming, differential dynamic programming, state incremental dynamic programming, and Howard's policy iteration method are among the techniques reviewed. Attempts have been made to delineate the successful applications, and speculative ideas are offered toward attacking problems which have not been solved satisfactorily.
Dynamics of Zonal Flows: Failure of Wave-Kinetic Theory, and New Geometrical Optics Approximations
Parker, Jeffrey B
2016-01-01
The self-organization of turbulence into regular zonal flows can be fruitfully investigated with quasilinear methods and statistical descriptions. A wave kinetic equation that assumes asymptotically large-scale zonal flows is pathological. From an exact description of quasilinear dynamics emerges two better geometrical optics approximations. These involve not only the mean flow shear but also the second and third derivative of the mean flow. One approximation takes the form of a new wave kinetic equation, but is only valid when the zonal flow is quasi-static and wave action is conserved.
Approximate Bisimulation and Optimization of Software Programs Based on Symbolic-Numeric Computation
Hui Deng
2013-01-01
Full Text Available To achieve behavior and structure optimization for a type of software program whose data exchange processes are represented by nonlinear polynomial systems, this paper establishes a novel formal description called a nonlinear polynomial transition system to represent the behavior and structure of the software program. Then, the notion of bisimulation for software programs is proposed based on the equivalence relation of corresponding nonlinear polynomial systems in their nonlinear polynomial transition systems. However, the exact equivalence is too strict in application. To enhance the flexibility of the relation among the different software systems, the notion of approximate bisimulation within a controllable error range and the calculation algorithm of approximate bisimulation based on symbolic-numeric computation are given. In this calculation, an approximate relation is represented as a MAX function that is resolved with the full filled method. At the same time, the actual error is calculable. An example on a multithreading program indicates that the approximate bisimulation relation is feasible and effective in behavior and structure optimization.
Rossi, Mariana; Paesani, Francesco; Bowman, Joel; Ceriotti, Michele
2014-01-01
Including quantum mechanical effects on the dynamics of nuclei in the condensed phase is challenging, because the complexity of exact methods grows exponentially with the number of quantum degrees of freedom. Efforts to circumvent these limitations can be traced down to two approaches: methods that treat a small subset of the degrees of freedom with rigorous quantum mechanics, considering the rest of the system as a static or classical environment, and methods that treat the whole system quantum mechanically, but using approximate dynamics. Here we perform a systematic comparison between these two philosophies for the description of quantum effects in vibrational spectroscopy, taking the Embedded Local Monomer (LMon) model and a mixed quantum-classical (MQC) model as representatives of the first family of methods, and centroid molecular dynamics (CMD) and thermostatted ring polymer molecular dynamics (TRPMD) as examples of the latter. We use as benchmarks D$_2$O doped with HOD and pure H$_2$O at three distinc...
Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques
Breuer, Heinz-Peter; Burgarth, Daniel; Petruccione, Francesco
2004-01-01
The reduced dynamics of a central spin coupled to a bath of N spin-1/2 particles arranged in a spin star configuration is investigated. The exact time evolution of the reduced density operator is derived, and an analytical solution is obtained in the limit of an infinite number of bath spins, where the model shows complete relaxation and partial decoherence. It is demonstrated that the dynamics of the central spin cannot be treated within the Born-Markov approximation. The Nakajima-Zwanzig an...
Approximate but Accurate Quantum Dynamics from the Mori Formalism: I. Nonequilibrium Dynamics
Montoya-Castillo, Andrés
2016-01-01
We present a formalism that explicitly unifies the commonly used Nakajima-Zwanzig approach for reduced density matrix dynamics with the more versatile Mori theory in the context of nonequilibrium dynamics. Employing a Dyson-type expansion to circumvent the difficulty of projected dynamics, we obtain a self-consistent equation for the memory kernel which requires only knowledge of normally evolved auxiliary kernels. To illustrate the properties of the current approach, we focus on the spin-boson model and limit our attention to the use of a simple and inexpensive quasi-classical dynamics, given by the Ehrenfest method, for the calculation of the auxiliary kernels. For the first time, we provide a detailed analysis of the dependence of the properties of the memory kernels obtained via different projection operators, namely the thermal (Redfield-type) and population based (NIBA-type) projection operators. We further elucidate the conditions that lead to short-lived memory kernels and the regions of parameter spa...
Classical dynamics of a charged particle in a laser field beyond the dipole approximation
Jameson, Paul; Khvedelidze, Arsen
2008-01-01
The classical dynamics of a charged particle traveling in a laser field modeled by an elliptically polarized monochromatic electromagnetic plane wave is discussed within the time reparametrization invariant form of the non-relativistic Hamilton-Jacobi theory. The exact parametric representation for a particle's orbit in an arbitrary plane wave background beyond the dipole approximation and including effect of the magnetic field is derived. For an elliptically polarized monochromatic plane wav...
A dynamic subgrid-scale modeling framework for large eddy simulation using approximate deconvolution
Maulik, Romit
2016-01-01
We put forth a dynamic modeling framework for sub-grid parametrization of large eddy simulation of turbulent flows based upon the use of the approximate deconvolution procedure to compute the Smagorinsky constant self-adaptively from the resolved flow quantities. Our numerical assessments for solving the Burgers turbulence problem shows that the proposed approach could be used as a viable tool to address the turbulence closure problem due to its flexibility.
Dynamic Slicing of Object-Oriented Programs
无
2001-01-01
Program slice has many applications such as program debugging,testing, maintena n ce, and complexity measurement. A static slice consists of all statements in pro gram P that may effect the value of variable v at some point p, and a dynamic s lice consists only of statements that influence the value of variable occurrence for specific program inputs. In this paper, we concern the problem of dynamic s licing of object-oriented programs which, to our knowledge, has not been addres s ed in the literatures. To solve this problem, we present the dynamic object-ori e nted dependence graph (DODG)which is an arc-classified digraph to explicitly re p resent various dynamic dependence between statement instances for a particular e xecution of an object-oriented program. Based on the DODG, we present a two-ph as e backward algorithm for computing a dynamic slice of an object-oriented program.
Boundary detection via dynamic programming
Udupa, Jayaram K.; Samarasekera, Supun; Barrett, William A.
1992-09-01
This paper reports a new method for detecting optimal boundaries in multidimensional scene data via dynamic programming (DP). In its current form the algorithm detects 2-D contours on slices and differs from other reported DP-based algorithms in an essential way in that it allows freedom in 2-D for finding optimal contour paths (as opposed to a single degree of freedom in the published methods). The method is being successfully used in segmenting object boundaries in a variety of medical applications including orbital volume from CT images (for craniofacial surgical planning), segmenting bone in MR images for kinematic analysis of the joints of the foot, segmenting the surface of the brain from the inner surface of the cranial vault, segmenting pituitary gland tumor for following the effect of a drug on the tumor, segmenting the boundaries of the heart in MR images, and segmenting the olfactory bulb for verifying hypotheses related to the size of this bulb in certain disease states.
Genomic Signal Search by Dynamic Programming
ZHENG Wei-Mou
2003-01-01
A general and flexible multi-motif model is proposed based on dynamic programming. By extending theGibbs sampler to the dynamic programming and introducing temperature, an efficient algorithm is developed. Branchpoint signalsequences and translation initiation sequences extracted from the rice genome are then examined.
Weak Dynamic Programming Principle for Viscosity Solutions
Bouchard, Bruno; Touzi, Nizar
2011-01-01
We prove a weak version of the dynamic programming principle for standard stochastic control problems and mixed control-stopping problems, which avoids the technical difficulties related to the measurable selection argument. In the Markov case, our result is tailor-maid for the derivation of the dynamic programming equation in the sense of viscosity solutions.
A Discrete Meta-Control Procedure for Approximating Solutions to Binary Programs
Zelda B. Zabinsky
2013-09-01
Full Text Available Large-scale binary integer programs occur frequently in many real-world applications. For some binary integer problems, finding an optimal solution or even a feasible solution is computationally expensive. In this paper, we develop a discrete meta-control procedure to approximately solve large-scale binary integer programs efficiently. The key idea is to map the vector of n binary decision variables into a scalar function defined over a time interval [0; n] and construct a linear quadratic tracking (LQT problem that can be solved efficiently. We prove that an LQT formulation has an optimal binary solution, analogous to a classical bang-bang control in continuous time. Our LQT approach can provide advantages in reducing computation while generating a good approximate solution. Numerical examples are presented to demonstrate the usefulness of the proposed method.
A Significance-Driven Programming Framework for Energy-Constrained Approximate Computing
Vassiliadis, Vassilis; Chalios, Charalambos; Parasyris, Konstantinos; Antonopoulos, Christos D.; Lalis, Spyros; Bellas, Nikolaos; Vandierendonck, Hans; Nikolopoulos, Dimitrios
2015-01-01
Approximate execution is a viable technique for energy-con\\-strained environments, provided that applications have the mechanisms to produce outputs of the highest possible quality within the given energy budget. We introduce a framework for energy-constrained execution with controlled and graceful quality loss. A simple programming model allows users to express the relative importance of computations for the quality of the end result, as well as minimum quality requirements. The significance...
Implicit Time Integration for Multiscale Molecular Dynamics Using Transcendental Padé Approximants.
Abi Mansour, Andrew; Ortoleva, Peter J
2016-04-12
Molecular dynamics systems evolve through the interplay of collective and localized disturbances. As a practical consequence, there is a restriction on the time step imposed by the broad spectrum of time scales involved. To resolve this restriction, multiscale factorization was introduced for molecular dynamics as a method that exploits the separation of time scales by coevolving the coarse-grained and atom-resolved states via Trotter factorization. Developing a stable time-marching scheme for this coevolution, however, is challenging because the coarse-grained dynamical equations depend on the microstate; therefore, these equations cannot be expressed in closed form. The objective of this paper is to develop an implicit time integration scheme for multiscale simulation of large systems over long periods of time and with high accuracy. The scheme uses Padé approximants to account for both the stochastic and deterministic features of the coarse-grained dynamics. The method is demonstrated for a protein either undergoing a conformational change or migrating under the influence of an external force. The method shows promise in accelerating multiscale molecular dynamics without a loss of atomic precision or the need to conjecture the form of coarse-grained governing equations. PMID:26845510
Pusok, Adina E.; Kaus, Boris J. P.; Popov, Anton A.
2016-04-01
Most of the major mountain belts and orogenic plateaus are found within the overlying plate of active or fossil subduction and/or collision zones. Moreover, they evolve differently from one another as the result of specific combinations of surface and mantle processes. These differences arise for several reasons, such as different rheological properties, different amounts of regional isostatic compensation, and different mechanisms by which forces are applied to the convergent plates. Previous 3D geodynamic models of subduction/collision processes have used various rheological approximations, making numerical results difficult to compare, since there is no clear image on the extent of these approximations on the dynamics. Here, we employ the code LaMEM to perform high-resolution long-term 3D simulations of subduction/continental collision in an integrated lithospheric and upper-mantle scale model. We test the effect of rheological approximations on mantle and lithosphere dynamics in a geometrically simplified model setup that resembles a tectonic map of the India-Asia collision zone. We use the "sticky-air" approach to allow for the development of topography and the dynamics of subduction and collision is entirely driven by slab-pull (i.e. "free subduction"). The models exhibit a wide range of behaviours depending on the rheological law employed: from linear to temperature-dependent visco-elasto-plastic rheology that takes into account both diffusion and dislocation creep. For example, we find that slab dynamics varies drastically between end member models: in viscous approximations, slab detachment is slow following a viscous thinning, while for a non-linear visco-elasto-plastic rheology, slab detachment is relatively fast, inducing strong mantle flow in the slab window. We also examine the stress states in the subducting and overriding plates and topography evolution in the upper plate, and we discuss the implications on lithosphere dynamics at convergent margins
Program Structure Combines Segmentation and Dynamic Storage
Tiffany, S. H.
1982-01-01
Programing techniques incorporate advantages of overlaying into segmented loads while retaining all dynamic load advantages of segmentation, employing those capabilities that best suit mode of operation, whether batch or interactive. User is allowed to load a program automatically in a variable manner, based solely on a single data input to the program, to maintain minimal field lengths for interactive use.
Konopelchenko, B G
2012-01-01
Quasiclassical approximation in the intrinsic description of the vortex filament dynamics is discussed. Within this approximation the governing equations are given by elliptic system of quasi-linear PDEs of the first order. Dispersionless Da Rios system and dispersionless Hirota equation are among them. They describe motion of vortex filament with slow varying curvature and torsion without or with axial flow. Gradient catastrophe for governing equations is studied. It is shown that geometrically this catastrophe manifests as a fast oscillation of a filament curve around the rectifying plane which resembles the flutter of airfoils. Analytically it is the elliptic umbilic singularity in the terminology of the catastrophe theory. It is demonstrated that its double scaling regularization is governed by the Painleve' I equation.
Approximating Model Equivalence in Interactive Dynamic Influence Diagrams Using Top K Policy Paths
Zeng, Y.; Chen, Y.; Doshi, Prashant
2011-01-01
approaches mainly cluster behaviorally equivalent models to reduce the complexity of I-DID solutions. In this paper, we seek to further reduce the model space by introducing an approximate measure of behavioral equivalence (BE) and using it to group models. Specifically, we focus on $K$ most probable paths......Interactive dynamic influence diagrams (I-DIDs) are graphical models for sequential decision making in uncertain settings shared by other agents. Algorithms for solving I-DIDs face the challenge of an exponentially growing space of behavioral models ascribed to other agents over time. Previous...... in the solution of each model and compare these policy paths to determine approximate BE. We discuss the challenges in computing the top $K$ policy paths and experimentally evaluate the performance of this heuristic approach in terms of the scalability and quality of the solution....
Cosmological dynamics: from the Eulerian to the Lagrangian frame. Part I. Newtonian approximation
We analyse the non-linear gravitational dynamics of a pressure-less fluid in the Newtonian limit of General Relativity in both the Eulerian and Lagrangian pictures. Starting from the Newtonian metric in the Poisson gauge, we transform to the synchronous and comoving gauge and obtain the Lagrangian metric within the Newtonian approximation. Our approach is fully non-perturbative, which implies that if our quantities are expanded according to the rules of standard perturbation theory, all terms are exactly recovered at any order in perturbation theory, only provided they are Newtonian. We explicitly show this result up to second order and in both gauges. Our transformation clarifies the meaning of the change of spatial and time coordinates from the Eulerian to the Lagrangian frame in the Newtonian approximation
Coherent Dynamics in Dressed Optical Lattices Beyond the Born-Oppenheimer Approximation
Reeves, Jeremy; Krinner, Ludwig; Stewart, Mike; Pazmino, Arturo; Schneble, Dominik
2015-05-01
Usual treatments of matter-wave diffraction assume that the zero-point energy in the diffracting potential is much smaller than the gap between the dressed levels. However, in near-resonant weak-driving scenarios, zero-point motion can mix the adiabatic dressed states, making the diffracting potentials highly non-adiabatic, such that the usual Born-Oppenheimer approximation for the external and internal degrees of freedom no longer applies. We model the dynamics of a matter wave in a microwave-coupled state-dependent lattice in this regime, and quantify the importance of these effects on recent experiments. Supported by NSF grant PHY-1205894.
Dynamics of Jaynes-Cummings Model in the Absence of Rotating-Wave Approximation
FAN Yun-Xia; LIU Tao; FENG Mang; WANG Ke-Lin
2007-01-01
The Jaynes-Cummings model (JCM) is studied in the absence of the rotating-wave approximation (RWA)by a coherent-state expansion technique. In comparison with the previous paper in which the coherent-state expansion was performed only to the third order, we carry out in this paper a complete expansion to demonstrate exactly the dynamics of the JCM without the RWA. Our study gives a systematic method to solve the non-RWA problem, which would be useful in various physical systems, e.g., in a system with an ultracold trapped ion experiencing the running waves of lasers.
Dynamics of Jaynes-Cummings Model in the Absence of Rotating-Wave Approximation
The Jaynes-Cummings model (JCM) is studied in the absence of the rotating-wave approximation (RWA) by a coherent-state expansion technique. In comparison with the previous paper in which the coherent-state expansion was performed only to the third order, we carry out in this paper a complete expansion to demonstrate exactly the dynamics of the JCM without the RWA. Our study gives a systematic method to solve the non-RWA problem, which would be useful in various physical systems, e.g., in a system with an ultracold trapped ion experiencing the running waves of lasers.
Dynamics of Jaynes-Cummings Model in the Absence of Rotating-Wave Approximation
Fan, Yun-Xia; Liu, Tao; Feng, Mang; Wang, Ke-Lin
2007-05-01
The Jaynes-Cummings model (JCM) is studied in the absence of the rotating-wave approximation (RWA) by a coherent-state expansion technique. In comparison with the previous paper in which the coherent-state expansion was performed only to the third order, we carry out in this paper a complete expansion to demonstrate exactly the dynamics of the JCM without the RWA. Our study gives a systematic method to solve the non-RWA problem, which would be useful in various physical systems, e.g., in a system with an ultracold trapped ion experiencing the running waves of lasers.
Approximating a Giving Up Smoking Dynamic on Adolescent Nicotine Dependence in Fractional Order
2016-01-01
In this work, we consider giving up smoking dynamic on adolescent nicotine dependence. First, we use the Caputo derivative to develop the model in fractional order. Then we apply two different numerical methods to compute accurate approximate solutions of this new model in fractional order and compare their results. In order to do this, we consider the generalized Euler method (GEM) and multi-step generalized differential transform method (MSGDTM). We also show the unique positive solution for this model and present numerical results graphically. PMID:27105426
Jiang, Bin; Song, Hongwei; Yang, Minghui; Guo, Hua
2016-04-01
The quantum dynamics of water dissociative chemisorption on the rigid Ni(111) surface is investigated using a recently developed nine-dimensional potential energy surface. The quantum dynamical model includes explicitly seven degrees of freedom of D2O at fixed surface sites, and the final results were obtained with a site-averaging model. The mode specificity in the site-specific results is reported and analyzed. Finally, the approximate sticking probabilities for various vibrationally excited states of D2O are obtained considering surface lattice effects and formally all nine degrees of freedom. The comparison with experiment reveals the inaccuracy of the density functional theory and suggests the need to improve the potential energy surface.
Approximation-Exact Penalty Function Method for Solving a Class of Stochastic Programming
WangGuang-min; WanZhong-ping
2003-01-01
We present an approximation-exact penalty function method for solving the single stage stochastic programming problem with continuous random variable. The original problem is transformed into a determinate nonlinear programming problem with a discrete random variable sequence, which is obtained by some discrete method. We construct an exact penalty function and obtain an unconstrained optimization. It avoids the difficulty in solution by the rapid growing of the number of constraints for discrete precision.Under lenient conditions, we prove the equivalence of the minimum solution of penalty function and the solution of the determinate programming, and prove that the solution sequences of the discrete problem converge to a solution to the original problem.
Stability and dynamical properties of Rosenau-Hyman compactons using Padé approximants.
Mihaila, Bogdan; Cardenas, Andres; Cooper, Fred; Saxena, Avadh
2010-05-01
We present a systematic approach for calculating higher-order derivatives of smooth functions on a uniform grid using Padé approximants. We illustrate our findings by deriving higher-order approximations using traditional second-order finite-difference formulas as our starting point. We employ these schemes to study the stability and dynamical properties of K(2,2) Rosenau-Hyman compactons including the collision of two compactons and resultant shock formation. Our approach uses a differencing scheme involving only nearest and next-to-nearest neighbors on a uniform spatial grid. The partial differential equation for the compactons involves first, second, and third partial derivatives in the spatial coordinate and we concentrate on four different fourth-order methods which differ in the possibility of increasing the degree of accuracy (or not) of one of the spatial derivatives to sixth order. A method designed to reduce round-off errors was found to be the most accurate approximation in stability studies of single solitary waves even though all derivates are accurate only to fourth order. Simulating compacton scattering requires the addition of fourth derivatives related to artificial viscosity. For those problems the different choices lead to different amounts of "spurious" radiation and we compare the virtues of the different choices. PMID:20866355
DYNAMICAL SPIN SUSCEPTIBILITY IN THE TD-LDA AND QSGW APPROXIMATIONS
SCHILFGAARDE, MARK VAN; KOTANI, TAKAO
2012-10-15
Abstract. This project was aimed at building the transverse dynamical spin susceptibility with the TD-LDA and the recently-developed Quasparticle Self-Consisent Approximations, which determines an optimum quasiparticle picture in a self-consistent manner within the GW approximation. Our main results were published into two papers, (J. Phys. Cond. Matt. 20, 95214 (2008), and Phys. Rev. B83, 060404(R) (2011). In the first paper we present spin wave dispersions for MnO, NiO, and -MnAs based on quasiparticle self-consistent GW approximation (QSGW). For MnO and NiO, QSGW results are in rather good agreement with experiments, in contrast to the LDA and LDA+U descriptions. For -MnAs, we find a collinear ferromagnetic ground state in QSGW, while this phase is unstable in the LDA. In the second, we apply TD-LDA to the CaFeAs2 the first attempt the first ab initio calculation of dynamical susceptibililty in a system with complex electronic structure Magnetic excitations in the striped phase of CaFe2As2 are studied as a function of local moment amplitude. We find a new kind of excitation: sharp resonances of Stoner-like (itinerant) excitations at energies comparable to the ´eel temperature, originating largely from a narrow band of Fe d states near the Fermi level, and coexisting with more conventional (localized) spin waves. Both kinds of excitations can show multiple branches, highlighting the inadequacy of a description based on a localized spin model.
Integrating Pareto Optimization into Dynamic Programming
Thomas Gatter; Robert Giegerich; Cédric Saule
2016-01-01
Pareto optimization combines independent objectives by computing the Pareto front of the search space, yielding a set of optima where none scores better on all objectives than any other. Recently, it was shown that Pareto optimization seamlessly integrates with algebraic dynamic programming: when scoring schemes A and B can correctly evaluate the search space via dynamic programming, then so can Pareto optimization with respect to A and B. However, the integration of Pareto optimization into ...
Adaptive dynamic programming for linear impulse systems
Xiao-hua WANG; Juan-juan YU; Yao HUANG; Hua WANG; Zhong-hua MIAO
2014-01-01
We investigate the optimization of linear impulse systems with the reinforcement learning based adaptive dynamic programming (ADP) method. For linear impulse systems, the optimal objective function is shown to be a quadric form of the pre-impulse states. The ADP method provides solutions that iteratively converge to the optimal objective function. If an initial guess of the pre-impulse objective function is selected as a quadratic form of the pre-impulse states, the objective function iteratively converges to the optimal one through ADP. Though direct use of the quadratic objective function of the states within the ADP method is theoretically possible, the numerical singularity problem may occur due to the matrix inversion therein when the system dimensionality increases. A neural network based ADP method can circumvent this problem. A neural network with polynomial activation functions is selected to approximate the pre-impulse objective function and trained iteratively using the ADP method to achieve optimal control. After a successful training, optimal impulse control can be derived. Simulations are presented for illustrative purposes.
Integrating Pareto Optimization into Dynamic Programming
Thomas Gatter
2016-01-01
Full Text Available Pareto optimization combines independent objectives by computing the Pareto front of the search space, yielding a set of optima where none scores better on all objectives than any other. Recently, it was shown that Pareto optimization seamlessly integrates with algebraic dynamic programming: when scoring schemes A and B can correctly evaluate the search space via dynamic programming, then so can Pareto optimization with respect to A and B. However, the integration of Pareto optimization into dynamic programming opens a wide range of algorithmic alternatives, which we study in substantial detail in this article, using real-world applications in biosequence analysis, a field where dynamic programming is ubiquitous. Our results are two-fold: (1 We introduce the operation of a “Pareto algebra product” in the dynamic programming framework of Bellman’s GAP. Users of this framework can now ask for Pareto optimization with a single keystroke. Careful evaluation of the implementation alternatives by means of an extended Bellman’s GAP compiler demonstrates the dependence of the best implementation choice on the application at hand. (2 We extract from our experiments several pieces of advice to programmers who do not use a system such as Bellman’s GAP, but who choose to hand-craft their dynamic programming recurrences, incorporating Pareto optimization from scratch.
Recent extensive studies of Escherichia coli (E. coli) chemotaxis have achieved a deep understanding of its microscopic control dynamics. As a result, various quantitatively predictive models have been developed to describe the chemotactic behavior of E. coli motion. However, a population-level partial differential equation (PDE) that rationally incorporates such microscopic dynamics is still insufficient. Apart from the traditional Keller–Segel (K–S) equation, many existing population-level models developed from the microscopic dynamics are integro-PDEs. The difficulty comes mainly from cell tumbles which yield a velocity jumping process. Here, we propose a Langevin approximation method that avoids such a difficulty without appreciable loss of precision. The resulting model not only quantitatively reproduces the results of pathway-based single-cell simulators, but also provides new inside information on the mechanism of E. coli chemotaxis. Our study demonstrates a possible alternative in establishing a simple population-level model that allows for the complex microscopic mechanisms in bacterial chemotaxis
Guidelines for dynamic international programs
Matters of global concern-deforestation, global warming, biodiversity loss, sustainable development, fuelwood crises, watershed destruction, and large-scale flooding-frequently involve forests and natural resources. In the future, university students will enter a global setting that more than ever depends on a strong knowledge of international issues. USA land-grant universities are attempting to prepare students for this challenge by improving their international programs including forestry. To improve university programs, several factors will need to be addressed and are discussed, with examples, in this article: commitment of the faculty; program specialization; geographic specialization; reward systems for international contributions; international collaboration; recycled dollars within the university; active teaching programs; research; extention and outreach; language training; international faculty; travel grants; twinning relationships with sister institutions; selective in pursuit of international development assistance; and study centers. 6 refs
Synthesis of Large Dynamic Concurrent Programs from Dynamic Specifications
Attie, Paul C.
2008-01-01
We present a tractable method for synthesizing arbitrarily large concurrent programs, for a shared memory model with common hardware-available primitives such as atomic registers, compare-and-swap, load-linked/store conditional, etc. The programs we synthesize are dynamic: new processes can be created and added at run-time, and so our programs are not finite-state, in general. Nevertheless, we successfully exploit automatic synthesis and model-checking methods based on propositional temporal ...
How to approximate viscoelastic dynamic topographies of stagnant lid planetary bodies?
Dumoulin, Caroline; Čadek, Ondřej; Choblet, Gaël
2013-04-01
Planetary mantles are viscoelastic media. However, since numerical models of thermal convection in a viscoelastic spherical shell are still very challenging, most of the studies concerning dynamic topography of planetary surfaces generated by mantle convection use one of the following simplified rheological set-up: i) IVF (instantaneous viscous flow), ii) viscous body with a free surface, or iii) hybrid methods combining viscous deformation and elastic filtering of the topography. Justifications for the use of such approximations instead of a fully viscoelastic rheology have been made on the basis of simple tests with step-like viscosity structures, with small to moderate viscosity contrasts. However, because the rheology of planetary materials is thermally activated, the radial stratification of viscosity is more likely to be a continuous function of depth, and global viscosity contrasts might be very large. In our study, we systematically compare viscoelastic dynamic topography induced by an internal load to topographies generated by the three different simplified approaches listed above using a realistic viscosity profile for a stagnant lid associated to the lithosphere of a one plate planete. To this purpose, we compute response functions of surface topography and geoid using three different semi-spectral models that all include self-gravitation: a) a linear Maxwell body with a pseudo free upper surface, b) a viscous body with a pseudo free upper surface, and c) a viscous body with a free-slip condition at the surface. Results obtained with this last model (IVF) can then be filtered using the elastic thin shell approximation: the effective elastic thickness then corresponds to the elastic thickness that is needed to fit the viscoelastic topography with an elastic filtering of the IVF topography. We show that the effective elastic thickness varies strongly with the degree of the load, with the depth of the load, and with the duration of the loading. These
Computer program for flexible rotor dynamics analysis
Shen, F. A.
1974-01-01
Program analyzes general nonaxisymmetric and nonsynchronous transient and steady-state rotor dynamic performance of bending- and shear-wise flexible rotor-bearing system under various operating conditions. Program can be used as analytical study tool for general transient spin-speed and/or non-axisymmetric rotor motion.
Development of a Computer Program to Compute Approximate Heat Balance for Furnace Design
O.A. Ighodalo
2011-08-01
Full Text Available This study presents the description of a computer program developed for purpose of carrying out an approximate heat balance for a rectangular furnace at the design stage. This is often necessary in order to determine the heat input, its expenditure and the fuel consumption. The program which was written in MATLAB estimates surface areas, calorimetric and actual furnace temperatures, input heat from fuel combustion and the heat output for metal melting, waste gases, and lining losses. Fuel requirement was obtained by equating total heat input and output. The various percentages were determined as well as the thermal indicators. The result of the application of the program to a furnace design of dimension 700×600×600 mm using gaseous fuel (Butane is presented. The percentage of heat lost through the waste gases, the unit energy consumption and coefficient of total heat utilization compare well with what is obtainable in practice as revealed in literatures. The program will be useful for furnace design purposes.
Hybrid Differential Dynamic Programming with Stochastic Search
Aziz, Jonathan; Parker, Jeffrey; Englander, Jacob
2016-01-01
Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASAs Dawn mission. The Dawn trajectory was designed with the DDP-based Static Dynamic Optimal Control algorithm used in the Mystic software. Another recently developed method, Hybrid Differential Dynamic Programming (HDDP) is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.
Classical dynamics of a charged particle in a laser field beyond the dipole approximation
Jameson, Paul
2008-01-01
The classical dynamics of a charged particle traveling in a laser field modeled by an elliptically polarized monochromatic electromagnetic plane wave is discussed within the time reparametrization invariant form of the non-relativistic Hamilton-Jacobi theory. The exact parametric representation for a particle's orbit in an arbitrary plane wave background beyond the dipole approximation and including effect of the magnetic field is derived. For an elliptically polarized monochromatic plane wave the particle's trajectory, as an explicit function of the laboratory frame's time, is given in terms of the Jacobian elliptic functions, whose modulus is proportional to the laser's intensity and depends on the polarization of radiation. It is shown that the system exposes the ``intensity duality'', correspondence between the motion in the backgrounds with various intensities. In virtue of the modular properties of the Jacobian functions, by starting with the representative ``fundamental solution'' and applying a certai...
Object Tracking System Using Approximate Median Filter, Kalman Filter and Dynamic Template Matching
G. Mallikarjuna Rao
2014-04-01
Full Text Available In this work, we dealt with the tracking of single object in a sequence of frames either from a live camera or a previously saved video. A moving object is detected frame-by-frame with high accuracy and efficiency using Median approximation technique. As soon as the object has been detected, the same is tracked by kalman filter estimation technique along with a more accurate Template Matching algorithm. The templates are dynamically generated for this purpose. This guarantees any change in object pose which does not be hindered from tracking procedure. The system is capable of handling entry and exit of an object. Such a tracking scheme is cost effective and it can be used as an automated video conferencing system and also has application as a surveillance tool. Several trials of the tracking show that the approach is correct and extremely fast, and it's a more robust performance throughout the experiments.
The dynamics of a spinning particle in a linear in spin Hamiltonian approximation
Lukes-Gerakopoulos, Georgios; Patsis, Panos A; Seyrich, Jonathan
2016-01-01
We investigate for order and chaos the dynamical system of a spinning test particle of mass $m$ moving in the spacetime background of a Kerr black hole of mass M. This system is approximated in our investigation by the linear in spin Hamiltonian function provided in [E. Barausse, and A. Buonanno, Phys.Rev. D 81, 084024 (2010)]. We study the corresponding phase space by using 2D projections on a surface of section and the method of color and rotation on a 4D Poincar\\'e section. Various topological structures coming from the non-integrability of the linear in spin Hamiltonian are found and discussed. Moreover, an interesting result is that from the value of the dimensionless spin $S/(m M)=10^{-4}$ of the particle and below, the impact of the non-integrability of the system on the motion of the particle seems to be negligible.
Piping and fitting dynamic reliability program
The Electric Power Research Institute (EPRI) in conjunction with the U.S. Nuclear Regulatory Commission (NRC) initiated the Piping and Fitting Dynamic Reliability (PFDR) Program. The ultimate objective of this program is to introduce new, improved, realistic and defensible ASME Code design rules which take advantage of the inherent dynamic margin in piping and which result in a more balanced piping design between infrequent dynamic loads and daily operating loads. The basis for the proposed changes in design criteria will be derived from an extensive testing program together with supporting analyses. The first of three testing programs is focusing on the behaviour of typical piping components when subjected to dynamic loading introduced through hydraulically operated sleds. A second testing program is investigating the behaviour of piping systems under dynamic loading and the third program is focusing on development of a laboratory type specimen which can be used to quantitatively evaluate low cycle fatigue in the presence of ratcheting. This paper represents a status report of results of the component tests to date
Approximate pole-placement controller using inverse plant dynamics for floor vibration control
Nyawako, Donald S.; Reynolds, Paul; Hudson, Malcolm J.
2013-04-01
Past research and field trials have demonstrated the viability of active vibration control (AVC) technologies for the mitigation of human induced vibrations in problematic floors. They make use of smaller units than their passive counterparts, provide quicker and more efficient control, can tackle multiple modes of vibration simultaneously and adaptability can be introduced to enhance their robustness. Predominantly single-input-single-output (SISO) and multi- SISO collocated sensor and actuator pairs have been utilized in direct output feedback schemes, for example, with direct velocity feedback (DVF). On-going studies have extended such past works to include model-based control approaches, for example, pole-placement (PP), which demonstrate increased flexibility of achieving desired vibration mitigation performances but for which stability issues must be adequately addressed. The work presented here is an extension to the pole-placement controller design using an algebraic approach that has been investigated in past studies. An approximate pole-placement controller formulated via the inversion of the floor dynamics, considered as minimum phase, is designed to achieve target closed-loop performances. Analytical studies and experimental tests are based on a laboratory structure and comparisons in vibration mitigation performances are made with a typical DVF control scheme with inner loop actuator compensation. It is shown that with minimal compensation, primarily in the form of notch filters and gain adjustment, the approximate pole-placement controller scheme is easily formulated and implemented and offers good vibration mitigation performance as well as the potential for isolation and control of specific target modes of vibration. Predicted attenuations of 22dB and 12dB in both the first and second vibration modes of the laboratory structure were also realized in the experimental studies for DVF and the approximate PP controller.
The structure of approximate two electron wavefunctions in intense laser driven ionization dynamics
The structure of approximate two-electron wavefunctions in strong-field-driven ionization dynamics is investigated in depth, both theoretically and numerically. Theoretical analyses clarify that for two-electron singlet systems, the previously proposed time-dependent extended Hartree–Fock (TD-EHF) method (1995 Phys. Rev. A 51 3999) is equivalent to the multiconfiguration time-dependent Hartree–Fock method with two occupied orbitals. The latter wavefunction is further transformed into the natural expansion form, enabling the direct propagation of the natural orbitals (NOs). These methods, as well as the conventional time-dependent Hartree–Fock (TDHF) method, are numerically assessed as regards providing a description of the ionization dynamics of a one-dimensional helium atom model. This numerical analysis (i) explains the reason behind the well-known failure of the TDHF method to describe tunneling ionization, (ii) demonstrates the interpretive power of the TD-EHF wavefunction in both the original nonorthogonal formulation and the NO-based formulation, and (iii) highlights different manifestations of the electron correlation (an effect beyond the single-determinant description), in tunneling ionization, high harmonic generation, and nonsequential double ionization. Possible extensions of the NO basis approach to multielectron systems are briefly discussed. (paper)
Analytical descriptions of cross-polarisation dynamics: relaxing the secular approximations
Hirschinger, J.; Raya, J.
2015-11-01
In this work, analytical expressions of the cross-polarisation (CP) dynamics under both static and magic-angle spinning (MAS) conditions are obtained by solving the generalised Liouville-von Neumann quantum mechanical equation beyond the standard approximations, i.e., reintroducing neglected non-secular terms in the system superoperator. Although the simple model of a two-spin system interacting with a spin bath gives a rather crude description of CP dynamics, it accounts well for the orientation dependence of CP in a static sample of ferrocene powder and permits to detect slight departures from the Hartmann-Hahn matching condition. This approach also has the advantage of yielding manageable analytical expressions that can be used even by less inclined or experienced workers to obtain results that are good enough in an operational sense. Moreover, the resulting spin diffusion rate constants containing different sources of anisotropy of the system-environment interaction as well as their dependence on the MAS frequency are related semi-quantitatively to the local network of dipolar interactions. Finally, it is shown that non-secular solutions improve significantly the analysis of CPMAS-based separated-local-field spectroscopy experimental data in the absence of homonuclear decoupling.
Garvie, Marcus R; Burkardt, John; Morgan, Jeff
2015-03-01
We describe simple finite element schemes for approximating spatially extended predator-prey dynamics with the Holling type II functional response and logistic growth of the prey. The finite element schemes generalize 'Scheme 1' in the paper by Garvie (Bull Math Biol 69(3):931-956, 2007). We present user-friendly, open-source MATLAB code for implementing the finite element methods on arbitrary-shaped two-dimensional domains with Dirichlet, Neumann, Robin, mixed Robin-Neumann, mixed Dirichlet-Neumann, and Periodic boundary conditions. Users can download, edit, and run the codes from http://www.uoguelph.ca/~mgarvie/ . In addition to discussing the well posedness of the model equations, the results of numerical experiments are presented and demonstrate the crucial role that habitat shape, initial data, and the boundary conditions play in determining the spatiotemporal dynamics of predator-prey interactions. As most previous works on this problem have focussed on square domains with standard boundary conditions, our paper makes a significant contribution to the area. PMID:25616741
A Superstabilizing $\\log(n)$-Approximation Algorithm for Dynamic Steiner Trees
Blin, Lélia; Rovedakis, Stephane
2009-01-01
In this paper we design and prove correct a fully dynamic distributed algorithm for maintaining an approximate Steiner tree that connects via a minimum-weight spanning tree a subset of nodes of a network (referred as Steiner members or Steiner group) . Steiner trees are good candidates to efficiently implement communication primitives such as publish/subscribe or multicast, essential building blocks for the new emergent networks (e.g. P2P, sensor or adhoc networks). The cost of the solution returned by our algorithm is at most $\\log |S|$ times the cost of an optimal solution, where $S$ is the group of members. Our algorithm improves over existing solutions in several ways. First, it tolerates the dynamism of both the group members and the network. Next, our algorithm is self-stabilizing, that is, it copes with nodes memory corruption. Last but not least, our algorithm is \\emph{superstabilizing}. That is, while converging to a correct configuration (i.e., a Steiner tree) after a modification of the network, it...
Planar multibody dynamics formulation, programming and applications
Nikravesh, Parviz E
2007-01-01
Introduction Multibody Mechanical Systems Types of Analyses Methods of Formulation Computer Programming Application Examples Unit System Remarks Preliminaries Reference Axes Scalars and Vectors Matrices Vector, Array, and Matrix Differentiation Equations and Expressions Remarks Problems Fundamentals of Kinematics A Particle Kinematics of a Rigid Body Definitions Remarks Problems Fundamentals of Dynamics Newton's Laws of Motion Dynamics of a Body Force Elements Applied Forces Reaction Force Remarks Problems Point-Coordinates: Kinematics Multipoint
A Dynamic Programming Approach to Individual Initialization in Genetic Programming
Křen, T.; Neruda, Roman
Los Alamitos: IEEE, 2015, s. 1752-1757. ISBN 978-1-4799-8696-5. [SMC 2015. International Conference on Systems, Man and Cybernetics. Hong Kong (HK), 09.10.2015-12.10.2015] R&D Projects: GA ČR GA15-18108S Grant ostatní: GA UK(CZ) 187115; SVV(CZ) 260 224 Institutional support: RVO:67985807 Keywords : genetic programming * initialization * dynamic programming Subject RIV: IN - Informatics, Computer Science
Dynamic Programming Model of Health and Retirement
Iskhakov, Fedor
2008-01-01
A structural dynamic programming model is applied for modeling labour market transitions among older age workers in Norway in 1992-2003. Special attention is given to early retirement pensiion and disability pension as two major exit routes from the labour force. Health status is represented by a latent variable reflecting the eligibility for participating in disability programs. Incomplete information maximum likelihood method is used in several stages to facilitate the estimation. The model...
Classical dynamics of a charged particle in a laser field beyond the dipole approximation
Jameson, Paul; Khvedelidze, Arsen
2008-05-01
The classical dynamics of a charged particle traveling in a laser field modeled by an elliptically polarized monochromatic electromagnetic plane wave is discussed within the time reparametrization invariant form of the nonrelativistic Hamilton-Jacobi theory. The exact parametric representation for a particle’s orbit in an arbitrary plane wave background beyond the dipole approximation and including effect of the magnetic field is derived. For an elliptically polarized monochromatic plane wave the particle’s trajectory, as an explicit function of the laboratory frame’s time, is given in terms of the Jacobian elliptic functions, whose modulus is proportional to the laser’s intensity and depends on the polarization of radiation. It is shown that the system exposes the intensity duality, correspondence between the motion in the backgrounds with various intensities. In virtue of the modular properties of the Jacobian functions, by starting with the representative “fundamental solution” and applying a certain modular transformation one can obtain the particle’s orbit in the monochromatic plane wave background with arbitrarily prescribed characteristics.
Mao, Runfang; Lee, Ming-Tsung; Vishnyakov, Aleksey; Neimark, Alexander V
2015-09-01
Using dissipative particle dynamics (DPD) simulations, we explore the specifics of micellization in the solutions of anionic and cationic surfactants and their mixtures. Anionic surfactant sodium dodecyl sulfate (SDS) and cationic surfactant cetyltrimethylammonium bromide (CTAB) are chosen as characteristic examples. Coarse-grained models of the surfactants are constructed and parameterized using a combination of atomistic molecular simulation and infinite dilution activity coefficient calibration. Electrostatic interactions of charged beads are treated using a smeared charge approximation: the surfactant heads and dissociated counterions are modeled as beads with charges distributed around the bead center in an implicit dielectric medium. The proposed models semiquantitatively describe self-assembly in solutions of SDS and CTAB at various surfactant concentrations and molarities of added electrolyte. In particular, the model predicts a decline in the free surfactant concentration with the increase of the total surfactant loading, as well as characteristic aggregation transitions in single-component surfactant solutions caused by the addition of salt. The calculated values of the critical micelle concentration reasonably agree with experimental observations. Modeling of catanionic SDS-CTAB mixtures show consecutive transitions to worm-like micelles and then to vesicles caused by the addition of CTAB to micellar solution of SDS. PMID:26241704
Microsoft Dynamics NAV 7 programming cookbook
Raul, Rakesh
2013-01-01
Written in the style of a cookbook. Microsoft Dynamics NAV 7 Programming Cookbook is full of recipes to help you get the job done.If you are a junior / entry-level NAV developer then the first half of the book is designed primarily for you. You may or may not have any experience programming. It focuses on the basics of NAV programming.If you are a mid-level NAV developer, you will find these chapters explain how to think outside of the NAV box when building solutions. There are also recipes that senior developers will find useful.
Quantum optical device accelerating dynamic programming
Grigoriev, D.; Kazakov, A.; Vakulenko, S
2005-01-01
In this paper we discuss analogue computers based on quantum optical systems accelerating dynamic programming for some computational problems. These computers, at least in principle, can be realized by actually existing devices. We estimate an acceleration in resolving of some NP-hard problems that can be obtained in such a way versus deterministic computers
Waste Heat Approximation for Understanding Dynamic Compression in Nature and Experiments
Jeanloz, R.
2015-12-01
Energy dissipated during dynamic compression quantifies the residual heat left in a planet due to impact and accretion, as well as the deviation of a loading path from an ideal isentrope. Waste heat ignores the difference between the pressure-volume isentrope and Hugoniot in approximating the dissipated energy as the area between the Rayleigh line and Hugoniot (assumed given by a linear dependence of shock velocity on particle velocity). Strength and phase transformations are ignored: justifiably, when considering sufficiently high dynamic pressures and reversible transformations. Waste heat mis-estimates the dissipated energy by less than 10-20 percent for volume compressions under 30-60 percent. Specific waste heat (energy per mass) reaches 0.2-0.3 c02 at impact velocities 2-4 times the zero-pressure bulk sound velocity (c0), its maximum possible value being 0.5 c02. As larger impact velocities are implied for typical orbital velocities of Earth-like planets, and c02 ≈ 2-30 MJ/kg for rock, the specific waste heat due to accretion corresponds to temperature rises of about 3-15 x 103 K for rock: melting accompanies accretion even with only 20-30 percent waste heat retained. Impact sterilization is similarly quantified in terms of waste heat relative to the energy required to vaporize H2O (impact velocity of 7-8 km/s, or 4.5-5 c0, is sufficient). Waste heat also clarifies the relationship between shock, multi-shock and ramp loading experiments, as well as the effect of (static) pre-compression. Breaking a shock into 2 steps significantly reduces the dissipated energy, with minimum waste heat achieved for two equal volume compressions in succession. Breaking a shock into as few as 4 steps reduces the waste heat to within a few percent of zero, documenting how multi-shock loading approaches an isentrope. Pre-compression, being less dissipative than an initial shock to the same strain, further reduces waste heat. Multi-shock (i.e., high strain-rate) loading of pre
Synthesis of Large Dynamic Concurrent Programs from Dynamic Specifications
Attie, Paul C
2008-01-01
We present a tractable method for synthesizing arbitrarily large concurrent programs, for a shared memory model with common hardware-available primitives such as atomic registers, compare-and-swap, load-linked/store conditional, etc. The programs we synthesize are dynamic: new processes can be created and added at run-time, and so our programs are not finite-state, in general. Nevertheless, we successfully exploit automatic synthesis and model-checking methods based on propositional temporal logic. Our method is algorithmically efficient, with complexity polynomial in the number of component processes (of the program) that are ``alive'' at any time. Our method does not explicitly construct the automata-theoretic product of all processes that are alive, thereby avoiding \\intr{state explosion}. Instead, for each pair of processes which interact, our method constructs an automata-theoretic product (\\intr{pair-machine}) which embodies all the possible interactions of these two processes. From each pair-machine, w...
The use of the time-dependent self-consistent field approximation (TDSCF) in the numerical solution of quantum curve crossing and tunneling dynamical problems is investigated. Particular emphasis is given to multiconfiguration TDSCF (MCTDSCF) approximations, which are shown to perform considerably better with only a small increase in computational effort. We investigate a number of simple models in which a 'system' characterized by two electronic potential surfaces evolves while interacting with a 'bath' mode described by an harmonic oscillator, and compare exact numerical solutions to one- and two-configuration TDSCF approximations. We also introduce and investigate a semiclassical approximation in which the 'bath' mode is described by semiclassical wavepackets (one for each electronic state) and show that for all models investigated this scheme works very well in comparison with the fully quantum MCTDSCF approximation. This provides a potentially very useful method to simulate strongly quantum systems coupled to an essentially classical environment. (orig.)
The determination of quasicrystal (QC) surface structures is a challenge to current surface structure techniques. Low-energy electron diffraction (LEED) is the primary technique for the determination of periodic surface structures, but application of dynamical LEED to quasicrystals requires the use of many approximations. In this study, two different approaches were used to apply dynamical LEED to the structure of the tenfold surface of decagonal Al73Ni10Co17. One method (method 1) involves the use of a quasicrystalline model along with approximations that average over the composition and local geometries. The other method (method 2) uses periodic models that approximate the actual local QC structure (approximants) in more exact, atomistic calculations. Although the results using the two methods were consistent, the results of the approximant analysis (method 2) suggested a different way to apply the approximations in method 1, resulting in a better fit between experimental and calculated beams. Thus, periodic approximant structure models can provide a simpler and more efficient method for the determination of local geometries in QC surfaces, and may also facilitate analyses using quasicrystal models
On Static and Dynamic Control-Flow Information in Program Analysis and Transformation
Damian, Daniel
's first-order, one-pass CPS transformation, we present a simpler CPS transformation of flow information with a simpler correctness proof. We continue by exploring Shivers's time-stamps-based technique for approximating program analyses over programs with dynamic control flow. We formalize a time...
Local minimization algorithms for dynamic programming equations
Kalise, Dante; Kröner, Axel; Kunisch, Karl
2015-01-01
The numerical realization of the dynamic programming principle for continuous-time optimal control leads to nonlinear Hamilton-Jacobi-Bellman equations which require the minimization of a nonlinear mapping over the set of admissible controls. This minimization is often performed by comparison over a finite number of elements of the control set. In this paper we demonstrate the importance of an accurate realization of these minimization problems and propose algorithms by which this can be achi...
Dynamic Programming, Maximum Principle and Vintage Capital
Fabbri, Giorgio; Iacopetta, Maurizio
2007-01-01
We present an application of the Dynamic Programming (DP) and of the Maximum Principle (MP) to solve an optimization over time when the production function is linear in the stock of capital (Ak model). Two views of capital are considered. In one, which is embraced by the great majority of macroeconomic models, capital is homogeneous and depreciates at a constant exogenous rate. In the other view each piece of capital has its own ﬁnite productive life cycle (vintage capital). The interpretatio...
Weak Dynamic Programming for Generalized State Constraints
Bouchard, Bruno; Nutz, Marcel
2012-01-01
We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a measurable selection but still implies the Hamilton-Jacobi-Bellman equation in the viscosity sense. We treat open state constraints as a special case of expectation constraints and prove a comparison theorem to obtain the equation for closed state constraints.
Eradication of Ebola Based on Dynamic Programming
Zhu, Jia-Ming; Wang, Lu; Liu, Jia-Bao
2016-01-01
This paper mainly studies the eradication of the Ebola virus, proposing a scientific system, including three modules for the eradication of Ebola virus. Firstly, we build a basic model combined with nonlinear incidence rate and maximum treatment capacity. Secondly, we use the dynamic programming method and the Dijkstra Algorithm to set up M-S (storage) and several delivery locations in West Africa. Finally, we apply the previous results to calculate the total cost, production cost, storage cost, and shortage cost. PMID:27313655
Eradication of Ebola Based on Dynamic Programming.
Zhu, Jia-Ming; Wang, Lu; Liu, Jia-Bao
2016-01-01
This paper mainly studies the eradication of the Ebola virus, proposing a scientific system, including three modules for the eradication of Ebola virus. Firstly, we build a basic model combined with nonlinear incidence rate and maximum treatment capacity. Secondly, we use the dynamic programming method and the Dijkstra Algorithm to set up M-S (storage) and several delivery locations in West Africa. Finally, we apply the previous results to calculate the total cost, production cost, storage cost, and shortage cost. PMID:27313655
Joint Chance-Constrained Dynamic Programming
Ono, Masahiro; Kuwata, Yoshiaki; Balaram, J. Bob
2012-01-01
This paper presents a novel dynamic programming algorithm with a joint chance constraint, which explicitly bounds the risk of failure in order to maintain the state within a specified feasible region. A joint chance constraint cannot be handled by existing constrained dynamic programming approaches since their application is limited to constraints in the same form as the cost function, that is, an expectation over a sum of one-stage costs. We overcome this challenge by reformulating the joint chance constraint into a constraint on an expectation over a sum of indicator functions, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the primal variables can be optimized by a standard dynamic programming, while the dual variable is optimized by a root-finding algorithm that converges exponentially. Error bounds on the primal and dual objective values are rigorously derived. We demonstrate the algorithm on a path planning problem, as well as an optimal control problem for Mars entry, descent and landing. The simulations are conducted using a real terrain data of Mars, with four million discrete states at each time step.
Zhou, L; Luo, Y X
2001-01-01
We present the dissipative dynamics of the field of two-photon Jaynes-Cummings model (JCM) with Stark shift in dispersive approximation and investigate the influence of dissipation on entanglement. We show the coherence properties of the field can be affected by the dissipative cavity when nonlinear two-photon process is involved.
On a Natural Dynamics for Linear Programming
Straszak, Damian
2015-01-01
In this paper we study dynamics inspired by Physarum polycephalum (a slime mold) for solving linear programs [NTY00, IJNT11, JZ12]. These dynamics are arrived at by a local and mechanistic interpretation of the inner workings of the slime mold and a global optimization perspective has been lacking even in the simplest of instances. Our first result is an interpretation of the dynamics as an optimization process. We show that Physarum dynamics can be seen as a steepest-descent type algorithm on a certain Riemannian manifold. Moreover, we prove that the trajectories of Physarum are in fact paths of optimizers to a parametrized family of convex programs, in which the objective is a linear cost function regularized by an entropy barrier. Subsequently, we rigorously establish several important properties of solution curves of Physarum. We prove global existence of such solutions and show that they have limits, being optimal solutions of the underlying LP. Finally, we show that the discretization of the Physarum dy...
Optimization of decision rules based on dynamic programming approach
Zielosko, Beata
2014-01-14
This chapter is devoted to the study of an extension of dynamic programming approach which allows optimization of approximate decision rules relative to the length and coverage. We introduce an uncertainty measure that is the difference between number of rows in a given decision table and the number of rows labeled with the most common decision for this table divided by the number of rows in the decision table. We fix a threshold γ, such that 0 ≤ γ < 1, and study so-called γ-decision rules (approximate decision rules) that localize rows in subtables which uncertainty is at most γ. Presented algorithm constructs a directed acyclic graph Δ γ T which nodes are subtables of the decision table T given by pairs "attribute = value". The algorithm finishes the partitioning of a subtable when its uncertainty is at most γ. The chapter contains also results of experiments with decision tables from UCI Machine Learning Repository. © 2014 Springer International Publishing Switzerland.
Approximate Modified Policy Iteration
Scherrer, Bruno; Ghavamzadeh, Mohammad; Geist, Matthieu
2012-01-01
Modified policy iteration (MPI) is a dynamic programming (DP) algorithm that contains the two celebrated policy and value iteration methods. Despite its generality, MPI has not been thoroughly studied, especially its approximation form which is used when the state and/or action spaces are large or infinite. In this paper, we propose three approximate MPI (AMPI) algorithms that are extensions of the well-known approximate DP algorithms: fitted-value iteration, fitted-Q iteration, and classification-based policy iteration. We provide an error propagation analysis for AMPI that unifies those for approximate policy and value iteration. We also provide a finite-sample analysis for the classification-based implementation of AMPI (CBMPI), which is more general (and somehow contains) than the analysis of the other presented AMPI algorithms. An interesting observation is that the MPI's parameter allows us to control the balance of errors (in value function approximation and in estimating the greedy policy) in the fina...
Xiaofeng Lin; Heng Zhang; Li Wei; Huixia Liu
2009-01-01
This paper applies a neural-network-based approximate dynamic programming (ADP) method, namely, the action dependent heuristic dynamic programming (ADHDP), to an industrial sucrose crystallization optimal control problem. The industrial sucrose crystallization is a nonlinear and slow time-varying process. It is quite difficult to establish a precise mechanism model of the crystallization, because of complex internal mechanism and interacting variables. We developed a neural network model of t...
Comparison of dynamical approximation schemes for non-linear gravitational clustering
Melott, A L
1994-01-01
I report on controlled comparison of gravitational approximation schemes linear/lognormal/adhesion/frozen-flow/Zel'dovich(ZA) and ZA's second--order generalization. In the last two cases we also created new versions of the approximation by truncation, i.e., by finding an optimum smoothing window (see text) for the initial conditions. The Zel'dovich approximation, with optimized initial smoothing, worked extremely well. Its second-order generalization was slightly better. The success of our best-choice was a result of the treatment of the phases of nonlinear Fourier components. The adhesion approximation produced the most accurate nonlinear power spectrum and density distribution, but its phase errors suggest mass condensations were moved somewhat incorrectly. Due to its better reproduction of the mass density distribution function and power spectrum, adhesion might be preferred for some uses. We recommend either n-body simulations or our modified versions of ZA, depending on the purpose. Modified ZA can rapid...
Ionization dynamics beyond the dipole approximation induced by the pulse envelope
Simonsen, Aleksander Skjerlie; Kjellsson, Tor; Førre, Morten; Lindroth, Eva; Selstø, Sølve
2016-05-01
When atoms and molecules are ionized by laser pulses of finite duration and increasingly high intensities, the validity of the much-used dipole approximation, in which the spatial dependence and magnetic component of the external field are neglected, eventually breaks down. We report that, when going beyond the dipole approximation for the description of atoms exposed to ultraviolet light, the spatial dependence of the pulse shape, the envelope, provides the dominant correction, while the spatial dependence of the carrier is negligible. We present a first-order beyond-dipole correction to the Hamiltonian which accounts exclusively for nondipole effects stemming from the carrier envelope of the pulse. We demonstrate by ab initio calculations for hydrogen that this approximation, which we refer to as the envelope approximation, reproduces the full interaction beyond the dipole approximation for absolute and differential observables and proves to be valid for a broad range of high-frequency fields. This is done both for the Schrödinger and the Dirac equation. Moreover, it is demonstrated that the envelope approximation provides an interaction-term which gives rise to faster numerical convergence in terms of partial waves compared to its exact counterpart.
Gontchar, Igor
2015-01-01
Accuracy of the Kramers approximate formula for the thermal decay rate of the metastable state is studied for the two-dimensional potential pocket. This is done by the comparison with the quasistationary rate resulting from the dynamical modeling. It is shown that the Kramers rate is in agreement with the quasistationary rate within the statistical errors provided the absorptive border is far enough from the potential ridge restricting the metastable state. As the absorptive border (or its part) gets closer to the ridge the Kramers formula underestimate the quasistationary rate. The difference reaches approximately the factor of 2 when the absorptive border coincides with the ridge.
In this work a two-particle irreducible (2PI) closed-time-path (CTP) effective action is used to describe the nonequilibrium dynamics of a Bose-Einstein condensate selectively loaded into every third site of a one-dimensional optical lattice. The motivation of this work is the recent experimental realization of this system. Patterned loading methods may be useful for quantum computing with trapped atoms. This system also serves to illustrate many basic issues in nonequilibrium quantum-field theory pertaining to the dynamics of quantum correlations and fluctuations which goes beyond the capability of a mean-field theory. By numerically evolving in time the initial-state configuration using the Bose-Hubbard Hamiltonian an exact quantum solution is available for this system in the case of few atoms and wells. One can also use it to test various approximate methods. Under the 2PI CTP scheme with this initial configuration, three different approximations are considered: (a) the Hartree-Fock-Bogoliubov (HFB) approximation (b) the next-to-leading-order 1/N expansion of the 2PI effective action up to second order in the interaction strength, and (c) a second-order perturbative expansion in the interaction strength. We present detailed comparisons between these approximations and determine their range of validity by contrasting them with the exact many-body solution for a moderate number of atoms and wells. As a general feature we observe that because the second-order 2PI approximations include multiparticle scattering in a systematic way, they are able to capture damping effects exhibited in the exact solution, which a mean-field collisionless approach fails to produce. While the second-order approximations show a clear improvement over the HFB approximation, our numerical results show that they fail at late times, when interaction effects are significant
Independent center, independent electron approximation for dynamics of molecules and clusters
A formalism is developed for evaluating probabilities and cross sections for multiple-electron transitions in scattering of molecules and clusters by charged collision partners. First, the molecule is divided into subclusters each made up of identical centers (atoms). Within each subcluster coherent scattering from identical centers may lead to observable phase terms and a geometrical structure factor. Then, using a mean field approximation to describe the interactions between centers we obtain AI∼ summation k product keiδkIAIk. Second, the independent electron approximation for each center may be obtained by neglecting the correlation between electrons in each center. The probability amplitude for each center is then a product of single electron transition probability amplitudes, aIki, i.e. AIk≅ product iaiki. Finally, the independent subcluster approximation is introduced by neglecting the interactions between different subclusters in the molecule or cluster. The total probability amplitude then reduces to a simple product of amplitudes for each subcluster, A≅ product IAI. Limitations of this simple approximation are discussed. copyright 1996 American Institute of Physics
Eradication of Ebola Based on Dynamic Programming
Jia-Ming Zhu
2016-01-01
Full Text Available This paper mainly studies the eradication of the Ebola virus, proposing a scientific system, including three modules for the eradication of Ebola virus. Firstly, we build a basic model combined with nonlinear incidence rate and maximum treatment capacity. Secondly, we use the dynamic programming method and the Dijkstra Algorithm to set up M-S (storage and several delivery locations in West Africa. Finally, we apply the previous results to calculate the total cost, production cost, storage cost, and shortage cost.
Damping in nuclear collective modes in a semiclassical fluid-dynamical approximation
A semiclassical fluiddynamical model based on an usual scaling approximation (SCA) was extended to investigate the role of one and two-body dissipation in the widths of nuclear collective modes. The competition between one and two-body viscosity in: i) the collisionless (elastic) limit; ii) the hydrodynamical case and iii) the general viscoelastic regime is examined over the whole range of nuclear collision time scales. Numerical solutions are investigated for the first magnetic 2- twist mode in 208Pb. (Author)
Dynamics of the 12C-12C system in the static molecular mean field approximation
The interaction between two 12C ions at low energy is investigated in the mean field (Hartree-Fock) approximation. The authors assume adiabaticity for the molecular motion and calculate the interaction energy by the constrained Hartree-Fock method, using the inderdistance d separating the two ions as the constrained quantity. This energy is calculated by using the Skyrme SIII force, without spin-orbit. (orig./AH)
A self-consistent approximation scheme is formulated for the calculation of the dynamical linear polarizability of classical electron monolayers. The derivation is carried out in two stages. In the first stage, the authors formulate a simple response function relation linking linear and quadratic polarizabilities; the dynamical coupling function is expressed entirely in terms of the latter. The basic elements in the derivation are the first BBGKY kinetic equation (prepared in the velocity average approximation) and the non-linear fluctuation-dissipation theorem. The new response function relation is exact at zero frequency and exactly satisfies the third frequency moment sum rule. In the second stage, self-consistency is guaranteed by approximating the quadratic polarizability in terms of linear ones. The theory is examined in the weak coupling limit where it is found that a dominant γ-independent non-RPA contribution to the damping is missing. The structure of the missing term is identified at arbitrary coupling strengths. Work is in progress to see how it can be incorporated into the approximation scheme. (author)
Automated Flight Routing Using Stochastic Dynamic Programming
Ng, Hok K.; Morando, Alex; Grabbe, Shon
2010-01-01
Airspace capacity reduction due to convective weather impedes air traffic flows and causes traffic congestion. This study presents an algorithm that reroutes flights in the presence of winds, enroute convective weather, and congested airspace based on stochastic dynamic programming. A stochastic disturbance model incorporates into the reroute design process the capacity uncertainty. A trajectory-based airspace demand model is employed for calculating current and future airspace demand. The optimal routes minimize the total expected traveling time, weather incursion, and induced congestion costs. They are compared to weather-avoidance routes calculated using deterministic dynamic programming. The stochastic reroutes have smaller deviation probability than the deterministic counterpart when both reroutes have similar total flight distance. The stochastic rerouting algorithm takes into account all convective weather fields with all severity levels while the deterministic algorithm only accounts for convective weather systems exceeding a specified level of severity. When the stochastic reroutes are compared to the actual flight routes, they have similar total flight time, and both have about 1% of travel time crossing congested enroute sectors on average. The actual flight routes induce slightly less traffic congestion than the stochastic reroutes but intercept more severe convective weather.
Runway Scheduling Using Generalized Dynamic Programming
Montoya, Justin; Wood, Zachary; Rathinam, Sivakumar
2011-01-01
A generalized dynamic programming method for finding a set of pareto optimal solutions for a runway scheduling problem is introduced. The algorithm generates a set of runway fight sequences that are optimal for both runway throughput and delay. Realistic time-based operational constraints are considered, including miles-in-trail separation, runway crossings, and wake vortex separation. The authors also model divergent runway takeoff operations to allow for reduced wake vortex separation. A modeled Dallas/Fort Worth International airport and three baseline heuristics are used to illustrate preliminary benefits of using the generalized dynamic programming method. Simulated traffic levels ranged from 10 aircraft to 30 aircraft with each test case spanning 15 minutes. The optimal solution shows a 40-70 percent decrease in the expected delay per aircraft over the baseline schedulers. Computational results suggest that the algorithm is promising for real-time application with an average computation time of 4.5 seconds. For even faster computation times, two heuristics are developed. As compared to the optimal, the heuristics are within 5% of the expected delay per aircraft and 1% of the expected number of runway operations per hour ad can be 100x faster.
Upper Bounds on Numerical Approximation Errors
Raahauge, Peter
2004-01-01
This paper suggests a method for determining rigorous upper bounds on approximationerrors of numerical solutions to infinite horizon dynamic programming models.Bounds are provided for approximations of the value function and the policyfunction as well as the derivatives of the value function. The...... approximations of a standard (strictly concave)growth model.KEYWORDS: Numerical approximation errors, Bellman contractions, Error bounds...
An approximate solution for interlaminar stresses in laminated composites: Applied mechanics program
Rose, Cheryl A.; Herakovich, Carl T.
1992-01-01
An approximate solution for interlaminar stresses in finite width, laminated composites subjected to uniform extensional, and bending loads is presented. The solution is based upon the principle of minimum complementary energy and an assumed, statically admissible stress state, derived by considering local material mismatch effects and global equilibrium requirements. The stresses in each layer are approximated by polynomial functions of the thickness coordinate, multiplied by combinations of exponential functions of the in-plane coordinate, expressed in terms of fourteen unknown decay parameters. Imposing the stationary condition of the laminate complementary energy with respect to the unknown variables yields a system of fourteen non-linear algebraic equations for the parameters. Newton's method is implemented to solve this system. Once the parameters are known, the stresses can be easily determined at any point in the laminate. Results are presented for through-thickness and interlaminar stress distributions for angle-ply, cross-ply (symmetric and unsymmetric laminates), and quasi-isotropic laminates subjected to uniform extension and bending. It is shown that the solution compares well with existing finite element solutions and represents an improved approximate solution for interlaminar stresses, primarily at interfaces where global equilibrium is satisfied by the in-plane stresses, but large local mismatch in properties requires the presence of interlaminar stresses.
Domínguez, Luis F.
2012-06-25
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 programming subproblem and a mixed-integer nonlinear programming subproblem to provide a series of parametric upper and lower bounds. The primal subproblem is formulated by fixing the integer variables and solved through a series of multiparametric quadratic programming (mp-QP) problems based on quadratic approximations of the objective function, while the deterministic master subproblem is formulated so as to provide feasible integer solutions for the next primal subproblem. To reduce the computational effort when infeasibilities are encountered at the vertices of the critical regions (CRs) generated by the primal subproblem, a simplicial approximation approach is used to obtain CRs that are feasible at each of their vertices. The algorithm terminates when there does not exist an integer solution that is better than the one previously used by the primal problem. Through a series of examples, the proposed algorithm is compared with a multiparametric mixed-integer outer approximation (mp-MIOA) algorithm to demonstrate its computational advantages. © 2012 American Institute of Chemical Engineers (AIChE).
We consider symmetry properties of differential equations in non-relativistic quantum mechanics and classical mechanics. Special emphasis is given to periodically driven systems. For a model system connections between symmetries of corresponding classical and quantal systems are established. The fundamental difference between variational symmetries and symmetries of the Euler-Lagrange-equations is discussed for the special case of classical mechanics. For nonintegrable systems with quasiregular regions in phase space we introduce the notion of approximate symmetry. As an example, we demonstrate the accuracy of such symmetry properties in certain domains of phase space for a periodically driven anharmonic oscillator. (orig.)
Approximate expression for the dynamic structure factor in the Lieb-Liniger model
Cherny, Alexander Yu.; Brand, Joachim
2009-01-01
Recently, Imambekov and Glazman [Phys. Rev. Lett. 100, 206805 (2008)] showed that the dynamic structure factor (DSF) of the 1D Bose gas demonstrates power-law behaviour along the limiting dispersion curve of the collective modes and calculated the corresponding exponents exactly. Combining these recent results with a previously obtained strong-coupling expansion we present an interpolation formula for the DSF of the 1D Bose gas. The obtained expression is further consistent with exact low ene...
Equilibria of dynamic games with many players: Existence, approximation, and market structure
Adlakha, Sachin; Johari, Ramesh; Gabriel Y. Weintraub
2015-01-01
In this paper we study stochastic dynamic games with many players; these are a fundamental model for a wide range of economic applications. The standard solution concept for such games is Markov perfect equilibrium (MPE), but it is well known that MPE computation becomes intractable as the number of players increases. We instead consider the notion of stationary equilibrium (SE), where players optimize assuming the empirical distribution of others' states remains constant at its long run aver...
Dynamics of a working process approximated to combustion at constant pressure
Andrusenko Oleg Evgenevich; Matveev Yury Ivanovich; Andrusenko Sergey Evgenevich
2011-01-01
The process of fuel combustion in the cylinder is considered in the paper. The interaction of the fuel combustion process with the gas distribution system and the fuel injection into the cylinder is investigated. The interconnection of the advance angle of fuel injection with the dynamics of loads on engine parts is studied. Experimental observations connected with fuel adjustment and parameter changes in working processes of the diesel engine are described. Practical advice is also given to ...
Including quantum mechanical effects on the dynamics of nuclei in the condensed phase is challenging, because the complexity of exact methods grows exponentially with the number of quantum degrees of freedom. Efforts to circumvent these limitations can be traced down to two approaches: methods that treat a small subset of the degrees of freedom with rigorous quantum mechanics, considering the rest of the system as a static or classical environment, and methods that treat the whole system quantum mechanically, but using approximate dynamics. Here, we perform a systematic comparison between these two philosophies for the description of quantum effects in vibrational spectroscopy, taking the Embedded Local Monomer model and a mixed quantum-classical model as representatives of the first family of methods, and centroid molecular dynamics and thermostatted ring polymer molecular dynamics as examples of the latter. We use as benchmarks D2O doped with HOD and pure H2O at three distinct thermodynamic state points (ice Ih at 150 K, and the liquid at 300 K and 600 K), modeled with the simple q-TIP4P/F potential energy and dipole moment surfaces. With few exceptions the different techniques yield IR absorption frequencies that are consistent with one another within a few tens of cm−1. Comparison with classical molecular dynamics demonstrates the importance of nuclear quantum effects up to the highest temperature, and a detailed discussion of the discrepancies between the various methods let us draw some (circumstantial) conclusions about the impact of the very different approximations that underlie them. Such cross validation between radically different approaches could indicate a way forward to further improve the state of the art in simulations of condensed-phase quantum dynamics
Da-chuan; XU; Shu-zhong; ZHANG
2007-01-01
In this paper,we consider a class of quadratic maximization problems.For a subclass of the problems,we show that the SDP relaxation approach yields an approximation solution with the ratio is dependent on the data of the problem with α being a uniform lower bound.In light of this new bound,we show that the actual worst-case performance ratio of the SDP relaxation approach (with the triangle inequalities added) is at least α + δd if every weight is strictly positive,where δd ＞ 0 is a constant depending on the problem dimension and data.
Versatile and declarative dynamic programming using pair algebras
Giegerich Robert
2005-09-01
Full Text Available Abstract Background Dynamic programming is a widely used programming technique in bioinformatics. In sharp contrast to the simplicity of textbook examples, implementing a dynamic programming algorithm for a novel and non-trivial application is a tedious and error prone task. The algebraic dynamic programming approach seeks to alleviate this situation by clearly separating the dynamic programming recurrences and scoring schemes. Results Based on this programming style, we introduce a generic product operation of scoring schemes. This leads to a remarkable variety of applications, allowing us to achieve optimizations under multiple objective functions, alternative solutions and backtracing, holistic search space analysis, ambiguity checking, and more, without additional programming effort. We demonstrate the method on several applications for RNA secondary structure prediction. Conclusion The product operation as introduced here adds a significant amount of flexibility to dynamic programming. It provides a versatile testbed for the development of new algorithmic ideas, which can immediately be put to practice.
In the experimental data processing computer PANAFACOM U-400 in the Institute of Plasma Physics, Nagoya University, general purpose programs have been prepared for checking on the data stored in it. These programs were originally developed for use in the on-line data processing system for JIPP T-2 experiment. They are in two subroutines for obtaining straight lines best fitting data points by the method of least squares and several subroutines for the graphic display of data points. With the subroutines, graphic display, statistical processing and the display of its results can be carried out for experimental data. The programs are cataloged as execution load modules in disk files. In case of using them, it is necessary only to assign required arguments and then call the subroutines by FORTRAN CALL statements. The graphic display subroutines are based on the standard GRASP of U-400 graphic processing software. No knowledge of GRASP is required, however. Users can readily use the programs only by referring to the present report. (J.P.N.)
Xiaofeng Lin
2009-10-01
Full Text Available This paper applies a neural-network-based approximate dynamic programming (ADP method, namely, the action dependent heuristic dynamic programming (ADHDP, to an industrial sucrose crystallization optimal control problem. The industrial sucrose crystallization is a nonlinear and slow time-varying process. It is quite difficult to establish a precise mechanism model of the crystallization, because of complex internal mechanism and interacting variables. We developed a neural network model of the crystallization based on the data from the actual sugar boiling process of sugar refinery. The ADHDP is a learningand approximation-based approach which can solve the optimization control problem of nonlinear system. The paper covers the basic principle of this learning scheme and the design of neural network controller based on the approach. The result of simulation shows the controller based on action dependent heuristic dynamic programming approach can optimize industrial sucrose crystallization.
Thoma, M.; Grosfeld, K.; Barbi, D.; Determann, J.; Goeller, S.; Mayer, C.; Pattyn, F.
2014-01-01
Glaciers and ice caps exhibit currently the largest cryospheric contributions to sea level rise. Modelling the dynamics and mass balance of the major ice sheets is therefore an important issue to investigate the current state and the future response of the cryosphere in response to changing environmental conditions, namely global warming. This requires a powerful, easy-to-use, versatile multi-approximation ice dynamics model. Based on the well-known and established ice sheet model of Pattyn (2003) we develop the modular multi-approximation thermomechanic ice model RIMBAY, in which we improve the original version in several aspects like a shallow ice-shallow shelf coupler and a full 3D-grounding-line migration scheme based on Schoof's (2007) heuristic analytical approach. We summarise the full Stokes equations and several approximations implemented within this model and we describe the different numerical discretisations. The results are cross-validated against previous publications dealing with ice modelling, and some additional artificial set-ups demonstrate the robustness of the different solvers and their internal coupling. RIMBAY is designed for an easy adaption to new scientific issues. Hence, we demonstrate in very different set-ups the applicability and functionality of RIMBAY in Earth system science in general and ice modelling in particular.
Goal representation heuristic dynamic programming on maze navigation.
Ni, Zhen; He, Haibo; Wen, Jinyu; Xu, Xin
2013-12-01
Goal representation heuristic dynamic programming (GrHDP) is proposed in this paper to demonstrate online learning in the Markov decision process. In addition to the (external) reinforcement signal in literature, we develop an adaptively internal goal/reward representation for the agent with the proposed goal network. Specifically, we keep the actor-critic design in heuristic dynamic programming (HDP) and include a goal network to represent the internal goal signal, to further help the value function approximation. We evaluate our proposed GrHDP algorithm on two 2-D maze navigation problems, and later on one 3-D maze navigation problem. Compared to the traditional HDP approach, the learning performance of the agent is improved with our proposed GrHDP approach. In addition, we also include the learning performance with two other reinforcement learning algorithms, namely Sarsa(λ) and Q-learning, on the same benchmarks for comparison. Furthermore, in order to demonstrate the theoretical guarantee of our proposed method, we provide the characteristics analysis toward the convergence of weights in neural networks in our GrHDP approach. PMID:24805221
Abay Molla Kassa
2014-07-01
Full Text Available In this paper, we developed a novel algorithmic approach for thesolution of multi-parametric non-convex programming problems withcontinuous decision variables. The basic idea of the proposedapproach is based on successive convex relaxation of each non-convexterms and sensitivity analysis theory. The proposed algorithm isimplemented using MATLAB software package and numericalexamples are presented to illustrate the effectiveness andapplicability of the proposed method on multi-parametric non-convexprogramming problems with polyhedral constraints.
Dynamically Computing Approximate Frequency Counts in Sliding Window over Data Stream
无
2006-01-01
This paper presents two one-pass algorithms for dynamically computing frequency counts in sliding window over a data stream-computing frequency counts exceeding user-specified threshold ε. The first algorithm constructs sub-windows and deletes expired sub-windows periodically in sliding window, and each sub-window maintains a summary data structure. The first algorithm outputs at most 1/ε + 1 elements for frequency queries over the most recent N elements. The second algorithm adapts multiple levels method to deal with data stream. Once the sketch of the most recent N elements has been constructed, the second algorithm can provides the answers to the frequency queries over the most recent n(n≤N) elements. The second algorithm outputs at most 1/ε+2 elements. The analytical and experimental results show that our algorithms are accurate and effective.
Yan Li
2012-01-01
Full Text Available We consider the dynamic proportional reinsurance in a two-dimensional compound Poisson risk model. The optimization in the sense of minimizing the ruin probability which is defined by the sum of subportfolio is being ruined. Via the Hamilton-Jacobi-Bellman approach we find a candidate for the optimal value function and prove the verification theorem. In addition, we obtain the Lundberg bounds and the Cramér-Lundberg approximation for the ruin probability and show that as the capital tends to infinity, the optimal strategies converge to the asymptotically optimal constant strategies. The asymptotic value can be found by maximizing the adjustment coefficient.
We consider one-dimensional interacting spinless fermions with a non-linear spectrum in a clean quantum wire (non-linear bosonization). We compute diagrammatically the one-dimensional dynamical structure factor, S(ω, q), beyond the Tomonaga-Luttinger approximation focusing on its tails, i.e. vertical bar ω vertical bar >> vq. We provide a re-derivation, through diagrammatics, of the result of Pustilnik, Mishchenko, Glazman, and Andreev. We also extend their results to finite temperatures and long-range interactions. As applications we determine curvature and interaction corrections to the small- momentum, high-frequency conductivity and the electron-electron scattering rate. (author)
Masmoudi, Nabil
2014-01-01
We present an approximate, but efficient and sufficiently accurate P-wave ray tracing and dynamic ray tracing procedure for 3D inhomogeneous, weakly orthorhombic media with varying orientation of symmetry planes. In contrast to commonly used approaches, the orthorhombic symmetry is preserved at any point of the model. The model is described by six weak-anisotropy parameters and three Euler angles, which may vary arbitrarily, but smoothly, throughout the model. We use the procedure for the calculation of rays and corresponding two-point traveltimes in a VSP experiment in a part of the BP benchmark model generalized to orthorhombic symmetry.
Speed of sound in solid molecular hydrogen-deuterium: Quantum Molecular Dynamics Approximation
Guerrero, Carlo Luis; Perlado, Jose Manuel
2016-05-01
Uniformity of the solid layer is one of the critical points for an efficient ignition of the Deuterium-Tritium (DT) target. During the compression process this layer, perturbations grow as the Rayleigh-Taylor instability. Knowing the mechanical properties of this layer and its thermo-mechanical limits is necessary if we want to control or to minimize these instabilities. In this work we have used a simplified approach, replacing the DT ice system with a mixture of hydrogen-deuterium (HD) because beta decay of tritium complicates the analysis in the former case. Through simulation with ab initio methods we have calculated the elastic constants, the bulk modulus and sound velocity for hydrogen isotopes in solid molecular state. In this work we present the results for hydrogen-deuterium mixtures 50%-50%, at 15 K and with a compression which covers the range of 1 to 15 GPa. This system is interesting for study the early stages of the dynamic compression and provides conditions that are close to the manufacture of DT target in inertial confinement fusion. Discontinuities in the curve that have been observed on pure hydrogen, which are associated with phase transitions and the phase hysteresis.
Dodin, Amro; Brumer, Paul
2015-01-01
We present closed-form analytic solutions to non-secular Bloch-Redfield master equations for quantum dynamics of a V-type system driven by weak coupling to a thermal bath. We focus on noise-induced Fano coherences among the excited states induced by incoherent driving of the V-system initially in the ground state. For suddenly turned-on incoherent driving, the time evolution of the coherences is determined by the damping parameter $\\zeta=\\frac{1}{2}(\\gamma_1+\\gamma_2)/\\Delta_p$, where $\\gamma_i$ are the radiative decay rates of the excited levels $i=1,2$, and $\\Delta_p=\\sqrt{\\Delta^2 + (1-p^2)\\gamma_1\\gamma_2}$ depends on the excited-state level splitting $\\Delta>0$ and the angle between the transition dipole moments in the energy basis. The coherences oscillate as a function of time in the underdamped limit ($\\zeta\\gg1$), approach a long-lived quasi-steady state in the overdamped limit ($\\zeta\\ll 1$), and display an intermediate behavior at critical damping ($\\zeta= 1$). The sudden incoherent turn-on generat...
Dodin, Amro; Tscherbul, Timur V; Brumer, Paul
2016-06-28
Closed-form analytic solutions to non-secular Bloch-Redfield master equations for quantum dynamics of a V-type system driven by weak coupling to a thermal bath, relevant to light harvesting processes, are obtained and discussed. We focus on noise-induced Fano coherences among the excited states induced by incoherent driving of the V-system initially in the ground state. For suddenly turned-on incoherent driving, the time evolution of the coherences is determined by the damping parameter ζ=12(γ1+γ2)/Δp, where γi are the radiative decay rates of the excited levels i = 1, 2, and Δp=Δ(2)+(1-p(2))γ1γ2 depends on the excited-state level splitting Δ > 0 and the angle between the transition dipole moments in the energy basis. The coherences oscillate as a function of time in the underdamped limit (ζ ≫ 1), approach a long-lived quasi-steady state in the overdamped limit (ζ ≪ 1), and display an intermediate behavior at critical damping (ζ = 1). The sudden incoherent turn-on is shown to generate a mixture of excited eigenstates |e1〉 and |e2〉 and their in-phase coherent superposition |ϕ+〉=1r1+r2(r1|e1〉+r2|e2〉), which is remarkably long-lived in the overdamped limit (where r1 and r2 are the incoherent pumping rates). Formation of this coherent superposition enhances the decay rate from the excited states to the ground state. In the strongly asymmetric V-system where the coupling strengths between the ground state and the excited states differ significantly, additional asymptotic quasistationary coherences are identified, which arise due to slow equilibration of one of the excited states. Finally, we demonstrate that noise-induced Fano coherences are maximized with respect to populations when r1 = r2 and the transition dipole moments are fully aligned. PMID:27369498
Dodin, Amro; Tscherbul, Timur V.; Brumer, Paul
2016-06-01
Closed-form analytic solutions to non-secular Bloch-Redfield master equations for quantum dynamics of a V-type system driven by weak coupling to a thermal bath, relevant to light harvesting processes, are obtained and discussed. We focus on noise-induced Fano coherences among the excited states induced by incoherent driving of the V-system initially in the ground state. For suddenly turned-on incoherent driving, the time evolution of the coherences is determined by the damping parameter ζ = /1 2 ( γ 1 + γ 2) / Δ p , where γi are the radiative decay rates of the excited levels i = 1, 2, and Δ p = √{ Δ 2 + ( 1 - p 2) γ 1 γ 2 } depends on the excited-state level splitting Δ > 0 and the angle between the transition dipole moments in the energy basis. The coherences oscillate as a function of time in the underdamped limit (ζ ≫ 1), approach a long-lived quasi-steady state in the overdamped limit (ζ ≪ 1), and display an intermediate behavior at critical damping (ζ = 1). The sudden incoherent turn-on is shown to generate a mixture of excited eigenstates |e1> and |e2> and their in-phase coherent superposition | ϕ + > = /1 √{ r 1 + r 2 } ( √{ r 1 } | e 1 > + √{ r 2 } | e 2 >) , which is remarkably long-lived in the overdamped limit (where r1 and r2 are the incoherent pumping rates). Formation of this coherent superposition enhances the decay rate from the excited states to the ground state. In the strongly asymmetric V-system where the coupling strengths between the ground state and the excited states differ significantly, additional asymptotic quasistationary coherences are identified, which arise due to slow equilibration of one of the excited states. Finally, we demonstrate that noise-induced Fano coherences are maximized with respect to populations when r1 = r2 and the transition dipole moments are fully aligned.
Spatial cluster detection using dynamic programming
Sverchkov Yuriy
2012-03-01
Full Text Available Abstract Background The task of spatial cluster detection involves finding spatial regions where some property deviates from the norm or the expected value. In a probabilistic setting this task can be expressed as finding a region where some event is significantly more likely than usual. Spatial cluster detection is of interest in fields such as biosurveillance, mining of astronomical data, military surveillance, and analysis of fMRI images. In almost all such applications we are interested both in the question of whether a cluster exists in the data, and if it exists, we are interested in finding the most accurate characterization of the cluster. Methods We present a general dynamic programming algorithm for grid-based spatial cluster detection. The algorithm can be used for both Bayesian maximum a-posteriori (MAP estimation of the most likely spatial distribution of clusters and Bayesian model averaging over a large space of spatial cluster distributions to compute the posterior probability of an unusual spatial clustering. The algorithm is explained and evaluated in the context of a biosurveillance application, specifically the detection and identification of Influenza outbreaks based on emergency department visits. A relatively simple underlying model is constructed for the purpose of evaluating the algorithm, and the algorithm is evaluated using the model and semi-synthetic test data. Results When compared to baseline methods, tests indicate that the new algorithm can improve MAP estimates under certain conditions: the greedy algorithm we compared our method to was found to be more sensitive to smaller outbreaks, while as the size of the outbreaks increases, in terms of area affected and proportion of individuals affected, our method overtakes the greedy algorithm in spatial precision and recall. The new algorithm performs on-par with baseline methods in the task of Bayesian model averaging. Conclusions We conclude that the dynamic
The combinatorial explosion produced by the multi-state, multi-subunit character of CaMKII has made analysis and modeling of this key signaling protein a significant challenge. Using rule-based and particle-based approaches, we construct exact models of CaMKII holoenzyme dynamics and study these models as a function of the number of subunits per holoenzyme, N. Without phosphatases the dynamics of activation are independent of the holoenzyme structure unless phosphorylation significantly alters the kinase activity of a subunit. With phosphatases the model is independent of holoenzyme size for N > 6. We introduce an infinite subunit holoenzyme approximation (ISHA), which simplifies the modeling by eliminating the combinatorial complexities encountered in any finite holoenzyme model. The ISHA is an excellent approximation to the full system over a broad range of physiologically relevant parameters. Finally, we demonstrate that the ISHA reproduces the behavior of exact models during synaptic plasticity protocols, which justifies its use as a module in large models of synaptic plasticity. (paper)
Three-dimensional programs were developed and proved to be fast and reliable tools for the analysis in each phase of the design of nuclear reactor building structures. Short descriptions and size of models used are given for the following analyses: preliminary analysis for all structures of a BWR reactor containment building; preliminary analysis for selection of structural solution of a reactor pedestal structure; independent checking analysis for the primary containment structures of a BWR; independent checking analysis of a reactor shield structure, and test analysis with a simplified model for the seismic response analysis of a reactor drywell structure. Description of analysis and model sizes for two complex structures is also given: building structure of a breeder reactor with detailed non-linear analysis of the internal support structure for 30 million pound hypothetic accident loads. Model sizes: 1570 and 1032 nodes respectively. Drywell structure, which serves as a primary containment and also carries the weight of the upper fuel pools. Loading conditions include internal and external pressures, thermal, seismic and other loads. Model size: 1350 nodes
Grigis A
2006-01-01
Full Text Available A method for determination and two methods for approximation of the domain of attraction Da(0 of the asymptotically stable zero steady state of an autonomous, ℝ-analytical, discrete dynamical system are presented. The method of determination is based on the construction of a Lyapunov function V, whose domain of analyticity is Da(0. The first method of approximation uses a sequence of Lyapunov functions Vp, which converge to the Lyapunov function V on Da(0. Each Vp defines an estimate Np of Da(0. For any x ∈ Da(0, there exists an estimate which contains x. The second method of approximation uses a ball B(R ⊂ Da(0 which generates the sequence of estimates Mp = f-p(B(R. For any x ∈ Da(0, there exists an estimate which contains x. The cases ||∂0f||<1 and ρ(∂0f < 1 ≤||∂0f|| are treated separately because significant differences occur.
A Dynamic Programming Approach to Adaptive Fractionation
Ramakrishnan, Jagdish; Bortfeld, Thomas; Tsitsiklis, John
2011-01-01
We formulate a previously introduced adaptive fractionation problem in a dynamic programming (DP) framework and explore various solution techniques. The two messages of this paper are: (i) the DP model is a useful framework for studying adaptive radiation therapy, particularly adaptive fractionation, and (ii) there is a potential for substantial decrease in dose to the primary organ-at-risk (OAR), or equivalently increase in tumor escalation, when using an adaptive fraction size. The essence of adaptive fractionation is to increase the fraction size when observing a "favorable" anatomy or when the tumor and OAR are far apart and to decrease the fraction size when they are close together. Given that a fixed prescribed dose must be delivered to the tumor over the course of the treatment, such an approach results in a lower cumulative dose to the OAR when compared to that resulting from standard fractionation. We first establish a benchmark by using the DP algorithm to solve the problem exactly. In this case, we...
Segmentation of Indus Texts: A Dynamic Programming Approach.
Siromoney, Gift; Huq, Abdul
1988-01-01
Demonstrates how a dynamic programing algorithm can be developed to segment unusually long written inscriptions from the Indus Valley Civilization. Explains the problem of segmentation, discusses the dynamic programing algorithm used, and includes tables which illustrate the segmentation of the inscriptions. (GEA)
We evaluate the accuracy of local-density approximations (LDAs) using explicit molecular dynamics simulations of binary electrolytes comprised of equisized ions in an implicit solvent. The Bikerman LDA, which considers ions to occupy a lattice, poorly captures excluded volume interactions between primitive model ions. Instead, LDAs based on the Carnaha-Starling (CS) hard-sphere equation of state capture simulated values of ideal and excess chemical potential profiles extremely well, as is the relationship between surface charge density and electrostatic potential. Excellent agreement between the EDL capacitances predicted by CS-LDAs and computed in molecular simulations is found even in systems where ion correlations drive strong density and free charge oscillations within the EDL, despite the inability of LDAs to capture the oscillations in the detailed EDL profiles
ALPprolog --- A New Logic Programming Method for Dynamic Domains
Drescher, Conrad
2011-01-01
Logic programming is a powerful paradigm for programming autonomous agents in dynamic domains, as witnessed by languages such as Golog and Flux. In this work we present ALPprolog, an expressive, yet efficient, logic programming language for the online control of agents that have to reason about incomplete information and sensing actions.
Molecular dynamics is a simulation technique that can be used to study failure in solids, provided the inter-atomic potential energy is able to account for the complex mechanisms at failure. Reactive potentials fitted on ab initio results or on experimental values have the ability to adapt to any complex atomic arrangement and, therefore, are suited to simulate failure. But the complexity of these potentials, together with the size of the systems considered, make simulations computationally expensive. In order to improve the efficiency of numerical simulations, simpler harmonic potentials can be used instead of complex reactive potentials in the regions where the system is close to its ground state and a harmonic approximation reasonably fits the actual reactive potential. However the validity and precision of such an approach has not been investigated in detail yet. We present here a methodology for constructing a reduced potential and combining it with the reactive one. We also report some important features of crack propagation that may be affected by the coupling of reactive and reduced potentials. As an illustrative case, we model a crystalline two-dimensional material (graphene) with a reactive empirical bond-order potential (REBO) or with harmonic potentials made of bond and angle springs that are designed to reproduce the second order approximation of REBO in the ground state. We analyze the consistency of this approximation by comparing the mechanical behavior and the phonon spectra of systems modeled with these potentials. These tests reveal when the anharmonicity effects appear. As anharmonic effects originate from strain, stress or temperature, the latter quantities are the basis for establishing coupling criteria for on the fly substitution in large simulations
A. J. G. Babu; Balasubramanian Ram
1988-01-01
This paper suggests a method of formulating any nonlinear integer programming problem, with any number of constraints, as an equivalent single constraint problem, thus reducing the dimensionality of the associated dynamic programming problem.
Costa, Rafael S.; Machado, Daniel; Rocha, Isabel;
2010-01-01
The construction of dynamic metabolic models at reaction network level requires the use of mechanistic enzymatic rate equations that comprise a large number of parameters. The lack of knowledge on these equations and the difficulty in the experimental identification of their associated parameters...... using the hybrid model composed of Michaelis–Menten and the approximate lin-log kinetics indicate that this is a possible suitable approach to model complex large-scale networks where the exact rate laws are unknown.......The construction of dynamic metabolic models at reaction network level requires the use of mechanistic enzymatic rate equations that comprise a large number of parameters. The lack of knowledge on these equations and the difficulty in the experimental identification of their associated parameters......, represent nowadays the limiting factor in the construction of such models. In this study, we compare four alternative modeling approaches based on Michaelis–Menten kinetics for the bi-molecular reactions and different types of simplified rate equations for the remaining reactions (generalized mass action...
We develop a method that can constrain any local exchange-correlation potential to preserve basic exact conditions. Using the method of Lagrange multipliers, we calculate for each set of given Kohn-Sham orbitals a constraint-preserving potential which is closest to the given exchange-correlation potential. The method is applicable to both the time-dependent (TD) and independent cases. The exact conditions that are enforced for the time-independent case are Galilean covariance, zero net force and torque, and Levy-Perdew virial theorem. For the time-dependent case we enforce translational covariance, zero net force, Levy-Perdew virial theorem, and energy balance. We test our method on the exchange (only) Krieger-Li-Iafrate (xKLI) approximate-optimized effective potential for both cases. For the time-independent case, we calculated the ground state properties of some hydrogen chains and small sodium clusters for some constrained xKLI potentials and Hartree-Fock (HF) exchange. The results (total energy, Kohn-Sham eigenvalues, polarizability, and hyperpolarizability) indicate that enforcing the exact conditions is not important for these cases. On the other hand, in the time-dependent case, constraining both energy balance and zero net force yields improved results relative to TDHF calculations. We explored the electron dynamics in small sodium clusters driven by cw laser pulses. For each laser pulse we compared calculations from TD constrained xKLI, TD partially constrained xKLI, and TDHF. We found that electron dynamics such as electron ionization and moment of inertia dynamics for the constrained xKLI are most similar to the TDHF results. Also, energy conservation is better by at least one order of magnitude with respect to the unconstrained xKLI. We also discuss the problems that arise in satisfying constraints in the TD case with a non-cw driving force.
Dynamic Internship Programs: Comparison Between Two Universities
Mark C. Wallace
2012-01-01
Internship and experiential learning programs are compared between The University of Rhode Island (URI), Department of Natural Resources Science (1992-1996), and Texas Tech University (TTU), Department of Natural Resources Management (1997-current) through the periods in which I was associated with them. I review and compare the kinds of administrative support and faculty involvement, the numbers of students and kinds of opportunities provided in each program. Programs differed markedly: URI ...
Granular contact dynamics using mathematical programming methods
Krabbenhoft, K.; Lyamin, A. V.; Huang, J.;
2012-01-01
granular contact dynamics formulation uses an implicit time discretization, thus allowing for large time steps. Moreover, in the limit of an infinite time step, the general dynamic formulation reduces to a static formulation that is useful in simulating common quasi-static problems such as triaxial tests...... is developed and it is concluded that the associated sliding rule, in the context of granular contact dynamics, may be viewed as an artifact of the time discretization and that the use of an associated flow rule at the particle scale level generally is physically acceptable. (C) 2012 Elsevier Ltd. All rights...
Dynamic Programming Algorithms in Speech Recognition
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.
Capacities, Measurable Selection and Dynamic Programming Part I: Abstract Framework
Karoui, Nicole El; Tan, Xiaolu
2013-01-01
We give a brief presentation of the capacity theory and show how it derives naturally a measurable selection theorem following the approach of Dellacherie (1972). Then we present the classical method to prove the dynamic programming of discrete time stochastic control problem, using measurable selection arguments. At last, we propose a continuous time extension, that is an abstract framework for the continuous time dynamic programming principle (DPP).
Applying dynamic programming to a gas-lift optimization problem
Camponogara, Eduardo; Nakashima, Paulo H.R. [Santa Catarina Univ., Florianopolis (Brazil). Dept. de Automacao e Sistemas]. E-mails: camponog@das.ufsc.br; phrn@das.ufsc.br
2003-07-01
The ever-increasing demand for nonrenewable resources and the pressure from stockholders are two forces pressing the oil industry for higher efficiency. The opportunities for advances abound in all sectors of the industry, in particular production processes in gas-lift oil wells, which are often favored to draw oil from high-depth reservoirs. Of concern in this paper is the task of distributing the limited supply of gas to the wells so as to induce an optimal oil production. Narrowing this task to the steady-state response of the wells gives rise to the gas-lift optimization problem, whose variables decide which wells should be active as well as the gas-injection and whose objective is profit maximization. The paper elaborates on a few properties of the problem and delivers a dynamic programming algorithm to find approximate solutions. The effectiveness of the algorithm was demonstrated by contrasting its solutions against upper bounds obtained with continuous relaxation. As closure, the paper outlines a few directions for future research. (author)
Optimal Control of a Fed-batch Fermentation Process by Neuro-Dynamic Programming
Tatiana Ilkova; Stoyan Tzonkov
2004-01-01
In this paper the method for optimal control of a fermentation process is presented, that is based on an approach for optimal control - Neuro-Dynamic programming. For this aim the approximation neural network is developed and the decision of the optimization problem is improved by an iteration mode founded on the Bellman equation. With this approach computing time and procedure are decreased and quality of the biomass at the end of the process is increased.
Optimal Control of a Fed-batch Fermentation Process by Neuro-Dynamic Programming
Tatiana Ilkova
2004-10-01
Full Text Available In this paper the method for optimal control of a fermentation process is presented, that is based on an approach for optimal control - Neuro-Dynamic programming. For this aim the approximation neural network is developed and the decision of the optimization problem is improved by an iteration mode founded on the Bellman equation. With this approach computing time and procedure are decreased and quality of the biomass at the end of the process is increased.
Robust Adaptive Dynamic Programming for Optimal Nonlinear Control Design
Jiang, Yu; Jiang, Zhong-Ping
2013-01-01
This paper studies the robust optimal control design for uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (robust-ADP). The objective is to fill up a gap in the past literature of ADP where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The...
Dynamic Performance Tuning Supported by Program Specification
Eduardo César
2002-01-01
Full Text Available Performance analysis and tuning of parallel/distributed applications are very difficult tasks for non-expert programmers. It is necessary to provide tools that automatically carry out these tasks. These can be static tools that carry out the analysis on a post-mortem phase or can tune the application on the fly. Both kind of tools have their target applications. Static automatic analysis tools are suitable for stable application while dynamic tuning tools are more appropriate to applications with dynamic behaviour. In this paper, we describe KappaPi as an example of a static automatic performance analysis tool, and also a general environment based on parallel patterns for developing and dynamically tuning parallel/distributed applications.
INDDGO: Integrated Network Decomposition & Dynamic programming for Graph Optimization
Groer, Christopher S [ORNL; Sullivan, Blair D [ORNL; Weerapurage, Dinesh P [ORNL
2012-10-01
It is well-known that dynamic programming algorithms can utilize tree decompositions to provide a way to solve some \\emph{NP}-hard problems on graphs where the complexity is polynomial in the number of nodes and edges in the graph, but exponential in the width of the underlying tree decomposition. However, there has been relatively little computational work done to determine the practical utility of such dynamic programming algorithms. We have developed software to construct tree decompositions using various heuristics and have created a fast, memory-efficient dynamic programming implementation for solving maximum weighted independent set. We describe our software and the algorithms we have implemented, focusing on memory saving techniques for the dynamic programming. We compare the running time and memory usage of our implementation with other techniques for solving maximum weighted independent set, including a commercial integer programming solver and a semi-definite programming solver. Our results indicate that it is possible to solve some instances where the underlying decomposition has width much larger than suggested by the literature. For certain types of problems, our dynamic programming code runs several times faster than these other methods.
Dynamic Learning Objects to Teach Java Programming Language
Narasimhamurthy, Uma; Al Shawkani, Khuloud
2010-01-01
This article describes a model for teaching Java Programming Language through Dynamic Learning Objects. The design of the learning objects was based on effective learning design principles to help students learn the complex topic of Java Programming. Visualization was also used to facilitate the learning of the concepts. (Contains 1 figure and 2…
Nonlinear beam dynamics experimental program at SPEAR
Since nonlinear effects can impose strict performance limitations on modern colliders and storage rings, future performance improvements depend on further understanding of nonlinear beam dynamics. Experimental studies of nonlinear beam motion in three-dimensional space have begun in SPEAR using turn-by-turn transverse and longitudinal phase-space monitors. This paper presents preliminary results from an on-going experiment in SPEAR
Tatiana Ilkova
2005-01-01
A fed-batch fermentation process is examined in this paper for experimental and further dynamic optimization. The static optimization is developed for to be found out the optimal initial concentrations of the basic biochemical variables - biomass, substrate and substrate in the feeding solution. For the static optimization of the process the method of Dynamic programming is used. After that these initial values are used for the dynamic optimization carried out by a submethod of Neuro-dynamic ...
De Backer, A.; Sand, A.; Ortiz, C. J.; Domain, C.; Olsson, P.; Berthod, E.; Becquart, C. S.
2016-02-01
The damage produced by primary knock-on atoms (PKA) in W has been investigated from the threshold displacement energy (TDE) where it produces one self interstitial atom-vacancy pair to larger energies, up to 100 keV, where a large molten volume is formed. The TDE has been determined in different crystal directions using the Born-Oppenheimer density functional molecular dynamics (DFT-MD). A significant difference has been observed without and with the semi-core electrons. Classical MD has been used with two different empirical potentials characterized as ‘soft’ and ‘hard’ to obtain statistics on TDEs. Cascades of larger energy have been calculated, with these potentials, using a model that accounts for electronic losses (Sand et al 2013 Europhys. Lett. 103 46003). Two other sets of cascades have been produced using the binary collision approximation (BCA): a Monte Carlo BCA using SDTrimSP (Eckstein et al 2011 SDTrimSP: Version 5.00. Report IPP 12/8) (similar to SRIM www.srim.org) and MARLOWE (RSICC Home Page. (https://rsicc.ornl.gov/codes/psr/psr1/psr-137.html) (accessed May, 2014)). The comparison of these sets of cascades gave a recombination distance equal to 12 Å which is significantly larger from the one we reported in Hou et al (2010 J. Nucl. Mater. 403 89) because, here, we used bulk cascades rather than surface cascades which produce more defects (Stoller 2002 J. Nucl. Mater. 307 935, Nordlund et al 1999 Nature 398 49). Investigations on the defect clustering aspect showed that the difference between BCA and MD cascades is considerably reduced after the annealing of the cascade debris at 473 K using our Object Kinetic Monte Carlo model, LAKIMOCA (Domain et al 2004 J. Nucl. Mater. 335 121).
Macroscopic reality and the dynamical reduction program
With reference to recently proposed theoretical models accounting for reduction in terms of a unified dynamics governing all physical processes, we analyze the problem of working out a worldview accommodating our knowledge about natural phenomena. We stress the relevant conceptual differences between the considered models and standard quantum mechanics. In spite of the fact that both theories describe individual physical systems within a genuine Hilbert space framework, the nice features of spontaneous reduction theories drastically limit the class of states which are dynamically stable. This allows one to work out a description of the world in terms of a mass density function in ordinary configuration space. A topology based on this function and differing radically from the one characterizing the Hilbert space is introduced and in terms of it the idea of similarity of macroscopic situations is made precise. Finally it is shown how the formalism and the proposed interpretation yield a natural criterion for establishing the psychophysical parallelism. The conclusion is that, within the considered theoretical models and at the nonrelativistic level, one can satisfy all sensible requirements for a consistent, unified, and objective description of reality at the macroscopic level. (author). 16 refs
Regression Dynamic Programming for Large Stochastic Reservoir Systems
Shoemaker, C. A.; Fan, D. K.
2001-12-01
Regression Dynamic Programming has been developed by the authors and D. Ruppert as a computationally efficient procedure for solving higher dimensional stochastic dynamic programming problems, such as those arising in the solution of the optimal release policy in a system of reservoirs with nonlinear dynamics and stochastic inflow and hydropower demand. The dimension of the problem is a function of the number of reservoirs and the number of hydrologic state variables. The dimensionality difficulties of DP are mitigated in Regression DP by coupling an experimental design procedure with a multidimensional spline fit that is determined by regression. This approach differs from that used by Chen, Ruppert, and Shoemaker (Oper. Res., 1999) in that we have applied a simpler and more computationally efficient regression technique than was previously done and we implemented a Latin Hypercube experimental design. Comparisons with an orthogonal array show that the Latin Hypercube is a more efficient experimental design for a given level of accuracy. This is also the first application of this method to reservoir systems. Several stochastic examples with nonlinear cost functions have been done, including one example with 13 reservoirs and another example with a hydrologic state variable and a nonlinear term associated with evaporation. The developed approach described is a general method for solving a true stochastic dynamic programming problem. Our Regression Dynamic Programming method does not make any assumptions about linearity, deterministic relationships, aggregation of state variables, or sampling of future scenarios, which are methods of changing the problem formulation that have been used in other published reservoir applications in order to avoid the computational effort of solving the true dynamic programming problem. In general, this gives Regression Dynamic Programming a significant advantage in terms of accuracy, especially for problems with a large number of time
Modelling of windmill induction generators in dynamic simulation programs
Akhmatov, Vladislav; Knudsen, Hans
1999-01-01
For AC networks with large amounts of induction generators-in case of e.g. windmills-the paper demonstrates a significant discrepancy in the simulated voltage recovery after faults in weak networks, when comparing result obtained with dynamic stability programs and transient programs, respectivel...... rotor. It is shown that it is possible to include a transient model in dynamic stability programs and thus obtain correct results also in dynamic stability programs. A mechanical model of the shaft system has also been included in the generator model......For AC networks with large amounts of induction generators-in case of e.g. windmills-the paper demonstrates a significant discrepancy in the simulated voltage recovery after faults in weak networks, when comparing result obtained with dynamic stability programs and transient programs, respectively...... with and without a model of the mechanical shaft. The reason for the discrepancies are explained, and it is shown that the phenomenon is due partly to the presence of DC offset currents in the induction machine stator, and partly to the mechanical shaft system of the wind turbine and the generator...
Step by step parallel programming method for molecular dynamics code
Parallel programming for a numerical simulation program of molecular dynamics is carried out with a step-by-step programming technique using the two phase method. As a result, within the range of a certain computing parameters, it is found to obtain parallel performance by using the level of parallel programming which decomposes the calculation according to indices of do-loops into each processor on the vector parallel computer VPP500 and the scalar parallel computer Paragon. It is also found that VPP500 shows parallel performance in wider range computing parameters. The reason is that the time cost of the program parts, which can not be reduced by the do-loop level of the parallel programming, can be reduced to the negligible level by the vectorization. After that, the time consuming parts of the program are concentrated on less parts that can be accelerated by the do-loop level of the parallel programming. This report shows the step-by-step parallel programming method and the parallel performance of the molecular dynamics code on VPP500 and Paragon. (author)
Dynamic electricity pricing—Which programs do consumers prefer?
Dynamic pricing is being discussed as one method of demand side management (DSM) which could be crucial for integrating more renewable energy sources into the electricity system. At the same time, there have been very few analyses of consumer preferences in this regard: Which type of pricing program are consumers most likely to choose and why? This paper sheds some light on these issues based on two empirical studies from Germany: (1) A questionnaire study including a conjoint analysis-design and (2) A field experiment with test-residents of a smart home laboratory. The results show that consumers are open to dynamic pricing, but prefer simple programs to complex and highly dynamic ones; smart home technologies including demand automation are seen as a prerequisite for DSM. The study provides some indications that consumers might be more willing to accept more dynamic pricing programs if they have the chance to experience in practice how these can be managed in everyday life. At the same time, the individual and societal advantages of such programs are not obvious to consumers. For this reason, any market roll-out will need to be accompanied by convincing communication and information campaigns to ensure that these advantages are perceived. - Highlights: • Little is known about consumer preferences on dynamic pricing. • Two studies are conducted to analyze this topic. • A survey shows that consumers without experience prefer conventional programs. • Test residents of a smart home were more open to dynamic pricing. • They also prefer well-structured programs
Non-convex dynamic programming and optimal investment
Penannen, Teemu; Perkkiö, Ari-Pekka; Rásonyi, Miklós
2015-01-01
We establish the existence of minimizers in a rather general setting of dynamic stochastic optimization without assuming either convexity or coercivity of the objective function. We apply this to prove the existence of optimal portfolios for non-concave utility maximization problems in financial market models with frictions (such as illiquidity), a first result of its kind. The proofs are based on the dynamic programming principle whose validity is established under quite general assumptions.
Including UPFC dynamic phasor model into transient stability program
Ni, Y; Liu, H.; Zhu, H; Li, Y
2005-01-01
In this paper a novel time simulation approach is introduced to implement transient stability analysis with FACTS devices, in which FACTS devices will use dynamic phasor models and interface properly with conventional electromechanical transient-model-based stability program. The unified power flow controller (UPFC) is used as an example to demo the realization of the approach. In the paper, the UPFC dynamic phasor model and control scheme are presented first and followed by the interface for...
Dynamic Programming for Mean-field type Control
Laurière, Mathieu; Pironneau, Olivier
2014-01-01
For mean-field type control problems, stochastic dynamic programming requires adaptation. We propose to reformulate the problem as a distributed control problem by assuming that the PDF $\\rho$ of the stochastic process exists. Then we show that Bellman's principle applies to the dynamic programming value function $V(\\tau,\\rho_\\tau)$ where the dependency on $\\rho_\\tau$ is functional as in P.L. Lions' analysis of mean-filed games (2007). We derive HJB equations and apply them to two examples, a...
Discrete Globalised Dual Heuristic Dynamic Programming in Control of the Two-Wheeled Mobile Robot
Marcin Szuster
2014-01-01
Full Text Available Network-based control systems have been emerging technologies in the control of nonlinear systems over the past few years. This paper focuses on the implementation of the approximate dynamic programming algorithm in the network-based tracking control system of the two-wheeled mobile robot, Pioneer 2-DX. The proposed discrete tracking control system consists of the globalised dual heuristic dynamic programming algorithm, the PD controller, the supervisory term, and an additional control signal. The structure of the supervisory term derives from the stability analysis realised using the Lyapunov stability theorem. The globalised dual heuristic dynamic programming algorithm consists of two structures: the actor and the critic, realised in a form of neural networks. The actor generates the suboptimal control law, while the critic evaluates the realised control strategy by approximation of value function from the Bellman’s equation. The presented discrete tracking control system works online, the neural networks’ weights adaptation process is realised in every iteration step, and the neural networks preliminary learning procedure is not required. The performance of the proposed control system was verified by a series of computer simulations and experiments realised using the wheeled mobile robot Pioneer 2-DX.
A note on dynamic programming in accounts receivable management
Dirickx, Y.M.I.; Kistner, K.-P.
1982-01-01
The paper considers a dynamic programming formulation of the accounts receivable problem for single outstanding amounts. An optimal collection policy can be computed efficiently by invoking a “planning horizon” result that determines a time period beyond which the decision process cannot extend. The optimality of so called monotone policies is shown under rather intuitive restrictions on the collection probabilities.
Parallel dynamic programming for on-line flight path optimization
Slater, G. L.; Hu, K.
1989-01-01
Parallel systolic algorithms for dynamic programming(DP) and their respective hardware implementations are presented for a problem in on-line trajectory optimization. The method is applied to a model for helicopter flight path optimization through a complex constraint region. This problem has application to an air traffic control problem and also to a terrain following/threat avoidance problem.