Orthogonality Assumption Research Articles

Determining partial differential cross sections for low-energy electron photodetachment involving conical intersections using the solution of a Lippmann-Schwinger equation constructed with standard electronic structure techniques

A method for obtaining partial differential cross sections for low energy electron photodetachment in which the electronic states of the residual molecule are strongly coupled by conical intersections is reported. The method is based on the iterative solution to a Lippmann-Schwinger equation, using a zeroth order Hamiltonian consisting of the bound nonadiabatically coupled residual molecule and a free electron. The solution to the Lippmann-Schwinger equation involves only standard electronic structure techniques and a standard three-dimensional free particle Green's function quadrature for which fast techniques exist. The transition dipole moment for electron photodetachment, is a sum of matrix elements each involving one nonorthogonal orbital obtained from the solution to the Lippmann-Schwinger equation. An expression for the electron photodetachment transition dipole matrix element in terms of Dyson orbitals, which does not make the usual orthogonality assumptions, is derived.

3D FINITE ELEMENT MODELLING OF CHIP FORMATION PROCESS FOR MACHINING INCONEL 718: COMPARISON OF FE SOFTWARE PREDICTIONS

Many efforts have been focused on the development of Finite Element (FE) machining models due to growing interest in solving practical machining problems in a computational environment in industry. Most of the current models are developed under 2D orthogonal plane strain assumptions, or make use of either arbitrary damage criterion or remeshing techniques for obtaining the chip. A complete understanding of the material removal process together with its effects on the machined parts and wear behaviour of the cutting tools requires accurate 3D computational models to analyze the entire physical phenomenon in materials undergoing large elastic-plastic deformations and large temperature changes as well as high strain rates. This work presents a comparison of 3D machining models developed using commercially available FE softwares ABAQUS/Explicit© and DEFORM™3D Machining. The work material is chosen as Inconel 718, a difficult-to-cut nickel-based alloy material. Computational results of temperature, strain and stress distributions obtained from the FE models for the effect of cutting speed are presented in comparison with results obtained from experimental tests. In addition, modified material model for Inconel 718 with flow softening is compared with the Johnson-Cook model. The predictions of forces and chip formation are improved with the modified material model.

Examining the SF-36 in an older population: analysis of data and presentation of Australian adult reference scores from the Dynamic Analyses to Optimise Ageing (DYNOPTA) project

To examine the psychometric properties of, and present reference scores for the SF-36 using data from a large community sample of older adults. Data are from the DYNOPTA project. We focus on data from five studies that included the SF-36, providing a sample of 41,338 participants aged 45-97 years. We examine the factor structure of the SF-36 and item-internal consistency. The psychometric properties of the eight scales of the SF-36 were largely consistent with previous research based on younger and/or smaller samples. However, the assumption of orthogonality between the second-order factors was not supported. In terms of age-related effects, most scales demonstrated a nonlinear effect with markedly poorer health evident for the oldest respondents. In addition, the scales measuring aspects of physical health (PH, BP, RP, GH) showed an overall linear decline in health with increasing age. There were, however, no consistent linear age-related differences in health evident for those scales most strongly associated with mental health (MH, RE, SF, VT). The results confirm the structural validity and internal consistency of the eight scales from the SF-36 with an older population and support its use to assess the health of older Australian adults.

The Failure of Orthogonality under Nonstationarity: Should We Care About It?

We consider two well‐known facts in econometrics: (i) the failure of the orthogonality assumption (i.e., no independence between the regressors and the error term), which implies biased and inconsistent Least Squares (LS) estimates and (ii) the consequences of using nonstationary variables, acknowledged since the seventies; LS might yield spurious estimates when the variables do have a trend component, whether stochastic or deterministic. In this work, an optimistic corollary is provided: it is proven that the LS regression, employed in nonstationary and cointegrated variables where the orthogonality assumption is not satisfied, provides estimates that converge to their true values. Monte Carlo evidence suggests that this property is maintained in samples of a practical size.

Sharp and Strict $L^p$-Inequalities for Hilbert-Space-Valued Orthogonal Martingales

The paper contains the proofs of sharp moment estimates for Hilbert-space valued martingales under the assumptions of differential subordination and orthogonality. The results generalize those obtained by Banuelos and Wang. As an application, we sharpen an inequality for stochastic integrals with respect to Brownian motion.

Taguchi Optimization of Process Parameters in Friction Stir Welding of 6061 Aluminum Alloy: A Review and Case Study

This study is intended to present a straightforward and computationally efficient methodology for optimizing the process parameters of friction stir welding (FSW) of 6061 aluminum alloy. In particular, it is shown how to minimize the heat affected zone (HAZ) distance to the weld line in the joined parts using a Taguchi optimization method and a temperature-field finite element model. The peak temperature during the process has also been minimized. Since the method is used for the first time in relation to the HAZ objective function, an auxiliary full factorial search is conducted to ensure Taguchi’s orthogonal design assumption for the FSW problems. Results confirm that the method can be suc-cessfully used for minimizing both the HAZ distance to the weld line and the peak temperature, with a minimal number of simulation runs via orthogonal arrays. In addition, a new ANOVA analysis on the L9 orthogonal array with three factors is performed and results indicate that among the parameters considered (i.e., the tool rotational speed, transverse speed, and the axial force), the most significant parameter on the weld quality is the rotational speed, followed by the axial force and transverse speed.

Taguchi Optimization of Process Parameters in Friction Stir Welding of 6061 Aluminum Alloy: A Review and Case Study

This study is intended to present a straightforward and computationally efficient methodology for optimizing the process parameters of friction stir welding (FSW) of 6061 aluminum alloy. In particular, it is shown how to minimize the heat affected zone (HAZ) distance to the weld line in the joined parts using a Taguchi optimization method and a temperature-field finite element model. The peak temperature during the process has also been minimized. Since the method is used for the first time in relation to the HAZ objective function, an auxiliary full factorial search is conducted to ensure Taguchi’s orthogonal design assumption for the FSW problems. Results confirm that the method can be suc-cessfully used for minimizing both the HAZ distance to the weld line and the peak temperature, with a minimal number of simulation runs via orthogonal arrays. In addition, a new ANOVA analysis on the L9 orthogonal array with three factors is performed and results indicate that among the parameters considered (i.e., the tool rotational speed, transverse speed, and the axial force), the most significant parameter on the weld quality is the rotational speed, followed by the axial force and transverse speed.

Relaxing the WDO Assumption in Blind Extraction of Speakers from Speech Mixtures

The time-frequency masking approach in blind speech extraction consists of two main steps: feature clustering in a space spanned over delay-time and attenuationrate, and spectrogram masking in order to reconstruct the sources. Usually a binary mask is generated under the strong W-disjoint orthogonal (WDO) assumption (disjoint orthogonal representations in the frequency domain). In practice, this assumption is most often violated leading to weak quality of reconstructed sources. In this paper we propose the WDO to be relaxed by allowing some frequency bins to be shared by both sources. As we detect instantaneous fundamental frequencies the mask creation is supported by exploring a harmonic structure of speech. The proposed method is proved to be effective and reliable in experiments with both simulated and real acquired mixtures.

Tensor Distance Based Multilinear Locality-Preserved Maximum Information Embedding

This brief paper presents a unified framework for tensor-based dimensionality reduction (DR) with a new tensor distance (TD) metric and a novel multilinear locality-preserved maximum information embedding (MLPMIE) algorithm. Different from traditional Euclidean distance, which is constrained by the orthogonality assumption, TD measures the distance between data points by considering the relationships among different coordinates. To preserve the natural tensor structure in low-dimensional space, MLPMIE directly works on the high-order form of input data and iteratively learns the transformation matrices. In order to preserve the local geometry and to maximize the global discrimination simultaneously, MLPMIE keeps both local and global structures in a manifold model. By integrating TD into tensor embedding, TD-MLPMIE performs tensor-based DR through the whole learning procedure, and achieves stable performance improvement on various standard datasets.

Scaling for the ensemble statistics prediction of a random system subjected to harmonic excitations

This paper is concerned with the ensemble statistics of the dynamic responses of a random system subjected to harmonic excitations. Random point process theory is employed to derive general scaling laws with the Gaussian orthogonal ensemble assumption about the system natural frequencies. A scaled model is built to simulate the high-frequency vibrations of the original system. Specific forms of the scaling laws are presented for a mass-loaded plate regarding the scaling factors for the structural parameters. The ensemble statistics predicted from the scaled model are compared favorably with those obtained from the original system.

On the structure of the quadratic subspace in discriminant analysis

The concept of quadratic subspace is introduced as a helpful tool for dimension reduction in quadratic discriminant analysis ( QDA). It is argued that an adequate representation of the quadratic subspace may lead to better methods for both data representation and classification. Several theoretical results describe the structure of the quadratic subspace, that is shown to contain some of the subspaces previously proposed in the literature for finding differences between the class means and covariances. A suitable assumption of orthogonality between location and dispersion subspaces allows us to derive a convenient reduced version of the full QDA rule. The behavior of these ideas in practice is illustrated with three real data examples.

Automobile Engine Variants and Price Discrimination

Using a structural model of demand for automobile engine variants, this paper finds that there is second-degree price discrimination: markups increase with engine size. Still, average markups are lower than when models have just one engine. The paper develops the first empirical demand framework suitable for markets with variants. There is an unobserved product characteristic and a consumer-specific logit term for classes of products, but both are fixed across variants. Fixed effects control for unobservables. The literature’s assumption of orthogonality between unobserved and observed product character

A sufficient condition for the harmonicity of functions of two variables

As is well known, one can weaken the continuity assumption in the claim that any continuous function u(x, y) satisfying the Laplace equation is harmonic. Tolstov relocated this assumption by the boundedness condition and, later on, the author of the present paper relocated it by the summability condition. The summability condition cannot be substantially weakened here. In the present paper, a generalization of the Laplace equation is studied. Assume that, at every point of a domain, the sum of second derivatives (treated in the Peano sense) of a function along a pair of orthogonal lines passing through the point vanishes, where the directions of the lines in the pair depend on the point in general. It is proved that the summability of the function is sufficient for its harmonicity. One cannot get rid of the orthogonality assumption for the above lines.

Robust Relative Transfer Function Estimation for Dual Microphone-Based Generalized Sidelobe Canceller

In this Letter, a robust system identification method is proposed for the generalized sidelobe canceller using dual microphones. The conventional transfer-function generalized sidelobe canceller employs the non-stationarity characteristics of the speech signal to estimate the relative transfer function and thus is difficult to apply when the noise is also non-stationary. Under the assumption of W-disjoint orthogonality between the speech and the non-stationary noise, the proposed algorithm finds the speech-dominant time-frequency bins of the input signal by inspecting the system output and the inter-microphone time delay. Only these bins are used to estimate the relative transfer function, so reliable estimates can be obtained under non-stationary noise conditions. The experimental results show that the proposed algorithm significantly improves the performance of the transfer-function generalized sidelobe canceller, while only sustaining a modest estimation error in adverse non-stationary noise environments.

W-Disjoint Orthogonality Based Residual Acoustic Echo Cancellation for Hands-Free Communication

A simple and novel residual acoustic echo cancellation method that employs binary masking is proposed to enhance the speech quality of hands-free communication in an automobile environment. In general, the W-disjoint orthogonality assumption is used for blind source separation using multi-microphones. However, in this Letter, it is utilized to mask the residual echo component in the time-frequency domain using a single microphone. The experimental results confirm the effectiveness of the proposed method in terms of the echo return loss enhancement and speech enhancement.

A simple cooperative transmission protocol for energy-efficient broadcasting over multi-hop wireless networks

This paper analyzes a broadcasting technique for wireless multi-hop sensor networks that uses a form of cooperative diversity called opportunistic large arrays (OLAs). We propose a method for autonomous scheduling of the nodes, which limits the nodes that relay and saves as much as 32% of the transmit energy compared to other broadcast approaches, without requiring global positioning system (GPS), individual node addressing, or inter-node interaction. This energy-saving is a result of cross-layer interaction, in the sense that the medium access control (MAC) and routing functions are partially executed in the physical (PHY) layer. Our proposed method is called OLA with a transmission threshold (OLA-T), where a node compares its received power to a threshold to decide if it should forward. We also investigate OLA with variable threshold (OLA-VT), which optimizes the thresholds as a function of level. OLA-T and OLA-VT are compared with OLA broadcasting without a transmission threshold, each in their minimum energy configuration, using an analytical method under the orthogonal and continuum assumptions. The trade-off between the number of OLA levels (or hops) required to achieve successful network broadcast and transmission energy saved is investigated. The results based on the analytical assumptions are confirmed with Monte Carlo simulations.

Understanding brain connectivity from EEG data by identifying systems composed of interacting sources

In understanding and modeling brain functioning by EEG/MEG, it is not only important to be able to identify active areas but also to understand interference among different areas. The EEG/MEG signals result from the superimposition of underlying brain source activities volume conducted through the head. The effects of volume conduction produce spurious interactions in the measured signals. It is fundamental to separate true source interactions from noise and to unmix the contribution of different systems composed by interacting sources in order to understand interference mechanisms. As a prerequisite, we consider the problem of unmixing the contribution of uncorrelated sources to a measured field. This problem is equivalent to the problem of unmixing the contribution of different uncorrelated compound systems composed by interacting sources. To this end, we develop a principal component analysis-based method, namely, the source principal component analysis (sPCA), which exploits the underlying assumption of orthogonality for sources, estimated from linear inverse methods, for the extraction of essential features in signal space. We then consider the problem of demixing the contribution of correlated sources that comprise each of the compound systems identified by using sPCA. While the sPCA orthogonality assumption is sufficient to separate uncorrelated systems, it cannot separate the individual components within each system. To address that problem, we introduce the Minimum Overlap Component Analysis (MOCA), employing a pure spatial criterion to unmix pairs of correlates (or coherent) sources. The proposed methods are tested in simulations and applied to EEG data from human µ and α rhythms.

Modified quasi-profile likelihoods from estimating functions

We discuss higher-order adjustments for a quasi-profile likelihood for a scalar parameter of interest, in order to alleviate some of the problems inherent to the presence of nuisance parameters, such as bias and inconsistency. Indeed, quasi-profile score functions for the parameter of interest have bias of order O ( 1 ) , and such bias can lead to poor inference on the parameter of interest. The higher-order adjustments are obtained so that the adjusted quasi-profile score estimating function is unbiased and its variance is the negative expected derivative matrix of the adjusted profile estimating equation. The modified quasi-profile likelihood is then obtained as the integral of the adjusted profile estimating function. We discuss two methods for the computation of the modified quasi-profile likelihoods: a bootstrap simulation method and a first-order asymptotic expression, which can be simplified under an orthogonality assumption. Examples in the context of generalized linear models and of robust inference are provided, showing that the use of a modified quasi-profile likelihood ratio statistic may lead to coverage probabilities more accurate than those pertaining to first-order Wald-type confidence intervals.

시간-주파수 영역에서의 스테레오 사운드 분리기법

본 논문은 스테레오 사운드에서 합쳐지기 이전의 개별적인 사운드를 분리해내는 기법을 제안한다. 기존의 Degenerate Unmixing Estimation Technique (DUET) 알고리즘의 W-Disjoint Orthogonal 가정에 기반을 두고 있으며, Windowed-Fourier 변환을 사용하여 시간-주파수 영역에서 주요 프로세스를 수행한다. 제안된 방식은 패닝 인덱스의 거리차이에 따라 가중치를 준 마스크를 사용하는 기법과 양쪽 채널의 성분을 비교하여 바이너리 기반의 마스크를 사용하는 방식이다. 전자는 부드러운 분리 특성을 보여주며, 후자는 높은 분리 특성을 보여주었다. 마지막에 실험을 통해 기존의 방식과 제안된 방식을 비교함으로써, 제안된 방식이 기존 방식 보다 좋은 성능을 가지고 있음을 알아볼 것이다. This paper presents a new demixing method that separates each source from a stereo sound mixture. Under the W-Disjoint Orthogonal assumption in DUET(Degenerate Unmixing Estimation Technique) algorithm. The proposed method is mainly processed in time-frequency domain by using windowed-fourier transform. In this paper there are two main contributions: a weighted mask by panning index distances and a binary mask by comparing each channel value. The former has tender demixing characteristic, and the latter has stronger demixing characteristic. In experimental results, we will show that both masks produce more robust demixing than the existing demixing methods do.

Both parallelism and orthogonality are used to perceive 3D slant of rectangles from 2D images

A 2D perspective image of a slanted rectangular object is sufficient for a strong 3D percept. Two computational assumptions that could be used to interpret 3D from images of rectangles are as follows: (1) converging lines in an image are parallel in the world, and (2) skewed angles in an image are orthogonal in the world. For an accurate perspective image of a slanted rectangle, either constraint implies the same 3D interpretation. However, if an image is rescaled, the 3D interpretations based on parallelism and orthogonality generally conflict. We tested the roles of parallelism and orthogonality by measuring perceived depth within scaled perspective images. Stimuli were monocular images of squares, slanted about a horizontal axis, with an elliptical hole. Subjects judged the length-to-width ratio of the holes, which provided a measure of perceived depth along the object. The rotational alignment of squares within their surface plane was varied from 0 degrees (trapezoidal projected contours) to 20 degrees (skewed projected contours). In consistent-cue conditions, images were accurate projections of either a 10 degree- or 20 degree-wide square, with slants of 75 degrees and 62 degrees, respectively. In cue-conflict conditions, images were generated either by magnifying a 10 degrees image to have a projected size of 20 degrees or by minifying a 20 degree image to have a projected size of 10 degrees. For the aligned squares, which do not produce a conflicting skew cue, we found that subjects' judgments depended primarily on projected size and not on the size used to generate the prescaled images. This is consistent with reliance on the convergence cue, corresponding to a parallelism assumption. As squares were rotated away from alignment, producing skewed projected contours, judgments were increasingly determined by the original image size. This is consistent with use of the skew cue, corresponding to an orthogonality assumption. Our results demonstrate that both parallelism and orthogonality constraints are used to perceive depth from linear perspective.