Krylov implicit integration factor discontinuous Galerkin methods on sparse grids for high dimensional reaction-diffusion equations

Computational costs of numerically solving multidimensional partial differential equations (PDEs) increase significantly when the spatial dimensions of the PDEs are high, due to large number of spatial grid points. For multidimensional reaction-diffusion equations, stiffness of the system provides additional challenges for achieving efficient numerical simulations. In this paper, we propose a class of Krylov implicit integration factor (IIF) discontinuous Galerkin (DG) methods on sparse grids to solve reaction-diffusion equations on high spatial dimensions. The key ingredient of spatial DG discretization is the multiwavelet bases on nested sparse grids, which can significantly reduce the numbers of degrees of freedom. To deal with the stiffness of the DG spatial operator in discretizing reaction-diffusion equations, we apply the efficient IIF time discretization methods, which are a class of exponential integrators. Krylov subspace approximations are used to evaluate the large size matrix exponentials resulting from IIF schemes for solving PDEs on high spatial dimensions. Stability and error analysis for the semi-discrete scheme are performed. Numerical examples of both scalar equations and systems in two and three spatial dimensions are provided to demonstrate the accuracy and efficiency of the methods. The stiffness of the reaction-diffusion equations is resolved well and large time step size computations are obtained

Mining heterogeneous information graph for health status classification

In the medical domain, there exists a large volume of data from multiple sources such as electronic health records, general health examination results, and surveys. The data contain useful information reflecting people’s health and provides great opportunities for studies to improve the quality of healthcare. However, how to mine these data effectively and efficiently still remains a critical challenge. In this paper, we propose an innovative classification model for knowledge discovery from patients’ personal health repositories. By based on analytics of massive data in the National Health and Nutrition Examination Survey, the study builds a classification model to classify patients’health status and reveal the specific disease potentially suffered by the patient. This paper makes significant contributions to the advancement of knowledge in data mining with an innovative classification model specifically crafted for domain-based data. Moreover, this research contributes to the healthcare community by providing a deep understanding of people’s health with accessibility to the patterns in various observations

Drug prescription support in dental clinics through drug corpus mining

The rapid increase in the volume and variety of data poses a challenge to safe drug prescription for the dentist. The increasing number of patients that take multiple drugs further exerts pressure on the dentist to make the right decision at point-of-care. Hence, a robust decision support system will enable dentists to make decisions on drug prescription quickly and accurately. Based on the assumption that similar drug pairs have a higher similarity ratio, this paper suggests an innovative approach to obtain the similarity ratio between the drug that the dentist is going to prescribe and the drug that the patient is currently taking. We conducted experiments to obtain the similarity ratios of both positive and negative drug pairs, by using feature vectors generated from term similarities and word embeddings of biomedical text corpus. This model can be easily adapted and implemented for use in a dental clinic to assist the dentist in deciding if a drug is suitable for prescription, taking into consideration the medical profile of the patients. Experimental evaluation of our model’s association of the similarity ratio between two drugs yielded a superior F score of 89%. Hence, such an approach, when integrated within the clinical work flow, will reduce prescription errors and thereby increase the health outcomes of patients

Drug prescription support in dental clinics through drug corpus mining

The rapid increase in the volume and variety of data poses a challenge to safe drug prescription for the dentist. The increasing number of patients that take multiple drugs further exerts pressure on the dentist to make the right decision at point-of-care. Hence, a robust decision support system will enable dentists to make decisions on drug prescription quickly and accurately. Based on the assumption that similar drug pairs have a higher similarity ratio, this paper suggests an innovative approach to obtain the similarity ratio between the drug that the dentist is going to prescribe and the drug that the patient is currently taking. We conducted experiments to obtain the similarity ratios of both positive and negative drug pairs, by using feature vectors generated from term similarities and word embeddings of biomedical text corpus. This model can be easily adapted and implemented for use in a dental clinic to assist the dentist in deciding if a drug is suitable for prescription, taking into consideration the medical profile of the patients. Experimental evaluation of our model’s association of the similarity ratio between two drugs yielded a superior F score of 89%. Hence, such an approach, when integrated within the clinical work flow, will reduce prescription errors and thereby increase the health outcomes of patients

Mining health knowledge graph for health risk prediction

Nowadays classification models have been widely adopted in healthcare, aiming at supporting practitioners for disease diagnosis and human error reduction. The challenge is utilising effective methods to mine real-world data in the medical domain, as many different models have been proposed with varying results. A large number of researchers focus on the diversity problem of real-time data sets in classification models. Some previous works developed methods comprising of homogeneous graphs for knowledge representation and then knowledge discovery. However, such approaches are weak in discovering different relationships among elements. In this paper, we propose an innovative classification model for knowledge discovery from patients’ personal health repositories. The model discovers medical domain knowledge from the massive data in the National Health and Nutrition Examination Survey (NHANES). The knowledge is conceptualised in a heterogeneous knowledge graph. On the basis of the model, an innovative method is developed to help uncover potential diseases suffered by people and, furthermore, to classify patients’ health risk. The proposed model is evaluated by comparison to a baseline model also built on the NHANES data set in an empirical experiment. The performance of proposed model is promising. The paper makes significant contributions to the advancement of knowledge in data mining with an innovative classification model specifically crafted for domain-based data. In addition, by accessing the patterns of various observations, the research contributes to the work of practitioners by providing a multifaceted understanding of individual and public health

Geography and similarity of regional cuisines in China

Food occupies a central position in every culture and it is therefore of great interest to understand the evolution of food culture. The advent of the World Wide Web and online recipe repositories has begun to provide unprecedented opportunities for data-driven, quantitative study of food culture. Here we harness an online database documenting recipes from various Chinese regional cuisines and investigate the similarity of regional cuisines in terms of geography and climate. We found that the geographical proximity, rather than climate proximity is a crucial factor that determines the similarity of regional cuisines. We develop a model of regional cuisine evolution that provides helpful clues to understand the evolution of cuisines and cultures.Comment: 13 pages, 11 figures and 2 table

A family of Barzilai-Borwein steplengths from the viewpoint of scaled total least squares

The Barzilai-Borwein (BB) steplengths play great roles in practical gradient methods for solving unconstrained optimization problems. Motivated by the observation that the two well-known BB steplengths correspond to the ordinary and the data least squares, respectively, we present a family of BB steplengths from the viewpoint of scaled total least squares. Numerical experiments demonstrate that a high performance can be received by a carefully-selected BB steplength in the new family.Comment: 13 pages, 2figure