A geometric Newton method for Oja's vector field

Newton's method for solving the matrix equation $F(X)\equiv AX-XX^TAX=0$ runs up against the fact that its zeros are not isolated. This is due to a symmetry of $F$ by the action of the orthogonal group. We show how differential-geometric techniques can be exploited to remove this symmetry and obtain a ``geometric'' Newton algorithm that finds the zeros of $F$. The geometric Newton method does not suffer from the degeneracy issue that stands in the way of the original Newton method

Hierarchical Mixtures of Experts and the EM Algorithm

We present a tree-structured architecture for supervised learning. The statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM's). Learning is treated as a maximum likelihood problem; in particular, we present an Expectation-Maximization (EM) algorithm for adjusting the parameters of the architecture. We also develop an on-line learning algorithm in which the parameters are updated incrementally. Comparative simulation results are presented in the robot dynamics domain

Computational analysis on the effects of variations in T and B cells. Primary immunodeficiencies and cancer neoepitopes

Computational approaches are essential to study the effects of inborn and somatic variations. Results from such studies contribute to better diagnosis and therapies. Primary immunodeficiencies (PIDs) are rare inborn defects of key immune response genes. Somatic variations are main drivers of most cancers. Large and diverse data on PID genes and proteins can enable systems biology studies on their dynamic effects on T and B cells. Amino acid substitutions (AASs) are somatic variations that drive cancers. However, AASs also cause cancer-associated antigens that are recognized by lymphocytes as non-self, and are called neoantigens. Detail analysis these neoantigens can be performed due to the availability of cancer data from many consortia.The purpose of this thesis was to investigate the effects of PIDs on T and B cells and to explore features of neoepitopes in cancers. The object of the first study was to detect the central T cell-specific protein network. The purpose of the second and third studies were to reconstruct the T and B cell network model and simulate the dynamic effects of PID perturbations. The aim of the fourth study was to characterize neoepitopes from pan-cancer datasets.The immunome interactome was reconstructed, and the links weighed with gene expression correlation of integrated, time series data (Paper I). The significance of the weighted links were computed with the Global Statistical Significance (GloSS) method, and the weighted interactome network was filtered to obtain the central T cell network. Next, the T cell network model was reconstructed from literature mining and the core T cell protein interaction network (Paper II). The B cell network model was reconstructed by mining the literature for central B cell interactions (Paper III). The normalized HillCube software was used to study the dynamic effects of PID perturbations in T and B cells. Proteome-wide amino AASs on putatively derived 8-, 9-, 10-, and 11-mer neoepitopes in 30 cancer types were analyzed with the NetMHC 4.0 software (Paper IV).The interconnectedness of the major T cell pathways are maintained in the central T cell PPI network. Empirical evidence from Gene Ontology term and essential genes enrichment analyses were in support for the central T cell network. In the T and B cell simulations for several knockout PIDs correspond to previous results. In the T cell model, simulations for TCR, PTPRC, LCK, ZAP70 and ITK indicated profound disruption in network dynamics. BCL10, CARD11, MALT1, NEMO and MAP3K14 simulations showed significant effects. In B cell, the simulations for LYN, BTK, STIM1, ORAI1, CD19, CD21 and CD81 indicated profound changes to many proteins in the network. Severe effects were observed in the BCL10, IKKB, knockout CARD11, MALT1, NEMO, IKKB and WIPF1 simulations. No major effects were observed for constitutively active PID proteins. The most likely epitopes are those which are detected by several macromolecular histocompartibility complexes (MHCs) and of several peptide lengths. 0.17% of all variants yield more than 100 neoepitopes. Amino acid distributions indicate that variants at all positions in neoepitopes of any length are, on average, more hydrophobic compared to the wild-type.The core T cell network approach is general and applicable to any system with adequate data. The T and B cell models enable the understanding of the dynamic effects of PID disease processes and reveals several novel proteins that may be of interest when diagnosing and treating immunological defects. The neoepitope characteristics can be employed for targeted cancer vaccine applications in personalized therapies