An investigation of the stability and diffusivity of flexible lipid vesicles for transdermal insulin delivery

Gemstone Team No More Needles

Performance and Robustness Analysis of Co-Prime and Nested Sampling

Coprime and nested sampling are well known deterministic sampling techniques that operate at rates significantly lower than the Nyquist rate, and yet allow perfect reconstruction of the spectra of wide sense stationary signals. However, theoretical guarantees for these samplers assume ideal conditions such as synchronous sampling, and ability to perfectly compute statistical expectations. This thesis studies the performance of coprime and nested samplers in spatial and temporal domains, when these assumptions are violated. In spatial domain, the robustness of these samplers is studied by considering arrays with perturbed sensor locations (with unknown perturbations). Simplified expressions for the Fisher Information matrix for perturbed coprime and nested arrays are derived, which explicitly highlight the role of co-array. It is shown that even in presence of perturbations, it is possible to resolve $O(M^2)$ under appropriate conditions on the size of the grid. The assumption of small perturbations leads to a novel ``bi-affine" model in terms of source powers and perturbations. The redundancies in the co-array are then exploited to eliminate the nuisance perturbation variable, and reduce the bi-affine problem to a linear underdetermined (sparse) problem in source powers. This thesis also studies the robustness of coprime sampling to finite number of samples and sampling jitter, by analyzing their effects on the quality of the estimated autocorrelation sequence. A variety of bounds on the error introduced by such non ideal sampling schemes are computed by considering a statistical model for the perturbation. They indicate that coprime sampling leads to stable estimation of the autocorrelation sequence, in presence of small perturbations. Under appropriate assumptions on the distribution of WSS signals, sharp bounds on the estimation error are established which indicate that the error decays exponentially with the number of samples. The theoretical claims are supported by extensive numerical experiments.

CONSERVATIVE AND PROGFESSIVE ASPECTS OF THE SONATA FROM LATE BEETHOVEN TO PROKOFIEV

The term 'sonata' arose in the early seventeenth-century Baroque period and was originally used to distinguish instrumental (sonata) music from vocal music. Later. the sonata style, as a reliable yet flexible compositional framework, was extensively shaped and utilized throughout the Classical period. Subsequently, in the Romantic period, freer creative, individualistic. and expressive musical elements began to be preferred by composers in their use of harmonj., tone color, form, and rhythm. However, even during the revolutionary Romantic period in music. the compositions which did not have a pre-defined format (character pieces, etc) were often comfortably framed and limited within the recognizable boundaries provided by the Classical sonata style. The sonata format, when used as a tool in musical composition, provides logical boundaries that may serve to organize any unexpected emotional expressions on the part of the composer. Yet the sonata framework is also flexible enough to allow freedom of expression. In the Romantic period and beyond, composers had relied, some more than others, upon the sonata's adaptable blend of stability and flexibility. In my opinion, it is more persuasive to express oneself musically within the framework of an established musical style. Thus, I have chosen my dissertation topic as the performance of six pieces incorporating elements of the reliable and flexible sonata style. The sonata of each composer that I have selected clearly demonstrates a tension between logic and emotion expressed within the sonata framework. However, the compositions can be divided interestingly into two groups, such as 'conservative' and 'progressive' group. The 'conservative' group consists of composers who seemed to strive for greater freedom of self-expression within the constraints of the traditional sonata form. On the other hand, the 'progressive' group consists of composers who seemed more to rely upon the sonata form to rein in and add stability to their highly individual and emotional musical ideas. It is my hope that this project will provide a stimulating viewpoint from which to consider the evolution and utilization of the sonata style especially as it is applied to the composition and performance of these six diverse and interesting pieces.