We investigate and discuss in detail the structure of the restricted singular value decomposition for a tensor triplet under t-product (T-RSVD). The algorithm is provided with a numerical example illustrating the main result. For applications, we consider color image watermarking processing with T-RSVD.

Detection and measurement of pain are crucial in designing effective pain management interventions to alleviate suffering and prevent functional decline in the medical domain. Traditional methods of pain identification rely on verbal patient reports or observable signs, which can be imprecise or subjective due to variability in patient self-assessments. Hence, there is a pressing need for automated methods to standardize pain measurement procedures. This paper proposes a novel facial expression-based automated pain assessment system as a behavioral indicator for pain evaluation. Our system integrates a fusion structure comprising Convolutional Neural Networks (CNNs) and Tensor-based extended Quantitative Expression Descriptors Analysis (TXQEDA). This innovative approach allows for joint learning of robust pain-related facial expression features from raw facial images, combining RGB appearance with shape-based latent representation. We extensively evaluated our proposed model using the UNBC-McMaster dataset for pain classification and intensity estimation. Our results demonstrate the efficacy of the proposed technique, achieving an impressive accuracy of 99.10% for pain level classification. Furthermore, our system excels in pain intensity estimation, showcasing its potential to provide precise and reliable assessments of pain severity. Overall, our research underscores the importance of automated pain assessment systems in improving patient care and clinical outcomes. By leveraging advanced deep learning techniques and fusion strategies, our proposed model offers a promising approach for standardizing pain measurement procedures and enhancing the quality of pain management interventions.

The paper portrays predictive models for dissolved oxygen (DO) levels in an urban lake using common water quality parameters like Temperature, pH, Conductivity and ORP at a time. Data were sampled using three real-time, industry-standard sensors, OPTOD, CTZN, and PHEHT, and then interpolated using the ArcGIS kriging technique. Correlation studies were analyzed through the ML algorithm, the correlation study signified a highly positive correlation between DO and other water parameters and the model was corroborated by R-score in order to create the linear regression model. In addition, an artificial neural network- a machine learning method using the Levenberg-Marquardt algorithm was developed to build a model to predict the do as well. Then, the performance of the models was validated and also the R² accuracy was checked of the predicted data against the actual data. Thus, the appropriateness of the ANN model for the forecasting of investigated attributes is indicated by the fact that the discrepancy between the forecasted and real ANN model is significantly lesser than that of the regression model. However, the model can be used to reveal DO data from unknown urban lake water.