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Towards determination of power loss at a rowing blade

To analyze on-water rowing performance, a valid determination of the power loss due to the generation of propulsion is required. This power los can be calculated as the dot product of the net water force vector ( ~ F w;o ) and the time derivative of the position vector of the point at the blade where ~ F w;o is applied (~r PoA = w ). In this article we presented a method that allows for accurate determination of both parameters using a closed system of three rotational equations of motion for three different locations at the oar. Additionally, the output of the method has been validated. An oar was instrumented with three pairs of strain gauges measuring local strain. Force was applied at different locations of the blade, while the oar was fixed at the oarlock and the end of the handle. Using a force transducer and kinematic registration, the force vector at the blade and the deflection of the oar were measured. These data were considered to be accurate and used to calibrate the measured strain for bending moments, the deflection of the oar and the angle of the blade relative to its unloaded position. Additionally, those data were used to validate the output values of the presented method plus the associated instantaneous power output. Good correspondence was found between the estimated perpendicular blade force and its reference (ICC = .999), while the parallel blade force could not be obtained (ICC = .000). The position of the PoA relative to the blade could be accurately obtained when the perpendicular force was 5.3 N (ICC = .927). Instantaneous power output values associated with the perpendicular force could be obtained with reasonable accuracy (ICC = .747). These results suggest that the power loss due to the perpendicular water force component can be accurately obtained, while an additional method is required to obtain the power losses due to the parallel force.

Sampling volumes in powder diffraction experiments.

We present a simple analytical formalism based on the Lorentz-Scherrer equation and Bernoulli statistics for estimating the fraction of crystallites (and the associated uncertainty parameters) contributing to all finite Bragg peaks of a typical powder pattern obtained from a static polycrystalline sample. We test and validate this formalism using numerical simulations, and show that they can be applied to experiments using monochromatic or polychromatic (pink-beam) radiation. Our results show that enhancing the sampling efficiency of a given powder diffraction experiment for such samples requires optimizing the sum of the multiplicities of reflections included in the pattern along with the wavelength used in acquiring the pattern. Utilizing these equations in planning powder diffraction experiments for sampling efficiency is also discussed.

Multiple articles in the category 'Math' on website 3D Game Engine Programming

Convergence of the sequence of parameters generated by alternating least squares algorithms

Several models in data analysis are estimated by minimizing the objective function defined as the residual sum of squares between the model and the data. A necessary and sufficient condition for the existence of a least squares estimator is that the objective function attains its infimum at a unique point. It is shown that the objective function for Parafac-2 need not attain its infimum, and that of DEDICOM, constrained Parafac-2, and, under a weak assumption, SCA and Dynamals do attain their infimum. Furthermore, the sequence of parameter vectors, generated by an alternating least squares algorithm, converges if it decreases the objective function to its infimum which is attained at one or finitely many points.

Time Series Analysis of 3D Coordinates Using Nonstochastic Observations

From the article: Abstract Adjustment and testing of a combination of stochastic and nonstochastic observations is applied to the deformation analysis of a time series of 3D coordinates. Nonstochastic observations are constant values that are treated as if they were observations. They are used to formulate constraints on the unknown parameters of the adjustment problem. Thus they describe deformation patterns. If deformation is absent, the epochs of the time series are supposed to be related via affine, similarity or congruence transformations. S-basis invariant testing of deformation patterns is treated. The model is experimentally validated by showing the procedure for a point set of 3D coordinates, determined from total station measurements during five epochs. The modelling of two patterns, the movement of just one point in several epochs, and of several points, is shown. Full, rank deficient covariance matrices of the 3D coordinates, resulting from free network adjustments of the total station measurements of each epoch, are used in the analysis.

Sentiment polarity classification of corporate review data with a bidirectional Long-Short Term Memory (biLSTM) neural network architecture

A considerable amount of literature has been published on Corporate Reputation, Branding and Brand Image. These studies are extensive and focus particularly on questionnaires and statistical analysis. Although extensive research has been carried out, no single study was found which attempted to predict corporate reputation performance based on data collected from media sources. To perform this task, a biLSTM Neural Network extended with attention mechanism was utilized. The advantages of this architecture are that it obtains excellent performance for NLP tasks. The state-of-the-art designed model achieves highly competitive results, F1 scores around 72%, accuracy of 92% and loss around 20%.