Correlations In Model Research Articles

Modeling of Correlation between Heat Treatment and Mechanical Properties of Ti–6Al–4V Alloy Using Feed Forward Back Propagation Neural Network

A model for predicting mechanical properties of Ti–6Al–4V alloy has been developed and the Feed Forward Back Propagation (FFBP) as one type of algorithm of the Artificial Neural Network has been applied as the prediction system. Hardness, ultimate tensile strength (UTS), yield strength (YS) and elongation that are basic mechanical properties of Ti–6AL–4V alloy are predicted as a function of heat treatment process. Other tensile testing parameter, i.e. strain rate, is also considered in the model because increase of strain rate will increase UTS and YS, but will decrease elongation. Since the FFBP is a supervised system, it requires a lot of input and output data pairs for training process. The data are acquired from literatures and preprocessed before training. Performance of the model are evaluated by the Normalized Root Mean Square Error (NRMSE) and the Coefficient Correlation (R). The NRMSE and the R values of both training and validation parts show almost excellent values. Therefore, the model using the FFBP is appropriate to predict the mechanical properties of Ti–6Al–4V alloy.

Three-Dimensional HAP-MIMO Channels: Modeling and Analysis of Space-Time Correlation

High-altitude platforms (HAPs) are one of the most promising alternative infrastructures for realizing next-generation high-data-rate wireless networks. This paper investigates the application of multiple-input-multiple-output (MIMO) techniques to HAP-based systems and proposes a 3-D geometry-based single-bounce reference model for Ricean fading channels. From this model, the space-time correlation function is derived for a 3-D nonisotropic scattering environment. The statistical properties of the reference model are analytically studied in terms of various parameters such as the elevation angle of the platform, the array configuration, the Doppler spread, and the distribution of the scatterers. Using the theoretical expressions, one can easily numerically evaluate the HAP antenna interelement spacing required to achieve uncorrelated responses in the HAP-MIMO channel matrix. The proposed model provides guidelines for the system design and performance analysis of HAP-MIMO communication systems with line-of-sight (LoS) and non-line-of-sight (NLoS) connections at the L and S frequency bands.

An analytic model of the stereodynamics of rotationally inelastic molecular collisions

We develop an analytic model of vector correlations in rotationally inelastic atom–diatom collisions and test it against the much examined Ar–NO (X2Π) system. Based on the Fraunhofer scattering of matter waves, the model furnishes complex scattering amplitudes needed to evaluate the polarization moments characterizing the quantum stereodynamics. The analytic polarization moments are found to be in an excellent agreement with experimental results and with close-coupling calculations available at thermal energies. The model reveals that the stereodynamics is governed by diffraction from the repulsive core of the Ar–NO potential, which can be characterized by a single Legendre moment.

Mathematical and computational modelling of correlations in dislocation dynamics

This work focuses on the mathematical and computational modelling of dislocation correlation in the context of dislocation dynamics modelling of mesoscale plasticity. A hierarchical system of kinetic equations describing the evolution of dislocation densities of various orders is presented to illustrate the role of correlation in dislocation dynamics, which is followed by a mathematical description of the spatial and line-orientation statistics of dislocation systems within the framework of stochastic fiber processes. In this framework, the pair correlation is related to the second moment measure of the dislocation distribution in the crystal and dislocation line-tangent spaces. The stochastic fiber process description of correlation is used in conjunction with the method of dislocation dynamics simulation to compute the pair correlation in both face-centered cubic and body-centered cubic crystals undergoing small homogeneous plastic deformation at a constant rate. An edge correction scheme is employed as part of the overall methodology for computing the pair correlation. The main characteristics of correlations, including its oscillatory behavior, anisotropy and symmetry, are studied in detail. The self-correlation and cross correlation of dislocations of various species are compared. The implications of the present results for the development of kinetic theory of dislocations are discussed.

Modeling of Oxygen Transfer Correlations for Stirred Tank Bioreactor Agitated with Atypical Helical Ribbon Impeller

Problem Statement: Mixing filamentous fungi entails delicate balance between promoting high volumetric oxygen transfer coefficient (kLa) while keeping low hydrodynamic stresses in the microenvironment of cultures. This study examined the oxygen transfer capability of a prototype low shear helical impeller as a potential replacement for the standard Rushton turbine. Approach: The dependence of kLa upon specific power uptake, superficial gas velocity and apparent viscosity were examined under coalescent, non-coalescent and viscous pseudoplastic fluids scenario using dynamic gassing out technique. Subsequently, collected data were treated under historical data design of response surface methodology. Results: Three empirical power law kLa correlations were developed for each fluid. Correlation comparison with literature models for single turbine agitation suggest higher kLa augmentation within 1.5-3.6 folds for helical impeller in distilled water and as high as 78% improvement in electrolytes fluid. However impeller performance is comparatively 10% lower against theoretical kLa of triple turbines arrangement for power uptake between 0-1600 W m-3. In case of carboxymethylcellulose, better oxygen transfer is expected for design with higher proportionality of impeller-to-tank internal diameter. Conclusions: Helical impeller performance as gas-liquid contactor is comparable to single and triple Rushtons turbines, with superficial gas velocity proved to be more influential than power uptake in non-viscous liquids and vice versa in viscous pseudoplastic fluids.

Modeling of Oxygen Transfer Correlations for Stirred Tank Bioreactor Agitated with Atypical Helical Ribbon Impeller

Modeling of Oxygen Transfer Correlations for Stirred Tank Bioreactor Agitated with Atypical Helical Ribbon Impeller

A system analysis of the general human constitution

The correlations between three systems of signs have been studied using the results of a complex anthropological examination of 669 young men and girls from 16 to 23 years old, including the measurement of 40 body, head, and face parameters, fingerprinting, and the determination of personal psychophysiologic characteristics based on Eysenck, Spielberger, Strelau and Cattell tests using different methods of the multivariate statistics. The author has suggested the original model of correlations between somatic, dermatoglyphic, and psychological signs in the structure of the general human constitution based on the statistically significant canonical correlations (obtained by the author) and taking into consideration the degree of influence exerted by a genetic and socio-economic complex of factors (according to the literature data) on the development and formation of the investigated systems of signs. The evidences of the concept stipulating the relative autonomy of morphofunctional systems as necessary for the integrity of an organism as a whole are presented according to the results of the work with the anthropologic material.

液相格子乱流における反応性スカラー拡散の研究 : 第1報,単一反応の場合(流体工学,流体機械)

A diffusion field with a one-step reaction (R+B→S) in a liquid grid-turbulence has been experimentally investigated. The instantaneous concentrations of two species R and S are measured simultaneously by the light absorption spectrometric method, while the concentration of species B is determined by the conservation law. The statistics of reactive scalar fields are compared with the nonreactive scalar ones. It is ascertained that the mean concentrations of reactants R and B decrease while that of product S increases in the downstream direction because of the chemical reaction. With regard to the scalar fluctuations, it is also observed that the r.m.s. values for species R become smaller than those in the nonreactive case under the present experimental conditions, whereas the r.m.s. values for species B become larger. Furthermore, the correlation coefficient between species R and B is negative and varies from -0.9 to -0.95 in the present measurement region. The present data give very important information for the modeling of the concentration correlation and chemical source term in a turbulent reactive flow.

液相格子乱流における反応性スカラー拡散の研究 : 第2報,連続競争反応の場合(流体工学,流体機械)

A diffusion field with a competitive-consecutive reaction (A+B→R, R+B→S) in a liquid grid-turbulence has been experimentally investigated. The instantaneous concentrations of two reactive species (R and S) and a nonreactive dye (C) are measured simultaneously by the light absorption spectrometric method. The concentration of species A and B are determined by the conservation law. The statistics of reactive scalar fields are compared with the nonreactive scalar ones. It is found that the mean concentrations of reactants A and B decrease while those of product R and S increase in the downstream direction by a chemical reaction. With regard to the scalar fluctuations, it is also observed that the r.m.s. values for species A become larger than those in the nonreactive case under the present experimental conditions, whereas the r.m.s. values for species B become smaller. Furthermore, the correlation coefficients between species A and B are negative and those between B and R are positive in the present measurement region. The present data give very important information for the modeling of the concentration correlation and chemical source term in a turbulent reactive flow.

Using second‐order generalized estimating equations to model heterogeneous intraclass correlation in cluster‐randomized trials

In cluster-randomized trials, it is commonly assumed that the magnitude of the correlation among subjects within a cluster is constant across clusters. However, the correlation may in fact be heterogeneous and depend on cluster characteristics. Accurate modeling of the correlation has the potential to improve inference. We use second-order generalized estimating equations to model heterogeneous correlation in cluster-randomized trials. Using simulation studies we show that accurate modeling of heterogeneous correlation can improve inference when the correlation is high or varies by cluster size. We apply the methods to a cluster-randomized trial of an intervention to promote breast cancer screening.

EXACTLY SOLVABLE PROTON–NEUTRON PAIRING HAMILTONIANS AND QUARTET CORRELATIONS

Exactly solvable models have played an important role in helping to elucidate the physics of strongly correlated systems. Recently, we have extended the Richardson-Gaudin (RG) models of SU(2) like particle pairing to higher rank algebras. In particular, we will discuss here the SO(8) RG model of proton-neutron pairing as a model of strong quartet correlations. The failure of proton-neutron BCS suggests that new approaches have to be developed to account for them.

A New Heat Transfer Correlation for Condensation in the Presence of Air and Its Implementation into RELAP5/MOD3.3

Passive safety systems utilized in most of the advanced nuclear reactors make use of the condensation phenomenon to cope with the design-basis accidents. The inhibiting effect of noncondensable gases on condensation is an extremely important phenomenon, and several experimental research studies have been performed in recent years. Moreover, some theoretical investigations, including assessment of system analysis codes and in this connection modeling of new correlations with a reasonable accuracy, also have been carried out. The experimental work conducted at the Middle East Technical University (METU) was undertaken to investigate the inhibiting effect of noncondensable gas on the condensation phenomenon. The constituted database covers the wide range of system parameters such as the mixture Reynolds number and the air mass fraction. In this study, a new heat transfer correlation is proposed defining condensation phenomenon in the presence of air and is modeled using the METU database. Both the mixture Reynolds number and the condensate Reynolds number are taken into consideration to simulate the possible effect of interfacial waviness. The suppression effect of air, which is accumulated at the condensate-mixture interface, on heat flux is considered by inclusion of air mass fraction. The mean deviation with respect to the experimental data is determined to be 19.4%. Furthermore, the correlation was tested on the RELAP5 code, and the accuracy is determined to be 20%. The overall performance of the correlation, as coded in the RELAP5 code, is satisfactorily good with respect to experimental data for local heat flux, heat transfer coefficient, air mass fraction, and wall subcooling degree. The results obtained by utilizing the correlation yielded much better results compared with the original RELAP5 model, namely Colburn-Hougen.

A proposal for modelling physical correlations of GPS phase observations

Physical correlations are generally not considered in the stochastic model of GPS observations. Consequently, the resulting estimated parameters (such as station coordinates) are affected and their variances are too optimistic and therefore not appropriate to statistically test the significance of the estimates. Considering atmospheric physics, turbulent irregularities in the lower atmosphere cause physical correlations between GPS signals propagating through them. Based on turbulence theory, a variance–covariance model for double-differenced (DD) GPS phase observations is developed in this paper, termed SIGMA-C model. The resulting fully populated variance–covariance matrix depends not only on the satellite-station geometry but also on the prevailing atmospheric conditions. It is shown that especially the wind velocity and its direction play a key role for the adequate modelling of physical correlations. The comparison of the correlations predicted by the SIGMA-C model and the empirical auto- and cross-correlation functions of DD from a specially designed GPS test network shows good agreement between data and model. Consequently, the SIGMA-C model seems to be suited for the proper description of physical correlations in GPS phase data. Furthermore, the application of the SIGMA-C model now attenuates the unbounded decrease of formal coordinate variances when the number of observations is increased. Hence for small GPS networks, the new model yields more realistic formal coordinate variances—even for high sampling rates and longer observation sessions.

Hall number, optical sum rule and carrier density for thet−t′−Jmodel

We revisit the relationship between three classical measures of particle number, namely, the chemical doping $x$, the Hall number ${x}_{\mathit{\text{Hall}}}$, and the particle number inferred from the optical sum rule ${x}_{\mathit{opt}}$. We study the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model of correlations on a square lattice, as a minimal model for high ${T}_{c}$ systems, using numerical methods to evaluate the low temperature Kubo conductivities. These measures disagree significantly in this type of system, owing to Mott Hubbard correlations. The Hall constant has a complex behavior with several changes of sign as a function of filling $x$, depending on the model parameters. Thus, ${x}_{\mathit{\text{Hall}}}$ depends sensitively on ${t}^{\ensuremath{'}}$ and $J$ due to a kind of quantum interference.

Order-Free Co-Regionalized Areal Data Models with Application to Multiple-Disease Mapping

With the ready availability of spatial databases and geographical information system software, statisticians are increasingly encountering multivariate modelling settings featuring associations of more than one type: spatial associations between data locations and associations between the variables within the locations. Although flexible modelling of multivariate point-referenced data has recently been addressed by using a linear model of co-regionalization, existing methods for multivariate areal data typically suffer from unnecessary restrictions on the covariance structure or undesirable dependence on the conditioning order of the variables. We propose a class of Bayesian hierarchical models for multivariate areal data that avoids these restrictions, permitting flexible and order-free modelling of correlations both between variables and across areal units. Our framework encompasses a rich class of multivariate conditionally autoregressive models that are computationally feasible via modern Markov chain Monte Carlo methods. We illustrate the strengths of our approach over existing models by using simulation studies and also offer a real data application involving annual lung, larynx and oesophageal cancer death-rates in Minnesota counties between 1990 and 2000.

Maximum-Likelihood Retrieval of Modeled Convective Rainfall Patterns from Midlatitude C-Band Weather Radar Data

A spatial characterization of the midlatitude meso- scale rain fields from C-band radar measurements is performed by means of a systematic analysis and modeling of convective rain-cell bidimensional shapes and spatial correlation. A large rainfall dataset that is derived from an operational C-band dual-polarized radar, which is placed in S. Pietro Capoflume near Bologna (Italy), has been collected and analyzed for this purpose. Different models of convective rainy horizontal structures are described and compared. Special attention is devoted to the consolidated unimodal models (or unimodal patterns) like Gaucell with a Gaussian rain-rate profile and Excell with an exponential rain-rate profile, and the hybrid models like Hycell and Dexcell based on a proper combination of the previous unimodal models. The new hybrid model Dexell, which is introduced here, is an extension of the Hycell model, which is previously proposed in literature. A pixel-by-pixel model numerical integration is carried out in order to perform a homogeneous comparison between the rain-cell model and the measured features such as peak, average, root mean square, gradient average, and gradient deviation of rain rate. A maximum-likelihood algorithm, which is expressed in terms of the principal component of the previous rain-cell features, is introduced to estimate rain-cell pattern parameters from the available radar data. A detailed sensitivity analysis, which is devoted to find the best behavior in terms of root-mean-square error and correlation coefficient between the modeled and measured rain-cell features, is finally carried out.

Accounting for Spatial Dependence in the Analysis of SPECT Brain Imaging Data

The size and complexity of brain imaging databases confront statistical analysts with a variety of issues when assessing brain activation differences between groups of subjects. Detecting small group differences in activation is compounded by the need to analyze hundreds of thousands of spatially correlated measurements per image. These analyses are especially problematic when, as is typical, the number of subjects in each group is small. In this article a comprehensive analysis of single-photon emission computed tomography (SPECT) brain images demonstrates that spatial modeling can increase the sensitivity of group comparisons. The key statistical approach for increasing the sensitivity of group comparisons is the spatial modeling of intervoxel correlations. Correlations among normalized SPECT counts in 2 × 2 × 2 mm3 voxels are shown to be very large in neighboring voxels and to decrease in magnitude until they become negligible among those approximately 5–7 voxels (10–14 mm) apart. Exploiting this correlation structure, blocks of contiguous voxels are defined within each of several structures within the deep brain so that the geometric centers of the blocks are no closer than the range at which voxel counts can be considered uncorrelated. Using kriging methods, block averages and their prediction variances are calculated. For each structure of interest, the block averages within the structure are weighted by their prediction variances, producing a structure average for each subject. The subject averages and their prediction variances are used in a linear model to compare group effects. This analysis is shown to be more sensitive to group mean differences than the voxel-by-voxel analysis commonly used by medical researchers. The procedures are applied to comparisons of SPECT brain imaging data from four groups of subjects, three of which have variants of the 1991 Gulf War syndrome and one of which is a control group. Commonly used voxel-by-voxel group comparisons do not identify any brain structures that are significantly different for the syndrome and control groups in the analysis of cholinergic response to a physostigmine drug challenge. Spatial modeling and analyses of these data do identify regions of the deep brain that exhibit statistically significant group differences. These results are consistent with medical evidence that these structures might have been affected by Gulf War chemical exposures.

Cluster properties from two-particle angular correlations inp+pcollisions ats=200and 410 GeV

We present results on two-particle angular correlations in proton-proton collisions at center-of-mass energies of 200 and 410 GeV. The PHOBOS experiment at the BNL Relativistic Heavy Ion Collider has a uniquely large coverage for charged particles, giving the opportunity to explore the correlations at both short- and long-range scales. At both energies, a complex two-dimensional correlation structure in Δη and Δϕ is observed. In the context of an independent cluster model of short-range correlations, the cluster size and its decay width are extracted from the two-particle pseudorapidity correlation function and compared with previous measurements in proton-proton and proton-antiproton collisions, as well as PYTHIA and HIJING predictions.3 MoreReceived 6 April 2007DOI:https://doi.org/10.1103/PhysRevC.75.054913©2007 American Physical Society

Model of Fluorescence Intermittency in Single Enzymes

The intermittent emission of fluorescent light from single enzymes, quantum dots, and other nanoscale systems is often characterized by statistical correlations in the emitted signal. A one-dimensional model of such correlations in enzymes, based on a model of protein conformational fluctuations developed by Kou and Xie (Phys. Rev. Lett. 2004, 93, 180603), is formulated in the present paper in terms of the dynamics of a particle moving stochastically between "on" and "off" states under the action of fractional Gaussian noise. The model yields predictions for the short and long time behavior of the following quantities: the time correlation function, C(t), of the fluctuations of the signal intensity, the distribution, f(t), of time intervals between intensity fluctuations, and the Mandel parameter, Q(t), describing the extent of bunching or anti-bunching in the signal. At short times, C(t) and f(t) are found to decay exponentially, while, at long times, they are found to decay as power laws, the exponents being functions solely of the nature of the temporal correlations in the noise. The results are in good qualitative agreement with results from single-molecule experiments on fluorescence intermittency in the enzyme cholesterol oxidase carried out by Xie and co-workers (Science 1998, 282, 1877). The Mandel parameter, Q(t), for this model is positive at short and long times, indicating super-Poisson statistics in these limits, consistent with bunching of the fluorescent signal.

Erratum: Simultaneity and non‐linear variability in financial markets: simulation and forecasting

Nature of the error: The reported forecast error in Table V, p. 380, was not calculated for a true out-of-sample forecast. Rather, the apparent decrease in the forecast error at short horizons was caused by the following problem. In the complex double-looping procedure required to implement the two-stage algorithm, the time indexes for the first-stage and second-stage forecasts were misaligned, due to incorrect programming. This meant that at one stage, what the program was reporting as the forecast was actually an in-sample fit of the regression. Corrected results: The problem in the code was not until detected several weeks later, when the same algorithm was being applied in forecasting in a real-time environment. Tests on these time series, ranging from server use to telecommunications traffic showed no decrease in the forecast error. After the code was corrected, the tests were re-run on the daily exchange rates analysed in the paper. In certain instances, the algorithm was found to generate significant decreases in the forecast error, but this was offset by an increase in the error at other dates. Over long periods of time, no decrease in the error was found. Additional tests were run to determine if variations on the algorithm, such as other second-stage models could improve the performance. Further tests were run to determine if the time points over which the algorithm successfully lowered the error could be predicted on the basis of past performance. All these tests were negative. Failure to detect the error: It is unlikely that this error could have been detected by external reviewers. The basis for the algorithm—a strong contemporaneous correlation between the residual and the rate of change—is empirically valid. Further, there are particular instances in which the algorithm does achieve substantial reductions in the forecast error. At particular points in time, even manual tests of the algorithm would have appeared to confirm the results in the paper. It was only after extensive tests of the new code on various time series that the earlier results were demonstrated to be incorrect. Other calculations in the paper: After the error in the forecasting code was detected, all other calculations in the paper were checked. These were found to be correct. Substantive implications: The paper made two arguments, one concerning the generating mechanisms that underlie non-linear variability, the other proposing a forecasting algorithm. The thesis that simultaneous equation systems can give rise to non-linear variability when some of the coefficients are stochastic is correct. Simultaneous equation models that combine an underlying theoretical model of economic relationships and time-varying correlations across equations do replicate the observed non-linearity in financial markets, including the fractal dimension. However, the failure of the forecasting algorithm undercuts the second thesis in the paper, that the scaling symmetries inherent in fractal processes can be exploited to forecast. While it is possible that future work may yield a better forecasting algorithm, most likely, this hypothesis is disconfirmed. The author regrets having failed to detect the incorrect results prior to publication.