Analysis of the Numerical Solutions of the Elder Problem Using Big Data and Machine Learning

In this study, the numerical solutions to the Elder problem are analyzed using Big Data technologies and data-driven approaches. The steady-state solutions to the Elder problem are investigated with regard to Rayleigh numbers (Ra), grid sizes, perturbations, and other parameters of the system studied. The complexity analysis is carried out for the datasets containing different solutions to the Elder problem, and the time of the highest complexity of numerical solutions is estimated. An approach to the identification of transient fingers and the visualization of large ensembles of solutions is proposed. Predictive models are developed to forecast steady states based on early-time observations. These models are classified into three possible types depending on the features (predictors) used in a model. The numerical results of the prediction accuracy are given, including the estimated confidence intervals for the accuracy, and the estimated time of 95% predictability. Different solutions, their averages, principal components, and other parameters are visualized.publishedVersio

Knowledge Generation with Rule Induction in Cancer Omics

The explosion of omics data availability in cancer research has boosted the knowledge of the molecular basis of cancer, although the strategies for its definitive resolution are still not well established. The complexity of cancer biology, given by the high heterogeneity of cancer cells, leads to the development of pharmacoresistance for many patients, hampering the efficacy of therapeutic approaches. Machine learning techniques have been implemented to extract knowledge from cancer omics data in order to address fundamental issues in cancer research, as well as the classification of clinically relevant sub-groups of patients and for the identification of biomarkers for disease risk and prognosis. Rule induction algorithms are a group of pattern discovery approaches that represents discovered relationships in the form of human readable associative rules. The application of such techniques to the modern plethora of collected cancer omics data can effectively boost our understanding of cancer-related mechanisms. In fact, the capability of these methods to extract a huge amount of human readable knowledge will eventually help to uncover unknown relationships between molecular attributes and the malignant phenotype. In this review, we describe applications and strategies for the usage of rule induction approaches in cancer omics data analysis. In particular, we explore the canonical applications and the future challenges and opportunities posed by multi-omics integration problems.Peer reviewe

Supervised and Ensemble Classification of Multivariate Functional Data: Applications to Lupus Diagnosis

abstract: This dissertation investigates the classification of systemic lupus erythematosus (SLE) in the presence of non-SLE alternatives, while developing novel curve classification methodologies with wide ranging applications. Functional data representations of plasma thermogram measurements and the corresponding derivative curves provide predictors yet to be investigated for SLE identification. Functional nonparametric classifiers form a methodological basis, which is used herein to develop a) the family of ESFuNC segment-wise curve classification algorithms and b) per-pixel ensembles based on logistic regression and fused-LASSO. The proposed methods achieve test set accuracy rates as high as 94.3%, while returning information about regions of the temperature domain that are critical for population discrimination. The undertaken analyses suggest that derivate-based information contributes significantly in improved classification performance relative to recently published studies on SLE plasma thermograms.Dissertation/ThesisDoctoral Dissertation Applied Mathematics 201