A probabilistic treatment of uncertainty in nonlinear dynamical systems

In this work, computationally efficient approximate methods are developed for analyzing uncertain dynamical systems. Uncertainties in both the excitation and the modeling are considered and examples are presented illustrating the accuracy of the proposed approximations.

For nonlinear systems under uncertain excitation, methods are developed to approximate the stationary probability density function and statistical quantities of interest. The methods are based on approximating solutions to the Fokker-Planck equation for the system and differ from traditional methods in which approximate solutions to stochastic differential equations are found. The new methods require little computational effort and examples are presented for which the accuracy of the proposed approximations compare favorably to results obtained by existing methods. The most significant improvements are made in approximating quantities related to the extreme values of the response, such as expected outcrossing rates, which are crucial for evaluating the reliability of the system.

Laplace's method of asymptotic approximation is applied to approximate the probability integrals which arise when analyzing systems with modeling uncertainty. The asymptotic approximation reduces the problem of evaluating a multidimensional integral to solving a minimization problem and the results become asymptotically exact as the uncertainty in the modeling goes to zero. The method is found to provide good approximations for the moments and outcrossing rates for systems with uncertain parameters under stochastic excitation, even when there is a large amount of uncertainty in the parameters. The method is also applied to classical reliability integrals, providing approximations in both the transformed (independently, normally distributed) variables and the original variables. In the transformed variables, the asymptotic approximation yields a very simple formula for approximating the value of SORM integrals. In many cases, it may be computationally expensive to transform the variables, and an approximation is also developed in the original variables. Examples are presented illustrating the accuracy of the approximations and results are compared with existing approximations.

Future of earthquake early warning : quantifying uncertainty and making fast automated decisions for applications

Earthquake early warning (EEW) systems have been rapidly developing over the past decade. Japan Meteorological Agency (JMA) has an EEW system that was operating during the 2011 M9 Tohoku earthquake in Japan, and this increased the awareness of EEW systems around the world. While longer-time earthquake prediction still faces many challenges to be practical, the availability of shorter-time EEW opens up a new door for earthquake loss mitigation. After an earthquake fault begins rupturing, an EEW system utilizes the first few seconds of recorded seismic waveform data to quickly predict the hypocenter location, magnitude, origin time and the expected shaking intensity level around the region. This early warning information is broadcast to different sites before the strong shaking arrives. The warning lead time of such a system is short, typically a few seconds to a minute or so, and the information is uncertain. These factors limit human intervention to activate mitigation actions and this must be addressed for engineering applications of EEW. This study applies a Bayesian probabilistic approach along with machine learning techniques and decision theories from economics to improve different aspects of EEW operation, including extending it to engineering applications.

Existing EEW systems are often based on a deterministic approach. Often, they assume that only a single event occurs within a short period of time, which led to many false alarms after the Tohoku earthquake in Japan. This study develops a probability-based EEW algorithm based on an existing deterministic model to extend the EEW system to the case of concurrent events, which are often observed during the aftershock sequence after a large earthquake.

To overcome the challenge of uncertain information and short lead time of EEW, this study also develops an earthquake probability-based automated decision-making (ePAD) framework to make robust decision for EEW mitigation applications. A cost-benefit model that can capture the uncertainties in EEW information and the decision process is used. This approach is called the Performance-Based Earthquake Early Warning, which is based on the PEER Performance-Based Earthquake Engineering method. Use of surrogate models is suggested to improve computational efficiency. Also, new models are proposed to add the influence of lead time into the cost-benefit analysis. For example, a value of information model is used to quantify the potential value of delaying the activation of a mitigation action for a possible reduction of the uncertainty of EEW information in the next update. Two practical examples, evacuation alert and elevator control, are studied to illustrate the ePAD framework. Potential advanced EEW applications, such as the case of multiple-action decisions and the synergy of EEW and structural health monitoring systems, are also discussed.

Microfluidics-based single-cell functional proteomics microchip for portraying protein signal transduction networks within the framework of physicochemical principles, with applications in fundamental and translational cancer research

Single-cell functional proteomics assays can connect genomic information to biological function through quantitative and multiplex protein measurements. Tools for single-cell proteomics have developed rapidly over the past 5 years and are providing unique opportunities. This thesis describes an emerging microfluidics-based toolkit for single cell functional proteomics, focusing on the development of the single cell barcode chips (SCBCs) with applications in fundamental and translational cancer research.

The microchip designed to simultaneously quantify a panel of secreted, cytoplasmic and membrane proteins from single cells will be discussed at the beginning, which is the prototype for subsequent proteomic microchips with more sophisticated design in preclinical cancer research or clinical applications. The SCBCs are a highly versatile and information rich tool for single-cell functional proteomics. They are based upon isolating individual cells, or defined number of cells, within microchambers, each of which is equipped with a large antibody microarray (the barcode), with between a few hundred to ten thousand microchambers included within a single microchip. Functional proteomics assays at single-cell resolution yield unique pieces of information that significantly shape the way of thinking on cancer research. An in-depth discussion about analysis and interpretation of the unique information such as functional protein fluctuations and protein-protein correlative interactions will follow.

The SCBC is a powerful tool to resolve the functional heterogeneity of cancer cells. It has the capacity to extract a comprehensive picture of the signal transduction network from single tumor cells and thus provides insight into the effect of targeted therapies on protein signaling networks. We will demonstrate this point through applying the SCBCs to investigate three isogenic cell lines of glioblastoma multiforme (GBM).

The cancer cell population is highly heterogeneous with high-amplitude fluctuation at the single cell level, which in turn grants the robustness of the entire population. The concept that a stable population existing in the presence of random fluctuations is reminiscent of many physical systems that are successfully understood using statistical physics. Thus, tools derived from that field can probably be applied to using fluctuations to determine the nature of signaling networks. In the second part of the thesis, we will focus on such a case to use thermodynamics-motivated principles to understand cancer cell hypoxia, where single cell proteomics assays coupled with a quantitative version of Le Chatelier's principle derived from statistical mechanics yield detailed and surprising predictions, which were found to be correct in both cell line and primary tumor model.

The third part of the thesis demonstrates the application of this technology in the preclinical cancer research to study the GBM cancer cell resistance to molecular targeted therapy. Physical approaches to anticipate therapy resistance and to identify effective therapy combinations will be discussed in detail. Our approach is based upon elucidating the signaling coordination within the phosphoprotein signaling pathways that are hyperactivated in human GBMs, and interrogating how that coordination responds to the perturbation of targeted inhibitor. Strongly coupled protein-protein interactions constitute most signaling cascades. A physical analogy of such a system is the strongly coupled atom-atom interactions in a crystal lattice. Similar to decomposing the atomic interactions into a series of independent normal vibrational modes, a simplified picture of signaling network coordination can also be achieved by diagonalizing protein-protein correlation or covariance matrices to decompose the pairwise correlative interactions into a set of distinct linear combinations of signaling proteins (i.e. independent signaling modes). By doing so, two independent signaling modes – one associated with mTOR signaling and a second associated with ERK/Src signaling have been resolved, which in turn allow us to anticipate resistance, and to design combination therapies that are effective, as well as identify those therapies and therapy combinations that will be ineffective. We validated our predictions in mouse tumor models and all predictions were borne out.

In the last part, some preliminary results about the clinical translation of single-cell proteomics chips will be presented. The successful demonstration of our work on human-derived xenografts provides the rationale to extend our current work into the clinic. It will enable us to interrogate GBM tumor samples in a way that could potentially yield a straightforward, rapid interpretation so that we can give therapeutic guidance to the attending physicians within a clinical relevant time scale. The technical challenges of the clinical translation will be presented and our solutions to address the challenges will be discussed as well. A clinical case study will then follow, where some preliminary data collected from a pediatric GBM patient bearing an EGFR amplified tumor will be presented to demonstrate the general protocol and the workflow of the proposed clinical studies.