Designing Gabor windows using convex optimization

Redundant Gabor frames admit an infinite number of dual frames, yet only the canonical dual Gabor system, constructed from the minimal l2-norm dual window, is widely used. This window function however, might lack desirable properties, e.g. good time-frequency concentration, small support or smoothness. We employ convex optimization methods to design dual windows satisfying the Wexler-Raz equations and optimizing various constraints. Numerical experiments suggest that alternate dual windows with considerably improved features can be found

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

Structure Learning in Coupled Dynamical Systems and Dynamic Causal Modelling

Identifying a coupled dynamical system out of many plausible candidates, each of which could serve as the underlying generator of some observed measurements, is a profoundly ill posed problem that commonly arises when modelling real world phenomena. In this review, we detail a set of statistical procedures for inferring the structure of nonlinear coupled dynamical systems (structure learning), which has proved useful in neuroscience research. A key focus here is the comparison of competing models of (ie, hypotheses about) network architectures and implicit coupling functions in terms of their Bayesian model evidence. These methods are collectively referred to as dynamical casual modelling (DCM). We focus on a relatively new approach that is proving remarkably useful; namely, Bayesian model reduction (BMR), which enables rapid evaluation and comparison of models that differ in their network architecture. We illustrate the usefulness of these techniques through modelling neurovascular coupling (cellular pathways linking neuronal and vascular systems), whose function is an active focus of research in neurobiology and the imaging of coupled neuronal systems

Synthesis and Optimization of Reversible Circuits - A Survey

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table

The modularity of aesthetic processing and perception in the human brain. Functional neuroimaging studies of neuroaesthetics.

By taking advantage of the advent of functional Magnetic Resonance Imaging (fMRI) this thesis argues that aesthetics belongs in the domain of neurobiology by investigating the different brain processes that are implicated in aesthetic perception from two perspectives. The first experiment explores a specific artistic style that has stressed the problem in the relationship between objects and context. This study investigates the neural responses associated with changes in visual perception, as when objects are placed in their normal context versus when the object-context relationship is violated. Indeed, an aim of this study was to cast a new light on this specific artistic style from a neuroscientific perspective. In contrast to basic rewards, which relate to the reproduction of the species, the evolution of abstract, cognitive representations facilitates the use of a different class of rewards related to hedonics. The second part investigates the hedonic processes involved in aesthetic judgments in order to explore if such higher order cognitive rewards use the same neural reward mechanism as basic rewards. In the first of these experiments we modulate the extent to which the neural correlates of aesthetic preference vary as a function of expertise in architecture. In the second experiment we aim to measure the more general effects of labelling works of art with cognitive semantic information in order to explore the neural modulation of aesthetic preference relative to this information. The main finding of this thesis is that stimulus affective value is represented separately in OFC, with positive reward (increasing aesthetic judgments) being represented in medial OFC and negative reward value is being represented in lateral OFC. Furthermore ventral striatum encode reward expectancy and the predictive value of a stimulus. These findings suggest a dissociation of reward processing with separate neural substrates in reward expectancy and stimulus affective value