Exploiting symmetries for exponential error reduction in path integral Monte Carlo

The path integral of a quantum system with an exact symmetry can be written as a sum of functional integrals each giving the contribution from quantum states with definite symmetry properties. We propose a strategy to compute each of them, normalized to the one with vacuum quantum numbers, by a Monte Carlo procedure whose cost increases power-like with the time extent of the lattice. This is achieved thanks to a multi-level integration scheme, inspired by the transfer matrix formalism, which exploits the symmetry and the locality in time of the underlying statistical system. As a result the cost of computing the lowest energy level in a given channel, its multiplicity and its matrix elements is exponentially reduced with respect to the standard path-integral Monte Carlo. We test the strategy with a one-dimensional harmonic oscillator, by computing the ratio of the parity odd over the parity even functional integrals and the two-point correlation function. The cost of the simulations scales as expected. In particular the effort for computing the lowest energy eigenvalue in the parity odd sector grows linearly with the time extent. At a fixed CPU time, the statistical error on the two-point correlation function is exponentially reduced with respect to the standard Monte Carlo procedure, and at large time distances it is lowered by many orders of magnitude.     

A parallel implementation of the Wang-Landau algorithm

The Wang-Landau algorithm is a flat-histogram Monte Carlo method that performs random walks in the configuration space of a system to obtain a close estimation of the density of states iteratively. It has been applied successfully to many research fields. In this paper, we propose a parallel implementation of the Wang-Landau algorithm on computers of shared memory architectures by utilizing the OpenMP API for distributed computing. This implementation is applied to Ising model systems with promising speedups. We also examine the effects on the running speed when using different strategies in accessing the shared memory space during the updating procedure. The allowance of data race is recommended in consideration of the simulation efficiency. Such treatment does not affect the accuracy of the final density of states obtained.     

Numerical integration using Wang-Landau sampling

We report a new application of Wang-Landau sampling to numerical integration that is straightforward to implement. It is applicable to a wide variety of integrals without restrictions and is readily generalized to higher-dimensional problems. The feasibility of the method results from a reinterpretation of the density of states in statistical physics to an appropriate measure for numerical integration. The properties of this algorithm as a new kind of Monte Carlo integration scheme are investigated with some simple integrals, and a potential application of the method is illustrated by the evaluation of integrals arising in perturbation theory of quantum many-body systems.     

Symmetries and exponential error reduction in Yang-Mills theories on the lattice

The partition function of a quantum field theory with an exact symmetry can be decomposed into a sum of functional integrals each giving the contribution from states with definite symmetry properties. The composition rules of the corresponding transfer matrix elements can be exploited to devise a multi-level Monte Carlo integration scheme for computing correlation functions whose numerical cost, at a fixed precision and at asymptotically large times, increases power-like with the time extent of the lattice. As a result the numerical effort is exponentially reduced with respect to the standard Monte Carlo procedure. We test this strategy in the SU(3) Yang-Mills theory by evaluating the relative contribution to the partition function of the parity odd states.     

State Dependent Parameter metamodelling and sensitivity analysis

In this paper we propose a general framework to deal with model approximation and analysis. We present a unified procedure which exploits sampling, screening and model approximation techniques in order to optimally fulfill basic requirements in terms of general applicability and flexibility, efficiency of estimation and simplicity of implementation. The sampling procedure applies Sobol' quasi-Monte Carlo sequences, which display optimal characteristics when linked to a screening procedure, such as the elementary effect test. The latter method is used to reduce the dimensionality of the problem and allows for a preliminary sorting of the factors in terms of their relative importance. Then we apply State Dependent Parameter (SDP) modelling (a model estimation approach, based on recursive filtering and smoothing estimation) to build an approximation of the computational model under analysis and to estimate the variance based sensitivity indices. The method is conceptually simple and very efficient, leading to a significant reduction in the cost of the analysis. All measures of interest are computed using a single set of quasi-Monte Carlo runs. The approach is flexible because, in principle, it can be applied with any available type of Monte Carlo sample.     

Digital redesign of continuous systems by matching of states at multiple sampling periods

This paper presents a method of digital approximation of a continuous-data system by the matching of states at multiple sampling periods. Two alternate methods are presented; one method samples the states every sampling period, and alters the forward and feedback gains, so as to match the states of the two systems at the end of N sampling periods. The second method requires the sampling of the states every N sampling periods, with the change of gains at each sampling period. An illustrative example using the one-axis dynamics of the Skylab Satellite is presented.     

Sampling-Based Tabu Search Approach for Online Path Planning

Abstract

Path planning in unknown environments is one of the most challenging research areas in robotics. In this class of path planning, the robot acquires the information from its sensory system. Sampling-based path planning is one of the famous approaches with low memory and computational requirements that has been studied by many researchers during the past few decades. We propose a sampling-based algorithm for path planning in unknown environments using Tabu search. The Tabu search component of our method guides the sampling to find the samples in the most promising areas and makes the sampling procedure more intelligent. The simulation results show the efficient performance of the proposed approach in different types of environments. We also compare the performance of the algorithm with some of the well-known path planning approaches, including Bug1, Bug2, SRT, potential fields and the visibility graph. Furthermore, two different sampling strategies were used in the sampling procedure, including uniform and Gaussian distributions.     

Fast recall of state-history in kinetic Monte Carlo simulations utilizing the Zobrist key

We present a novel application of the Zobrist hashing method, known in the computer chess literature, to simulation of diffusional phase transformations in metal alloys. A history of previously visited states can be easily maintained, allowing very fast lookup of energies and transition rates calculated earlier in the simulation. The method has been applied to the simulation of a Fe-1at.%Cu system, with simple potentials and a transition rate for diffusional events approximated from the difference in internal energy between trial states. In this simple model at temperatures of 1073 K we find that 61.2% of the states considered during the simulation have been seen previously, and that this proportion rises to 85.1% at 773 K and even to 99.9% at 373 K. Rapid recall of these states reduces the computational time taken for the same sequence of atom-vacancy exchange moves by a factor of 6.3 at 773 K rising to over 100 at 373 K. We suggest that a similar speedup factor will be found using more sophisticated models of diffusion and that the method can, with small modifications, be applied to a wide range of kinetic Monte Carlo simulations of atomistic diffusion processes.     

Self-Tuning Asynchronous Filter for Linear Gaussian System and Applications

In this paper, optimal filtering problem for a class of linear Gaussian systems is studied. The system states are updated at a fast uniform sampling rate and the measurements are sampled at a slow uniform sampling rate. The updating rate of system states is several times the sampling rate of measurements and the multiple is constant. To solve the problem, we will propose a self-tuning asynchronous filter whose contributions are twofold. First, the optimal filter at the sampling times when the measurements are available is derived in the linear minimum variance sense. Furthermore, considering the variation of noise statistics, a regulator is introduced to adjust the filtering coefficients adaptively. The case studies of wheeled robot navigation system and air quality evaluation system will show the effectiveness and practicability in engineering.      

Application of Wang-Landau sampling to a protein model using SMMP

We apply Wang-Landau sampling to the continuous energy model of a protein using Simple Molecular Mechanics for Protein (SMMP). We also tried to parallelize the Wang-Landau sampling method and compare our results with previous results derived from the multicanonical and parallel tempering methods.     

Deriving real-time action systems in a sampling logic

Action systems have been shown to be applicable for modelling and constructing systems in both discrete and hybrid domains. We present a novel semantics for action systems using a sampling logic that facilitates reasoning about the truly concurrent behaviour between an action system and its environment. By reasoning over the apparent states, the sampling logic allows one to determine whether a state predicate is definitely or possibly true over an interval. We present a semantics for action systems that allows the time taken to sample inputs and evaluate expressions (and hence guards) into account. We develop a temporal logic based on the sampling logic that facilitates formalisation of safety, progress, timing and transient properties. Then, we incorporate this logic to the method of enforced properties, which facilitates stepwise refinement of action systems.     

Dynamic high-gain scaling: State and output feedback with application to systems with ISS appended dynamics driven by all States

We propose a dynamic high-gain scaling technique and solutions to coupled Lyapunov equations leading to results on state-feedback, output-feedback, and input-to-state stable (ISS) appended dynamics with nonzero gains from all states and input. The observer and controller designs have a dual architecture and utilize a single dynamic scaling. A novel procedure for designing the dynamics of the high-gain parameter is introduced based on choosing a Lyapunov function whose derivative is negative if either the high-gain parameter or its derivative is large enough (compared to functions of the states). The system is allowed to contain uncertain terms dependent on all states and uncertain appended ISS dynamics with nonlinear gains from all system states and input. In contrast, previous results require uncertainties to be bounded by a function of the output and require the appended dynamics to be ISS with respect to the output, i.e., require the gains from other states and the input to be zero. The generated control laws have an algebraically simple structure and the associated Lyapunov functions have a simple quadratic form with a scaling. The design is based on the solution of two pairs of coupled Lyapunov equations for which a constructive procedure is provided. The proposed observer/controller structure provides a globally asymptotically stabilizing output-feedback solution for the benchmark open problem proposed in our earlier work with the provision that a magnitude bound on the unknown parameter be given.     

Structural decomposition of linear multivariable systems using symbolic computations

We introduce a procedure written in the mathematics software suite Maple, which transforms linear time-invariant systems to a special coordinate basis that reveals the internal structure of the system. The procedure creates exact decompositions, based on matrices that contain elements represented by symbolic variables or exact fractions. Throughout the procedure, transformations are constructed with the goal of avoiding unnecessary changes to the original states. The procedure is intended to complement numerical software algorithms developed by others for the same purpose. We discuss various system-theoretic aspects of the special coordinate basis as well as numerical issues related to the decomposition procedure, and illustrate use of the procedure by examples.     

DETERMINATION OF UNBIASED RECONSTRUCTIONS

A more general algorithm for determining unbiased reconstructions is presented. Variegated states from subsystems may be employed in the reconstruction. Only independent states need be employed, and a procedure to generate independent states is provided. The new methodology allows an unbiased reconstruction from limited variegated information or from a minimal information base. The theory presented directly and readily impacts many fundamental disciplines (e.g. communication theory, pattern recognition, etc).     

Observer‐based cooperative distributed fault‐tolerant model predictive control with imperfect network communication and asynchronous measurements

Intermittent actuator and sensor faults tolerant are simultaneously considered in a distributed control system with imperfect communication network. The asynchronous measurements of different output variables in one sampling period are synchronized through a novel two‐stage model‐based projection method. Different from centralized control network, in both layer‐to‐layer and in‐layer communication, the packet delay, loss and disordering are corrected by the predicted data from model predictive control. Moreover, a completely distributed state observer is established for both system states and sensor faults problem with bounded noise uncertainties. For the intermittent actuator faults, actuator plug‐and‐play design methods based on model predictive control has been introduced, making the actuator faults estimation omitted. The distributed stability conditions are derived for the proposed fault‐tolerant controller, and the online feasibility is explained in detail. Numerical simulation is given to verify the design procedure.     

Delay-partitioning approach to stability analysis of state estimation for neutral-type neural networks with both time-varying delays and leakage term via sampled-data control

This paper mainly focuses on further improved stability analysis of state estimation for neutral-type neural networks with both time-varying delays and leakage delay via sampled-data control by delay-partitioning approach. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states and a sampled-data estimator is constructed. To fully use the sawtooth structure characteristics of the sampling input delay, sufficient conditions are derived such that the system governing the error dynamics is asymptotically stable. The design method of the desired state estimator is proposed. We construct a suitable Lyapunov–Krasovskii functional (LKF) with triple and quadruple integral terms then by using a novel free-matrix-based integral inequality (FMII) including well-known integral inequalities as special cases. Moreover, the design procedure can be easily achieved by solving a set of linear matrix inequalities (LMIs), which can be easily facilitated by using the standard numerical software. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed results.     

井径信号数字化及处理系统

井径测井信号数字化及处理系统是一套对下井仪器传送上来的测井信号进行采集并处理的系统.其目的在于用计算机代替人工的解释过程,对套损情况进行判断,为油井大修提供依据,维持油田的正常生产.以计算机为主控核心单元,主要实现数据的采集、保存、显示、解释和打印输出等功能.