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The Current practice of air-fuel ratio control relies on empirical models and traditional PID controllers, which require extensive calibration to maintain the post-catalyst air-fuel ratio close to stoichiometry. In contrast, this work utilizes a physics-based Three-Way Catalyst (TWC) model to develop a model predictive control (MPC) strategy for air-fuel ratio control based on internal TWC oxygen storage dynamics. In this paper, parameters of the physics-based temperature and oxygen storage models of the TWC are identified using vehicle test data for a catalyst aged to 150,000 miles. A linearized oxygen storage model is then developed from the identified nonlinear model, which is shown via simulation to follow the nonlinear model with minimal error during nominal operation. This motivates the development of a Linear MPC (LMPC) framework using the linearized TWC oxygen storage model, reducing the requisite computational effort relative to a nonlinear MPC strategy. In this work, the LMPC utilizing a linearized physics-based TWC model is proven suitable for tracking a desired oxygen storage level by controlling the commanded engine air-fuel ratio, which is also a novel contribution. The offline simulation results show successful tracking performance of the developed LMPC framework. 

Long noncoding RNA (lncRNA) plays key roles in tumorigenesis. Misexpression of lncRNA can lead to changes in expression profiles of various target genes, which are involved in cancer initiation and progression. So, identifying key lncRNAs for a cancer would help develop the cancer therapy. Usually, to identify key lncRNAs for a cancer, expression profiles of lncRNAs for normal and cancer samples are required. But, this kind of data are not available for all cancers. In the present study, a computational framework is developed to identify cancer specific key lncRNAs using the lncRNA expression of cancer patients only. The framework consists of two state-of-the-art feature selection techniques - Recursive Feature Elimination (RFE) and Least Absolute Shrinkage and Selection Operator (LASSO); and five machine learning models - Naive Bayes, K-Nearest Neighbor, Random Forest, Support Vector Machine, and Deep Neural Network. For experiment, expression values of lncRNAs for 8 cancers - BLCA, CESC, COAD, HNSC, KIRP, LGG, LIHC, and LUAD - from TCGA are used. The combined dataset consists of 3,656 patients with expression values of 12,309 lncRNAs. Important features or key lncRNAs are identified by using feature selection algorithms RFE and LASSO. Capability of these key lncRNAs in classifying 8 different cancers is checked by the performance of five classification models. This study identified 37 key lncRNAs that can classify 8 different cancer types with an accuracy ranging from 94% to 97%. Finally, survival analysis supports that the discovered key lncRNAs are capable of differentiating between high-risk and low-risk patients. 

Breast cancer is highly sporadic and heterogeneous in nature. Even the patients with same clinical stage do not cluster together in terms of genomic profiles such as mRNA expression. In order to prevent and cure breast cancer completely, it is essential to decipher the detailed heterogeneity of breast cancer at genomic level. Putting the cancer patients on a time scale, which represents the trajectory of cancer development, may help discover the detailed heterogeneity. This in turn would help establish the mechanisms for prevention and complete cure of breast cancer. The goal of this study is to discover the heterogeneity of breast cancer by ordering the cancer patients using pseudotime. This is achieved through two objectives: First, a computational framework is developed to place the cancer patients on a time scale, meaning construct a trajectory of cancer development, by inferring pseudotime from static mRNA expression data; Second, discovering breast cancer heterogeneity at different time periods of the trajectory using statistical and machine learning techniques. In this study, the trajectory of breast cancer progression was constructed using static mRNA expression profiles of 1072 breast cancer patients by inferring pseudotime. Three sets of key genes discovered using supervised machine learning techniques are used to develop the trajectories. The first set of genes are PAM50 genes which is available in literature. The second and third sets of genes were discovered in the present study using the clinical stages of breast cancer (Stage-I, Stage-II, Stage-III, and Stage-IV). The proposed computational framework has the capability of deciphering heterogeneity in breast cancer at a granular level. The results also show the existence of multiple parallel trajectories at different time periods of cancer development or progression. 

Two graph theoretic concepts—clique and bipartite graphs—are explored to identify the network biomarkers for cancer at the gene network level. The rationale is that a group of genes work together by forming a cluster or a clique-like structures to initiate a cancer. After initiation, the disease signal goes to the next group of genes related to the second stage of a cancer, which can be represented as a bipartite graph. In other words, bipartite graphs represent the cross-talk among the genes between two disease stages. To prove this hypothesis, gene expression values for three cancers— breast invasive carcinoma (BRCA), colorectal adenocarcinoma (COAD) and glioblastoma multiforme (GBM)—are used for analysis. First, a co-expression gene network is generated with highly correlated gene pairs with a Pearson correlation coefficient ≥ 0.9. Second, clique structures of all sizes are isolated from the co-expression network. Then combining these cliques, three different biomarker modules are developed—maximal clique-like modules, 2-clique-1-bipartite modules, and 3-clique-2-bipartite modules. The list of biomarker genes discovered from these network modules are validated as the essential genes for causing a cancer in terms of network properties and survival analysis. This list of biomarker genes will help biologists to design wet lab experiments for further elucidating the complex mechanism of cancer.