Search results for "approximation"
showing 10 items of 818 documents
Quantum-chemical determination of Born–Oppenheimer breakdown parameters for rotational constants: the open-shell species CN, CO+ and BO
2013
The quantum-chemical protocol for computing Born-Oppenheimer breakdown corrections to rotational constants in the case of diatomic molecules is extended to open-shell species. The deviation from the Born-Oppenheimer equilibrium rotational constant is obtained by considering three contributions: the adiabatic correction to the equilibrium bond distance, the electronic contribution to the moment of inertia requiring the computation of the rotational g-tensor, and the so-called Dunham correction. Values for the Born-Oppenheimer breakdown parameters of CN, CO+, and BO in their (2)sigma(+) electronic ground states are reported based on coupled-cluster calculations of the involved quantities and …
Nuclear anapole moment interaction in BaF from relativistic coupled-cluster theory
2018
We present high accuracy relativistic coupled cluster calculations of the P-odd interaction coefficient $W_A$ describing the nuclear anapole moment effect on the molecular electronic structure. The molecule under study, BaF, is considered a promising candidate for the measurement of the nuclear anapole moment, and the preparation for the experiment is now underway [Altunas et al., Phys. Rev. Lett. 120, 142501 (2018)]. Influence of various computational parameters (size of the basis set, treatment of relativistic effects, and treatment of electron correlation) on the calculated $W_A$ coefficient is investigated and a recommended value of 147.7 Hz with an estimated uncertainty of 1.5% is prop…
Vertical Beam Polarization at MAMI
2017
For the first time a vertically polarized electron beam has been used for physics experiments at MAMI in the energy range between 180 and 855 MeV. The beam-normal single-spin asymmetry $A_{\mathrm{n}}$, which is a direct probe of higher-order photon exchange beyond the first Born approximation, has been measured in the reaction $^{12}\mathrm C(\vec e,e')^{12}\mathrm C$. Vertical polarization orientation was necessary to measure this asymmetry with the existing experimental setup. In this paper we describe the procedure to orient the electron polarization vector vertically, and the concept of determining both its magnitude and orientation with the available setup. A sophisticated method has …
Hierarchical adaptive cross approximation GMRES technique for solution of acoustic problems using the boundary element method
2009
In this paper a new Rapid Acoustic Boundary Element Method (RABEM) is presented using a Hierarchical GMRES solver for 3D acoustic problems. The Adaptive Cross Approximation is used to generate both the system matrix and the right hand side vector. The ACA is also used to evaluate the potential and the particle velocity values at selected internal points. Two different GMRES solution strategies (without preconditioner and with a block diagonal preconditioner) are developed and tested for low and high frequency problems. Implementation of different boundary conditions (i.e. Dirichlet, Neumann and mixed Robin) is also described. The applications presented include the problem of noise acting on…
Scatter Search and Path Relinking: Foundations and Advanced Designs
2004
Scatter Search and its generalized form Path Relinking, are evolutionary methods that have been successfully applied to hard optimization problems. Unlike genetic algorithms, they operate on a small set of solutions and employ diversification strategies of the form proposed in Tabu Search, which give precedence to strategic learning based on adaptive memory, with limited recourse to randomization. The fundamental concepts and principles were first proposed in the 1970s as an extension of formulations, dating back to the 1960s, for combining decision rules and problem constraints. (The constraint combination approaches, known as surrogate constraint methods, now independently provide an impo…
Fuzzy modeling and control for a class of inverted pendulum system
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/936868 Open Access Focusing on the issue of nonlinear stability control system about the single-stage inverted pendulum, the T-S fuzzy model is employed. Firstly, linear approximation method would be applied into fuzzy model for the single-stage inverted pendulum. At the same time, for some nonlinear terms which could not be dealt with via linear approximation method, this paper will adopt fan range method into fuzzy model. After the T-S fuzzy model, the PDC technology is utilized to design the fuzzy controller secondly. Numerical simulation res…
Determining the Parameters of a Sugeno Fuzzy Controller Using a Parallel Genetic Algorithm
2013
Developed in the mid 1970s, the technique based on genetic algorithms proved its usefulness in finding optimal or near optimal solutions to problems for which accurate solving strategies are either non-existent or require excessively long running time. We implemented a genetic algorithm to determine the parameters of a Sugeno fuzzy controller for the Truck Backer-Upper problem (This problem is considered an acknowledged benchmark in nonlinear system identification.). Less known at first than Mamdami fuzzy controllers, Sugeno fuzzy controllers became popular once they were included into the ANFIS neuro-fuzzy Matlab library. By their nature, Sugeno controllers can be regarded as interpolation…
LOW-RANK APPROXIMATION BASED NON-NEGATIVE MULTI-WAY ARRAY DECOMPOSITION ON EVENT-RELATED POTENTIALS
2014
Non-negative tensor factorization (NTF) has been successfully applied to analyze event-related potentials (ERPs), and shown superiority in terms of capturing multi-domain features. However, the time-frequency representation of ERPs by higher-order tensors are usually large-scale, which prevents the popularity of most tensor factorization algorithms. To overcome this issue, we introduce a non-negative canonical polyadic decomposition (NCPD) based on low-rank approximation (LRA) and hierarchical alternating least square (HALS) techniques. We applied NCPD (LRAHALS and benchmark HALS) and CPD to extract multi-domain features of a visual ERP. The features and components extracted by LRAHALS NCP…
Preattentive and attentive responses to changes in small numerosities of tones in adult humans
2016
The brain hosts a primitive number sense to non-symbolically represent numerosities of objects or events. Small exact numerosities (~4 or less) can be individuated in parallel. In contrast, large numerosities (more than ~4) can only be approximated. However, whether small numerosities can be approximated without their parallel individuation remains unclear. Parallel individuation is suggested to be an attentive process and numerical approximation an automatic process. We, therefore, tested whether small numerosities can be represented preattentively. We recorded adult humans׳ event-related potentials (ERPs) and behavioral responses to 300-ms sequences of six tones (each of either 440 Hz or …
Mixed predictability and cross-validation to assess non-linear Granger causality in short cardiovascular variability series
2006
A method to evaluate the direction and strength of causal interactions in bivariate cardiovascular and cardiorespiratory series is presented. The method is based on quantifying self and mixed predictability of the two series using nearest-neighbour local linear approximation. It returns two causal coupling indexes measuring the relative improvement in predictability along direct and reverse directions, and a directionality index indicating the preferential direction of interaction. The method was implemented through a cross-validation approach that allowed quantification of directionality without constraining the embedding of the series, and fully exploited the available data to maximise th…