Background: Dynamic prediction of patient mortality risk in the ICU with time series data is limited due to high dimensionality, uncertainty in sampling intervals, and other issues. A new deep learning method, temporal convolution network (TCN), makes it possible to deal with complex clinical time series data in ICU. We aimed to develop and validate it to predict mortality risk using time series data from MIMIC III dataset.Methods: A total of 21,139 records of ICU stays were analysed and 17 physiological variables from the MIMIC III dataset were used to predict mortality risk. Then we compared the model performance of the attention-based TCN with that of traditional artificial intelligence (AI) methods.Results: The area under receiver operating characteristic (AUCROC) and area under precision-recall curve (AUC-PR) of attention-based TCN for predicting the mortality risk 48 h after ICU admission were 0.837 (0.824 -0.850) and 0.454, respectively. The sensitivity and specificity of attention-based TCN were 67.1% and 82.6%, respectively, compared to the traditional AI method, which had a low sensitivity (< 50%).Conclusions: The attention-based TCN model achieved better performance in the prediction of mortality risk with time series data than traditional AI methods and conventional score-based models. The attention-based TCN mortality risk model has the potential for helping decision-making for critical patients.Trial registration: Data used for the prediction of mortality risk were extracted from the freely accessible MIMIC III dataset. The project was approved by the Institutional Review Boards of Beth Israel Deaconess Medical Center (Boston, MA) and the Massachusetts Institute of Technology (Cambridge, MA). Requirement for individual patient consent was waived because the project did not impact clinical care and all protected health information was deidentified. The data were accessed via a data use agreement between PhysioNet, a National Institutes of Health–supported data repository (https://www.physionet.org/), and one of us (Yu-wen Chen, Certification Number: 28341490). All methods were carried out in accordance with the institutional guidelines and regulations.

This paper presents a method to infer skin lesion segmentation based on multiple deep convolutional neural network (DCNN) models by employing fully connected conditional random fields (CRFs). This method is on the strength of the synergism between ensemble learning which is responsible for introducing diversity from multiple DCNN models and CRFs inference which is in charge of probabilistic inference based on random fields over dermoscopy images. Contrasting to single DCNN models, the proposed method can gain better segmentation by comprehensively utilizing the advances and performance preferences of multiple different DCNN models. In comparison with simple ensemble schemes, it can effectively and precisely refine the fuzzy lesion boundary by utilizing the information in test images to maximize label agreement between similar pixels. Further, an engineering bonus is the feasibility of parallelization for the heavy operation, predicting on multiple DCNN models. In experiments, we tested the effectiveness and robustness of the proposed method on the mainstream datasets ISIC 2017 and PH2, and the results were competitive with the state-of-art methods. we also confirmed that the proposed method can capture the local information in fuzzy dermoscopy images being able to find more accurate lesion borders with a good boost on Boundary Recall (BR) metric. Moreover, since the hyper-parameters in CRFs are explainable, it is possible to adjust them manually to reach better results case by case, being attractive in practice. This work is of value on integration between the deep learning technologies and probabilistic inference in resolving lesion segmentation, and has great potential to be applied in similar tasks.

Dixon resultant is a fundamental tool of elimination theory in the study and practice of algebraic geometry. It has provided the efficient and practical solutions to some benchmark problems in a variety of application domains, such as automated reasoning, automatic control, and solid modelling. The major task of solutions is to construct the Dixon resultant matrix, the entries of which are more complicated than the entries of other resultant matrices. An existing extended recurrence formula can construct the Dixon resultant matrix fast. In this paper, we present a detailed analysis of the computational complexity of the recurrence formula for the general multivariate setting. Parallel computation can be applied to speed up the recursive procedure. Furthermore, we also generalize the computational complexity of three bivariate polynomials to the general multivariate case by using the construction of standard Dixon resultant matrix. Some experimental results are demonstrated by a range of nontrivial examples.