Optimal Experimental Design in the Context of Objective-Based Uncertainty Quantification

In many real-world engineering applications, model uncertainty is inherent. Largescale dynamical systems cannot be perfectly modeled due to systems complexity, lack of enough training data, perturbation, or noise. Hence, it is often of interest to acquire more data through additional experiments to enhance system model. On the other hand, high cost of experiments and limited operational resources make it necessary to devise a cost-effective plan to conduct experiments. In this dissertation, we are concerned with the problem of prioritizing experiments, called experimental design, aimed at uncertainty reduction in dynamical systems. We take an objective-based view where both uncertainty and modeling objective are taken into account for experimental design. To do so, we utilize the concept of mean objective cost of uncertainty to quantify uncertainty. The first part of this dissertation is devoted to the experimental design for gene regulatory networks. Owing to the complexity of these networks, accurate inference is practically challenging. Moreover, from a translational perspective it is crucial that gene regulatory network uncertainty be quantified and reduced in a manner that pertains to the additional cost of network intervention that it induces. We propose a criterion to rank potential experiments based on the concept of mean objective cost of uncertainty. To lower the computational cost of the experimental design, we also propose a network reduction scheme by introducing a novel cost function that takes into account the disruption in the ranking of potential experiments caused by gene deletion. We investigate the performance of both the optimal and the approximate experimental design methods on synthetic and real gene regulatory networks. In the second part, we turn our attention to canonical expansions. Canonical expansions are convenient representations that can facilitate the study of random processes. We discuss objective-based experimental design in the context of canonical expansions for three major applications: filtering, signal detection, and signal compression. We present the general experimental design framework for linear filtering and specifically solve it for Wiener filtering. Then we focus on Karhunen-Loève expansion to study experimental design for signal detection and signal compression applications when the noise variance and the signal covariance matrix are unknown, respectively. In particular, we find the closed-form solution for the intrinsically Bayesian robust Karhunen-Loève compression which is required for the experimental design in the case of signal compression

Quantization and Compressive Sensing

Quantization is an essential step in digitizing signals, and, therefore, an indispensable component of any modern acquisition system. This book chapter explores the interaction of quantization and compressive sensing and examines practical quantization strategies for compressive acquisition systems. Specifically, we first provide a brief overview of quantization and examine fundamental performance bounds applicable to any quantization approach. Next, we consider several forms of scalar quantizers, namely uniform, non-uniform, and 1-bit. We provide performance bounds and fundamental analysis, as well as practical quantizer designs and reconstruction algorithms that account for quantization. Furthermore, we provide an overview of Sigma-Delta ($\Sigma\Delta$) quantization in the compressed sensing context, and also discuss implementation issues, recovery algorithms and performance bounds. As we demonstrate, proper accounting for quantization and careful quantizer design has significant impact in the performance of a compressive acquisition system.Comment: 35 pages, 20 figures, to appear in Springer book "Compressed Sensing and Its Applications", 201

Classical and quantum shortcuts to adiabaticity for scale-invariant driving

A shortcut to adiabaticity is a driving protocol that reproduces in a short time the same final state that would result from an adiabatic, infinitely slow process. A powerful technique to engineer such shortcuts relies on the use of auxiliary counterdiabatic fields. Determining the explicit form of the required fields has generally proven to be complicated. We present explicit counterdiabatic driving protocols for scale-invariant dynamical processes, which describe for instance expansion and transport. To this end, we use the formalism of generating functions, and unify previous approaches independently developed in classical and quantum studies. The resulting framework is applied to the design of shortcuts to adiabaticity for a large class of classical and quantum, single-particle, non-linear, and many-body systems.Comment: 17 pages, 5 figure

Taylor Dispersion with Adsorption and Desorption

We use a stochastic approach to show how Taylor dispersion is affected by kinetic processes of adsorption and desorption onto surfaces. A general theory is developed, from which we derive explicitly the dispersion coefficients of canonical examples like Poiseuille flows in planar and cylindrical geometries, both in constant and sinusoidal velocity fields. These results open the way for the measurement of adsorption and desorption rate constants using stationary flows and molecular sorting using the stochastic resonance of the adsorption and desorption processes with the oscillatory velocity field.Comment: 6 pages, 4 figure

Regression Discontinuity Designs Using Covariates

We study regression discontinuity designs when covariates are included in the estimation. We examine local polynomial estimators that include discrete or continuous covariates in an additive separable way, but without imposing any parametric restrictions on the underlying population regression functions. We recommend a covariate-adjustment approach that retains consistency under intuitive conditions, and characterize the potential for estimation and inference improvements. We also present new covariate-adjusted mean squared error expansions and robust bias-corrected inference procedures, with heteroskedasticity-consistent and cluster-robust standard errors. An empirical illustration and an extensive simulation study is presented. All methods are implemented in \texttt{R} and \texttt{Stata} software packages