Selected configuration interaction with truncation energy error and application to the Ne atom

Selected configuration interaction (SCI) for atomic and molecular electronic structure calculations is reformulated in a general framework encompassing all CI methods. The linked cluster expansion is used as an intermediate device to approximate CI coefficients BK of disconnected configurations (those that can be expressed as products of combinations of singly and doubly excited ones) in terms of CI coefficients of lower-excited configurations where each K is a linear combination of configuration-state-functions (CSFs) over all degenerate elements of K. Disconnected configurations up to sextuply excited ones are selected by Brown's energy formula, ΔEK=(E-HKK)BK2/(1-BK2), with BK determined from coefficients of singly and doubly excited configurations. The truncation energy error from disconnected configurations, Δdis, is approximated by the sum of ΔEKS of all discarded Ks. The remaining (connected) configurations are selected by thresholds based on natural orbital concepts. Given a model CI space M, a usual upper bound ES is computed by CI in a selected space S, and EM=E S+ΔEdis+δE, where δE is a residual error which can be calculated by well-defined sensitivity analyses. An SCI calculation on Ne ground state featuring 1077 orbitals is presented. Convergence to within near spectroscopic accuracy (0.5 cm-1) is achieved in a model space M of 1.4× 109 CSFs (1.1 × 1012 determinants) containing up to quadruply excited CSFs. Accurate energy contributions of quintuples and sextuples in a model space of 6.5 × 1012 CSFs are obtained. The impact of SCI on various orbital methods is discussed. Since ΔEdis can readily be calculated for very large basis sets without the need of a CI calculation, it can be used to estimate the orbital basis incompleteness error. A method for precise and efficient evaluation of ES is taken up in a companion paper

A chemical Hamiltonian approach study of the basis set superposition error changes on electron densities and one- and two-center energy components

A comparision of the local effects of the basis set superposition error (BSSE) on the electron densities and energy components of three representative H-bonded complexes was carried out. The electron densities were obtained with Hartee-Fock and density functional theory versions of the chemical Hamiltonian approach (CHA) methodology. It was shown that the effects of the BSSE were common for all complexes studied. The electron density difference maps and the chemical energy component analysis (CECA) analysis confirmed that the local effects of the BSSE were different when diffuse functions were present in the calculations

Effect of basis set superposition error on the electron density of molecular complexes

The effect of basis set superposition error (BSSE) on molecular complexes is analyzed. The BSSE causes artificial delocalizations which modify the first order electron density. The mechanism of this effect is assessed for the hydrogen fluoride dimer with several basis sets. The BSSE-corrected first-order electron density is obtained using the chemical Hamiltonian approach versions of the Roothaan and Kohn-Sham equations. The corrected densities are compared to uncorrected densities based on the charge density critical points. Contour difference maps between BSSE-corrected and uncorrected densities on the molecular plane are also plotted to gain insight into the effects of BSSE correction on the electron density

Second-order Møller-Plesset perturbation theory without basis set superposition error : II : open-shell systems

The basis set superposition error-free second-order MØller-Plesset perturbation theory of intermolecular interactions was studied. The difficulties of the counterpoise (CP) correction in open-shell systems were also discussed. The calculations were performed by a program which was used for testing the new variants of the theory. It was shown that the CP correction for the diabatic surfaces should be preferred to the adiabatic ones

How does basis set superposition error change the potential surfaces for hydrogen-bonded dimers?

We describe a simple method to automate the geometric optimization of molecular orbital calculations of supermolecules on potential surfaces that are corrected for basis set superposition error using the counterpoise (CP) method. This method is applied to the H-bonding complexes HF/HCN, HF/H2O, and HCCH/H2O using the 6-31G(d,p) and D95 + + (d,p) basis sets at both the Hartree-Fock and second-order Møller-Plesset levels. We report the interaction energies, geometries, and vibrational frequencies of these complexes on the CP-optimized surfaces; and compare them with similar values calculated using traditional methods, including the (more traditional) single point CP correction. Upon optimization on the CP-corrected surface, the interaction energies become more negative (before vibrational corrections) and the H-bonding stretching vibrations decrease in all cases. The extent of the effects vary from extremely small to quite large depending on the complex and the calculational method. The relative magnitudes of the vibrational corrections cannot be predicted from the H-bond stretching frequencies alone

Numerical and experimental analysis of natural convection in a cavity with flush mounted heat sources on a side wall

This work considers a problem of interest in several technological applications such as the thermal control of electronic equipment. It is also important to study the heat transfer performance of these components under off-normal conditions, such as during failure of cooling fans. The effect of natural convection on the flow and heat transfer in a cavity with two flush mounted heat sources on the left vertical wall, simulating electronic components, is studied numerically and experimentally. The influence of the power distribution, spacing between the heat sources and cavity aspect ratio have been investigated. An analysis of the average Nusselt number of the two heat sources was performed to investigate the behavior of the heat transfer coefficients. The results obtained numerically and experimentally, after an error analysis, showed a good agreement.

Analysis of diametrical wear of grinding wheel and roundness errors in the machining of steel VC 131

Due to the high industrial competitiveness, the rigorous laws of environmental protection, the necessary reduction of costs, the mechanical industry sees itself forced to worry more and more with the refinement of your processes and products. In this context, can be mentioned the need to eliminate the roundness errors that appear after the grinding process. This work has the objective of verifying if optimized nozzles for the application of cutting fluid in the grinding process can minimize the formation of the roundness errors and the diametrical wear of grinding wheel in the machining of the steel VC 131 with 60 HRc, when compared to the conventional nozzles. These nozzles were analyzed using two types of grinding wheels and two different cutting fluids. Was verified that the nozzle of 3mm of diameter, integral oil and the CBN grinding wheel, were the best options to obtain smaller roundness errors and the lowest diametrical wears of grinding wheels.

"The capacity of contrastive analysis to successfully predict the errors of second language learners - a case study"

The aim of this dissertation is to show the power of contrastive analysis in successfully predicting the errors a language learner will make by means of a concrete case study. First, there is a description of what language transfer is and why it is important in the matter of second language acquisition. Second, a brief explanation of the history and development of contrastive analysis will be offered. Third, the focus of the thesis will move to an analysis of errors usually made by language learners. To conclude, the dissertation will focus on the concrete case study of a Russian learner of English: after an analysis of the errors the student is likely to make, a recorded conversation will be examined.

In the aftermath of medical error : Caring for patients, family, and the healthcare workers involved

Medical errors, in particular those resulting in harm, pose a serious situation for patients ("first victims") and the healthcare workers involved ("second victims") and can have long-lasting and distressing consequences. To prevent a second traumatization, appropriate and empathic interaction with all persons involved is essential besides error analysis. Patients share a nearly universal, broad preference for a complete disclosure of incidents, regardless of age, gender, or education. This includes the personal, timely and unambiguous disclosure of the adverse event, information relating to the event, its causes and consequences, and an apology and sincere expression of regret. While the majority of healthcare professionals generally support and honest and open disclosure of adverse events, they also face various barriers which impede the disclosure (e.g., fear of legal consequences). Despite its essential importance, disclosure of adverse events in practice occurs in ways that are rarely acceptable to patients and their families. The staff involved often experiences acute distress and an intense emotional response to the event, which may become chronic and increase the risk of depression, burnout and post-traumatic stress disorders. Communication with peers is vital for people to be able to cope constructively and protectively with harmful errors. Survey studies among healthcare workers show, however, that they often do not receive sufficient individual and institutional support. Healthcare organizations should prepare for medical errors and harmful events and implement a communication plan and a support system that covers the requirements and different needs of patients and the staff involved.

Convergence analysis and validation of low cost distance metrics for computational cost reduction of the Iterative Closest Point algorithm

The Iterative Closest Point algorithm (ICP) is commonly used in engineering applications to solve the rigid registration problem of partially overlapped point sets which are pre-aligned with a coarse estimate of their relative positions. This iterative algorithm is applied in many areas such as the medicine for volumetric reconstruction of tomography data, in robotics to reconstruct surfaces or scenes using range sensor information, in industrial systems for quality control of manufactured objects or even in biology to study the structure and folding of proteins. One of the algorithm’s main problems is its high computational complexity (quadratic in the number of points with the non-optimized original variant) in a context where high density point sets, acquired by high resolution scanners, are processed. Many variants have been proposed in the literature whose goal is the performance improvement either by reducing the number of points or the required iterations or even enhancing the complexity of the most expensive phase: the closest neighbor search. In spite of decreasing its complexity, some of the variants tend to have a negative impact on the final registration precision or the convergence domain thus limiting the possible application scenarios. The goal of this work is the improvement of the algorithm’s computational cost so that a wider range of computationally demanding problems from among the ones described before can be addressed. For that purpose, an experimental and mathematical convergence analysis and validation of point-to-point distance metrics has been performed taking into account those distances with lower computational cost than the Euclidean one, which is used as the de facto standard for the algorithm’s implementations in the literature. In that analysis, the functioning of the algorithm in diverse topological spaces, characterized by different metrics, has been studied to check the convergence, efficacy and cost of the method in order to determine the one which offers the best results. Given that the distance calculation represents a significant part of the whole set of computations performed by the algorithm, it is expected that any reduction of that operation affects significantly and positively the overall performance of the method. As a result, a performance improvement has been achieved by the application of those reduced cost metrics whose quality in terms of convergence and error has been analyzed and validated experimentally as comparable with respect to the Euclidean distance using a heterogeneous set of objects, scenarios and initial situations.

The framework of the virtual laser tracker - A systematic approach to the assessment of error sources and uncertainty in laser tracker measurement

Laser trackers have been widely used in many industries to meet increasingly high accuracy requirements. In laser tracker measurement, it is complex and difficult to perform an accurate error analysis and uncertainty evaluation. This paper firstly reviews the working principle of single beam laser trackers and state-of- The- Art of key technologies from both industrial and academic efforts, followed by a comprehensive analysis of uncertainty sources. A generic laser tracker modelling method is formulated and the framework of the virtual tracker is proposed. The VLS can be used for measurement planning, measurement accuracy optimization and uncertainty evaluation. The completed virtual laser tracking system should take all the uncertainty sources affecting coordinate measurement into consideration and establish an uncertainty model which will behave in an identical way to the real system. © Springer-Verlag Berlin Heidelberg 2010.

Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation

In this article we consider the application of the generalization of the symmetric version of the interior penalty discontinuous Galerkin finite element method to the numerical approximation of the compressible Navier--Stokes equations. In particular, we consider the a posteriori error analysis and adaptive mesh design for the underlying discretization method. Indeed, by employing a duality argument (weighted) Type I a posteriori bounds are derived for the estimation of the error measured in terms of general target functionals of the solution; these error estimates involve the product of the finite element residuals with local weighting terms involving the solution of a certain dual problem that must be numerically approximated. This general approach leads to the design of economical finite element meshes specifically tailored to the computation of the target functional of interest, as well as providing efficient error estimation. Numerical experiments demonstrating the performance of the proposed approach will be presented.

Reciprocal Modulation of Cognitive and Emotional Aspects in Pianistic Performances

Background: High level piano performance requires complex integration of perceptual, motor, cognitive and emotive skills. Observations in psychology and neuroscience studies have suggested reciprocal inhibitory modulation of the cognition by emotion and emotion by cognition. However, it is still unclear how cognitive states may influence the pianistic performance. The aim of the present study is to verify the influence of cognitive and affective attention in the piano performances. Methods and Findings: Nine pianists were instructed to play the same piece of music, firstly focusing only on cognitive aspects of musical structure (cognitive performances), and secondly, paying attention solely on affective aspects (affective performances). Audio files from pianistic performances were examined using a computational model that retrieves nine specific musical features (descriptors) - loudness, articulation, brightness, harmonic complexity, event detection, key clarity, mode detection, pulse clarity and repetition. In addition, the number of volunteers' errors in the recording sessions was counted. Comments from pianists about their thoughts during performances were also evaluated. The analyses of audio files throughout musical descriptors indicated that the affective performances have more: agogics, legatos, pianos phrasing, and less perception of event density when compared to the cognitive ones. Error analysis demonstrated that volunteers misplayed more left hand notes in the cognitive performances than in the affective ones. Volunteers also played more wrong notes in affective than in cognitive performances. These results correspond to the volunteers' comments that in the affective performances, the cognitive aspects of piano execution are inhibited, whereas in the cognitive performances, the expressiveness is inhibited. Conclusions: Therefore, the present results indicate that attention to the emotional aspects of performance enhances expressiveness, but constrains cognitive and motor skills in the piano execution. In contrast, attention to the cognitive aspects may constrain the expressivity and automatism of piano performances.

Analytical solution to the zero-inertia problem for surge flow phenomena in nonprismatic channels

Surge flow phenomena. e.g.. as a consequence of a dam failure or a flash flood, represent free boundary problems. ne extending computational domain together with the discontinuities involved renders their numerical solution a cumbersome procedure. This contribution proposes an analytical solution to the problem, It is based on the slightly modified zero-inertia (ZI) differential equations for nonprismatic channels and uses exclusively physical parameters. Employing the concept of a momentum-representative cross section of the moving water body together with a specific relationship for describing the cross sectional geometry leads, after considerable mathematical calculus. to the analytical solution. The hydrodynamic analytical model is free of numerical troubles, easy to run, computationally efficient. and fully satisfies the law of volume conservation. In a first test series, the hydrodynamic analytical ZI model compares very favorably with a full hydrodynamic numerical model in respect to published results of surge flow simulations in different types of prismatic channels. In order to extend these considerations to natural rivers, the accuracy of the analytical model in describing an irregular cross section is investigated and tested successfully. A sensitivity and error analysis reveals the important impact of the hydraulic radius on the velocity of the surge, and this underlines the importance of an adequate description of the topography, The new approach is finally applied to simulate a surge propagating down the irregularly shaped Isar Valley in the Bavarian Alps after a hypothetical dam failure. The straightforward and fully stable computation of the flood hydrograph along the Isar Valley clearly reflects the impact of the strongly varying topographic characteristics on the How phenomenon. Apart from treating surge flow phenomena as a whole, the analytical solution also offers a rigorous alternative to both (a) the approximate Whitham solution, for generating initial values, and (b) the rough volume balance techniques used to model the wave tip in numerical surge flow computations.