On a Vector-Valued Measure of Multivariate Skewness

The canonical skewness vector is an analytically simple function of the third-order, standardized moments of a random vector. Statistical applications of this skewness measure include semiparametric modeling, independent component analysis, model-based clustering, and multivariate normality testing. This paper investigates some properties of the canonical skewness vector with respect to representations, transformations, and norm. In particular, the paper shows its connections with tensor contraction, scalar measures of multivariate kurtosis and Mardia’s skewness, the best-known scalar measure of multivariate skewness. A simulation study empirically compares the powers of tests for multivariate normality based on the squared norm of the canonical skewness vector and on Mardia’s skewness. An example with financial data illustrates the statistical applications of the canonical skewness vector.

Quantifying the feminine self(ie): Gender display and social media feedback in young women’s Instagram selfies

A growing body of research suggests that young women tend to replicate normative feminine cues popularized through mass media in their selfies, or self-taken mobile phone photographs. Among these stereotypical cues are posing behaviors documented in Goffman’s gender display framework, which visualize a power imbalance between men and women. We completed a content analysis to investigate gender display in young women’s Instagram selfies alongside its relationship to feedback such as likes and comments. In this study, a novel scalar measure of gender display captures both the categorical manifestation and the exaggeration of gender stereotypical cues. We found that gender display is prevalent in women’s Instagram selfies but presented in subtle ways. In addition, women who incorporate and exaggerate gender displays in their selfies tend to receive more feedback. We suggest that gender stereotyping in Instagram selfies is related to reinforcing feedback and call for closer measurement and contextualization of gender performance in user-generated content.

Acoustic microstreaming near a plane wall due to a pulsating free or coated bubble: velocity, vorticity and closed streamlines

Acoustic microstreaming due to an oscillating microbubble, either coated or free, is analytically investigated. The detailed flow field is obtained and the closed streamlines of the ring vortex generated by microstreaming are plotted in both Eulerian and Lagrangian descriptions. Analytical expressions are found for the ring vortex showing that its length depends only on the separation of the microbubble from the wall and the dependence is linear. The circulation as a scalar measure of the vortex is computed quantitatively identifying its spatial location. The functional dependence of circulation on bubble separation and coating parameters is shown to be similar to that of the shear stress.

Scalar measure of the interdependence between random vectors

The problem of assessing tightness of the interdependence between random vectors of different dimensionality is considered. These random vectors can obey arbitrary multidimensional continuous distribution laws. An analytical expression is derived for the coefficient of tightness of the interdependence between random vectors. It is expressed in terms of the coefficients of determination of conditional regressions between the components of random vectors. For the case of Gaussian random vectors, a simpler formula is obtained, expressed through the determinants of each of the random vectors and determinant of their association. It is shown that the introduced coefficient meets all the basic requirements imposed on the degree of tightness of the interdependence between random vectors. This approach is more preferable compared to the method of canonical correlations providing determination of the actual tightness of the interdependence between random vectors. Moreover, it can also be used in case of non-linear correlation dependence between the components of random vectors. The measure thus introduced is rather simply interpretable and can be applied in practice to real data samplings. Examples of calculating the tightness of the interdependence between Gaussian random vectors of different dimensionality are given.

Choice of scalar measure for crystal curvature to image dislocation substructure in terms of discrete orientation data

Starting from Nye’s tensor, alternative characteristics of crystal curvature indicative of dislocation content are considered subject to very low thickness of investigated matter under the free surface and discreteness of orientation sampling. Analysis within the framework of continuum mechanics, undertaken to allow for such conditions peculiar to the electron backscatter diffraction (EBSD) technique, has shown the variable part of orientations expressed in a vector form to be most sensitive to lattice defects when projected to the free surface plane. Hence, as verified with EBSD data on a grain junction in a low deformed IF steel, magnitude of the projected field allows one to map plastic strains inhomogeneous within grains whereas divergence of this field distinctly images and quantifies low-angle dislocation boundaries formed at low strains.

Generation and Optimization of Traveling Vibrating Waves in Self-Assembling Swimming Smart Boxes

This paper presents vibration analysis and structural optimization of a self-assembled structure for swimming. The third mode shape of the structure in the longitudinal direction resembles the body waveform of a swimming eel fish. At the final destination, the box self-assembles using shape memory alloys. MFCs (Piezoelectric Micro Fiber Composites) are actuated at the fundamental natural frequency of the structure. This excites the primary mode of resonance. We optimize the thickness of the panels and the stiffness of the joints to most efficiently generate the swimming waveforms that resembles the body waveform of eel. Traveling wave is generated using two piezoelectric batches actuators bonded on the first and fourth segments of the beams in the longitudinal direction. Excitation of the piezoelectrics results in coupled system dynamics equations that can be translated into generation of waves. Theoretical analysis based on the distributed parameter model was conducted in this paper. A scalar measure of the traveling to standing wave ratio was created using 2-dimensional Fourier Transform of the wave form. The results then were compared to common method in the literature for assessment of standing to traveling wave ratio.

Displaying Economic Value

The distinction between forecast quality and economic value in a cost–loss formulation is well known. Also well known is their complex relationship, even with some instances of a reversal between the two, where higher quality is associated with lower economic value, and vice versa. It is reasonable to expect such counterintuitive results when forecast quality and economic value—both, multifaceted quantities—are summarized by single scalar measures. Diagrams are often used to display forecast quality in order to better represent the multidimensional nature of forecast quality. Here, it is proposed that economic value be displayed as a region on a plot of hit rate versus false-alarm rate. Such a display obviates any need to summarize economic value by a scalar measure. The choice of the axes is motivated by the relative operating characteristic (ROC) diagram, and, so, this manner of displaying economic value is useful for deterministic as well as probabilistic forecasts.