Differential Equation Models and Numerical Methods for Reverse Engineering Genetic Regulatory Networks

This dissertation develops and analyzes differential equation-based mathematical models and efficient numerical methods and algorithms for genetic regulatory network identification. The primary objectives of the dissertation are to design, analyze, and test a general variational framework and numerical methods for seeking its approximate solutions for reverse engineering genetic regulatory networks from microarray datasets using the approach based on differential equation modeling. In the proposed variational framework, no structure assumption on the genetic network is presumed, instead, the network is solely determined by the microarray profile of the network components and is identified through a well chosen variational principle which minimizes a biological energy functional. The variational principle serves not only as a selection criterion to pick up the right biological solution of the underlying differential equation model but also provide an effective mathematical characterization of the small-world property of genetic regulatory networks which has been observed in lab experiments. Five specific models within the variational framework and efficient numerical methods and algorithms for computing their solutions are proposed and analyzed in the dissertation. Model validations using both synthetic network datasets and real world subnetwork datasets of Saccharomyces cerevisiae (yeast) and E. Coli are done on all five proposed variational models and a performance comparison vs some existing genetic regulatory network identification methods is also provided. As microarray data is typically noisy, in order to take into account the noise effect in the mathematical models, we propose a new approach based on stochastic differential equation modeling and generalize the deterministic variational framework to a stochastic variational framework which relies on stochastic optimization. Numerical algorithms are also proposed for computing solutions of the stochastic variational models. To address the important issue of post-processing computed networks to reflect the small-world property of underlying genetic regulatory networks, a novel threshholding technique based on the Random Matrix Theory is proposed and tested on various synthetic network datasets

PERFORMANCE EVALUATION OF DIFFERENT INTERFERENCE MODELS IN WIRELESS MESH NETWORKS, BY MEANS OF GENETIC ALGORITHMS

Comparison among different interference models, in order to maximize the throughput in a wireless mesh network (WMN). We have developed an implementation of genetic algorithms to deal with the joint link scheduling and routing problem in a WMN

Mapping eQTL networks with mixed graphical Markov models

Expression quantitative trait loci (eQTL) mapping constitutes a challenging problem due to, among other reasons, the high-dimensional multivariate nature of gene-expression traits. Next to the expression heterogeneity produced by confounding factors and other sources of unwanted variation, indirect effects spread throughout genes as a result of genetic, molecular and environmental perturbations. From a multivariate perspective one would like to adjust for the effect of all of these factors to end up with a network of direct associations connecting the path from genotype to phenotype. In this paper we approach this challenge with mixed graphical Markov models, higher-order conditional independences and q-order correlation graphs. These models show that additive genetic effects propagate through the network as function of gene-gene correlations. Our estimation of the eQTL network underlying a well-studied yeast data set leads to a sparse structure with more direct genetic and regulatory associations that enable a straightforward comparison of the genetic control of gene expression across chromosomes. Interestingly, it also reveals that eQTLs explain most of the expression variability of network hub genes.Comment: 48 pages, 8 figures, 2 supplementary figures; fixed problems with embedded fonts; figure 7 sideways for improving display; minor fixes; major revision of the paper after journal review; fixed missing .bbl file; 36 pages, 6 figures, 2 table

Quantitative model for inferring dynamic regulation of the tumour suppressor gene p53

Background: The availability of various "omics" datasets creates a prospect of performing the study of genome-wide genetic regulatory networks. However, one of the major challenges of using mathematical models to infer genetic regulation from microarray datasets is the lack of information for protein concentrations and activities. Most of the previous researches were based on an assumption that the mRNA levels of a gene are consistent with its protein activities, though it is not always the case. Therefore, a more sophisticated modelling framework together with the corresponding inference methods is needed to accurately estimate genetic regulation from "omics" datasets. Results: This work developed a novel approach, which is based on a nonlinear mathematical model, to infer genetic regulation from microarray gene expression data. By using the p53 network as a test system, we used the nonlinear model to estimate the activities of transcription factor (TF) p53 from the expression levels of its target genes, and to identify the activation/inhibition status of p53 to its target genes. The predicted top 317 putative p53 target genes were supported by DNA sequence analysis. A comparison between our prediction and the other published predictions of p53 targets suggests that most of putative p53 targets may share a common depleted or enriched sequence signal on their upstream non-coding region. Conclusions: The proposed quantitative model can not only be used to infer the regulatory relationship between TF and its down-stream genes, but also be applied to estimate the protein activities of TF from the expression levels of its target genes

RIDDLE: Race and ethnicity Imputation from Disease history with Deep LEarning

Anonymized electronic medical records are an increasingly popular source of research data. However, these datasets often lack race and ethnicity information. This creates problems for researchers modeling human disease, as race and ethnicity are powerful confounders for many health exposures and treatment outcomes; race and ethnicity are closely linked to population-specific genetic variation. We showed that deep neural networks generate more accurate estimates for missing racial and ethnic information than competing methods (e.g., logistic regression, random forest). RIDDLE yielded significantly better classification performance across all metrics that were considered: accuracy, cross-entropy loss (error), and area under the curve for receiver operating characteristic plots (all $p < 10^{-6}$). We made specific efforts to interpret the trained neural network models to identify, quantify, and visualize medical features which are predictive of race and ethnicity. We used these characterizations of informative features to perform a systematic comparison of differential disease patterns by race and ethnicity. The fact that clinical histories are informative for imputing race and ethnicity could reflect (1) a skewed distribution of blue- and white-collar professions across racial and ethnic groups, (2) uneven accessibility and subjective importance of prophylactic health, (3) possible variation in lifestyle, such as dietary habits, and (4) differences in background genetic variation which predispose to diseases

Forecasting Regional Employment in Germany by Means of Neural Networks and Genetic Algorithms

The aim of this paper is to develop and apply Neural Network (NN) models in order to forecast regional employment patterns in Germany. NNs are statistical tools based on learning algorithms with a distribution over a large amount of quantitative data. NNs are increasingly deployed in the social sciences as a useful technique for interpolating data when a clear specification of the functional relationship between dependent and independent variables is not available. In addition to traditional NN models, a further set of NN models will be developed in this paper, incorporating Genetic Algorithm (GA) techniques in order to detect the networks’ structure. GAs are computer-aided optimization tools that imitate natural biological evolution in order to find the solution that best fits the given case. Our experiments employ a data set consisting of a panel of 439 districts distributed over the former West and East Germany,. The West and East data sets have different time horizons, as employment information by district is available from 1987 and 1993 for West and East Germany, respectively. Separate West and East models are tested, before carrying out a unified experiment on the full data set for Germany. The above models are then evaluated by means of several statistical indicators, in order to test their ability to provide out- of-sample forecasts. A comparison between traditional and GAenhanced models is ultimately proposed. The results show that the West and East NN models perform with different degrees of precision, because of the different data sets’ time horizons.forecasting; neural networks; regional labour markets

Bayesian neural networks for detecting epistasis in genetic association studies

Background: Discovering causal genetic variants from large genetic association studies poses many difficult challenges. Assessing which genetic markers are involved in determining trait status is a computationally demanding task, especially in the presence of gene-gene interactions. Results: A non-parametric Bayesian approach in the form of a Bayesian neural network is proposed for use in analyzing genetic association studies. Demonstrations on synthetic and real data reveal they are able to efficiently and accurately determine which variants are involved in determining case-control status. By using graphics processing units (GPUs) the time needed to build these models is decreased by several orders of magnitude. In comparison with commonly used approaches for detecting interactions, Bayesian neural networks perform very well across a broad spectrum of possible genetic relationships. Conclusions: The proposed framework is shown to be a powerful method for detecting causal SNPs while being computationally efficient enough to handle large datasets. Electronic supplementary material The online version of this article (doi:10.1186/s12859-014-0368-0) contains supplementary material, which is available to authorized users

Impact of Security Factors in Software Project Risk Assessment Using Neural Networks

"Software risk” is the measurement of the probability of an unwanted output that could affect the software product’s development process. It always includes the chance of being uncertain and a potential for loss. This paper extends the concepts of Constructive Cost Model (COCOMO) model into fuzzy Expert COCOMO by introducing security factors as additional parameters for the assessment of risk of a software project. This approach is validated with the NASA60 project data and proved that Genetic Algorithm provided efficient risk values with different levels of security parameters. However, in the earlier methods, there was a limitation in effectively dealing with linguistic forms of imprecise and uncertain inputs. This resulted in increase in the cost of designing the mechanisms for security purposes, that formed a major part in the overall cost in the development process of the software product. The risk value of a software project could well be reduced by taking security factors into consideration. The neural network techniques used for validating the risk values are Kohonen neural network, Radial Basis neural (RBF) network, Learning Vector Quantization, Genetic Algorithm(GA). A comparison study has been provided for all the neural network models implemented in order to examine their performances