Online Handwriting Recognition Method with a Non-Inertial Reference Frame Based on the Measurement of Linear Accelerations and Differential Geometry: An Alternative to Quaternions.

This work describes a mathematical model for handwriting devices without a specific reference surface (SRS). The research was carried out on two hypotheses: the first considers possible circular segments that could be made during execution for the reconstruction of the trace, and the second is the combination of lines and circles. The proposed system has no flat reference surface, since the sensor is inside the pencil that describes the trace, not on the surface as in tablets or cell phones. An inertial sensor was used for the measurements, in this case, a commercial Micro-Electro Mechanical sensor of linear acceleration. The tracking device is an IMU sensor and a processing card that allows inertial measurements of the pen during on-the-fly tracing. It is essential to highlight that the system has a non-inertial reference frame. Comparing the two proposed models shows that it is possible to construct shapes from curved lines and that the patterns obtained are similar to what is recognized; this method provides an alternative to quaternion calculus for poorly specified orientation problems.

Geometric Analysis of Signals for Inference of Multiple Faults in Induction Motors.

Multiple fault identification in induction motors is essential in industrial processes due to the high costs that unexpected failures can cause. In real cases, the motor could present multiple faults, influencing systems that classify isolated failures. This paper presents a novel methodology for detecting multiple motor faults based on quaternion signal analysis (QSA). This method couples the measured signals from the motor current and the triaxial accelerometer mounted on the induction motor chassis to the quaternion coefficients. The QSA calculates the quaternion rotation and applies statistics such as mean, variance, kurtosis, skewness, standard deviation, root mean square, and shape factor to obtain their features. After that, four classification algorithms are applied to predict motor states. The results of the QSA method are validated for ten classes: four single classes (healthy condition, unbalanced pulley, bearing fault, and half-broken bar) and six combined classes. The proposed method achieves high accuracy and performance compared to similar works in the state of the art.

Velocity tracking of cardiac vector loops to identify signs of stress-induced ischaemia.

Coronary artery disease (CAD) is among the leading causes of death worldwide. Initial studies require an electrocardiogram stress test often followed by cardiac imaging procedures. However, conventional indices still show insufficient diagnostic performance. We propose quaternion methods to evaluate abnormal alterations during ventricular depolarization and repolarization. Assessment was conducted during a Bruce protocol treadmill stress test and after the end of the exercise. We developed an algorithm to automatically determine the beginning and end of exercise and then, computed the angular and linear velocities. Statistical analysis for feature selection and classification between ischaemic and non-ischaemic patients was used. The most significant markers were maximum linear velocity during ventricular depolarization (p < 5E-9) and maximum angular velocity during the second half of the repolarization loop (p < 5E-16). The latter reached sensitivity / specificity pair of 78 / 92 (AUC 0.89). A linear classifier showed a trend of reduction in cardiac vector velocity in at-risk patients after the end of exercise. The sensitivity / specificity pair reached was 86 / 100. Trajectory deviations of depolarization / repolarization loops that result from ischaemia effects, could be responsible for the observed reduction in dynamic changes during exercise. Further studies could provide non-invasive complementary tools to detect CAD risk. Graphical abstract This data is mandatory, please provide.

As principais diferenças entre a Psicologia Analítica e a Psicologia Simbólica Junguiana / The main differences between Analytical Psychology and Jungian Symbolic Psychology / Las principales diferencias entre la Psicología Analítica y la Psicología Simbólica Junguiana

Este texto apresenta 27 pontos em que a Psicologia Simbólica Junguiana difere da Psicologia Analítica. Esta descrição tem um caráter didático e objetiva facilitar a compreensão das modificações introduzidas pela Psicologia Simbólica Junguiana na Psicologia Analítica. O autor ressalta que considera suas formulações um desenvolvimento da Psicologia Analítica e que estão em consonância com a criatividade e o espírito científico de Jung.

This article presents twenty seven aspects in which Jungian Symbolic Psychology differs from Analytical Psychology. This description has a didactic character and aims to facilitate the understanding of the modifications introduced in Analytical Psychology by Jungian Symbolic Psychology. The author stresses considering his formulations a development of Analytical Psychology, harmonic with Jung's creativity and scientific spirit.

Este texto presenta veintisiete puntos en los que la Psicología Simbólica Junguiana difiere de la Psicología Analítica. Esta descripción tiene un carácter didáctico y objetivo para facilitar la comprensión de las modificaciones introducidas por la Psicología Simbólica Junguiana en Psicología Analítica. El autor señala que considera que sus formulaciones son un desarrollo de la Psicología Analítica y que están en línea con la creatividad y el espíritu científico de Jung.

Quaternion-Based Robust Attitude Estimation Using an Adaptive Unscented Kalman Filter.

This paper presents the Quaternion-based Robust Adaptive Unscented Kalman Filter (QRAUKF) for attitude estimation. The proposed methodology modifies and extends the standard UKF equations to consistently accommodate the non-Euclidean algebra of unit quaternions and to add robustness to fast and slow variations in the measurement uncertainty. To deal with slow time-varying perturbations in the sensors, an adaptive strategy based on covariance matching that tunes the measurement covariance matrix online is used. Additionally, an outlier detector algorithm is adopted to identify abrupt changes in the UKF innovation, thus rejecting fast perturbations. Adaptation and outlier detection make the proposed algorithm robust to fast and slow perturbations such as external magnetic field interference and linear accelerations. Comparative experimental results that use an industrial manipulator robot as ground truth suggest that our method overcomes a trusted commercial solution and other widely used open source algorithms found in the literature.

Quaternion-Based Signal Analysis for Motor Imagery Classification from Electroencephalographic Signals.

Quaternions can be used as an alternative to model the fundamental patterns of electroencephalographic (EEG) signals in the time domain. Thus, this article presents a new quaternion-based technique known as quaternion-based signal analysis (QSA) to represent EEG signals obtained using a brain-computer interface (BCI) device to detect and interpret cognitive activity. This quaternion-based signal analysis technique can extract features to represent brain activity related to motor imagery accurately in various mental states. Experimental tests in which users where shown visual graphical cues related to left and right movements were used to collect BCI-recorded signals. These signals were then classified using decision trees (DT), support vector machine (SVM) and k-nearest neighbor (KNN) techniques. The quantitative analysis of the classifiers demonstrates that this technique can be used as an alternative in the EEG-signal modeling phase to identify mental states.