One of the most powerful properties of mathematical systems theory is the fact that interconnecting systems yields composites that are themselves systems. This property allows for the engineering of complex systems by aggregating simpler systems into intricate patterns. We call these interconnection patterns the "structure" of the system. Similarly, this property also enables the understanding of complex systems by decomposing them into simpler parts. We likewise call the relationship between these parts the "structure" of the system. At first glance, these may appear to represent identical views of structure of a system. However, further investigation invites the question: are these two notions of structure of a system the same? This dissertation answers this question by developing a theory of dynamical structure. The work begins be distinguishing notions of structure from their associated mathematical representations, or models, of a system. Focusing on linear time invariant (LTI) systems, the key technical contributions begin by extending the definition of the dynamical structure function to all LTI systems and proving essential invariance properties as well as extending necessary and sufficient conditions for the reconstruction of the dynamical structure function from data. Given these extensions, we then develop a framework for analyzing the structures associated with different representations of the same system and use this framework to show that interconnection (or subsystem) structures are not necessarily the same as decomposition (or signal) structures. We also show necessary and sufficient conditions for the reconstruction of the interconnection (or subsystem) structure for a class of systems. In addition to theoretical contributions, this work also makes key contributions to specific applications. In particular, network reconstruction algorithms are developed that extend the applicability of existing methods to general LTI systems while improving the computational complexity. Also, a passive reconstruction method was developed that enables reconstruction without actively probing the system. Finally, the structural theory developed here is used to analyze the vulnerability of a system to simultaneous attacks (coordinated or uncoordinated), enabling a novel approach to the security of cyber-physical-human systems.

We investigate the signal and noise transform characteristics from the projection domain to the image domain in a linear systems theory framework and predictions of the DQE within this framework are made. A simulation study of a photon counting silicon detector is made from which the energy information is used in order to produce synthetic monoenergetic images. From these images the MTF, NPS, and DQE are estimated and are compared to the respective quantities predicted from the model. Within this model we find that the DQE in the projection domain has similar global characteristics as in the image domain, and that the sampling step in the imaging chain affects the DQE close to the zero frequency. / Vi undersöker hur signal och brus egenskaper transformeras från projektionsdomänen till bilddomänen i ett linjärt-skiftinvariant system och förutsägelser av DQE inom detta ramverk görs. Vidare görs en simuleringsstudie av en fotonräknande kiseldetektor från vilken energiinformationen används för att producera syntetiska monoenergetiska bilder. Från dessa bilder uppskattas MTF, NPS och DQE och jämförs med respektive storheter förutspådda från modellen. Inom modellen finner vi att DQE i projektionsdomänen har liknande globala egenskaper som i bilddomänen, och att samplingssteget i bildkedjan påverkar DQE nära nollfrekvensen.

The interconnection of molecular machines with different functionalities to form molecular communication systems can increase the number of design possibilities and overcome the limited reliability of the individual molecular machines. Artificial information exchange using molecular signals would also expand the capabilities of single engineered cell populations by providing them a way to cooperate across heterogeneous cell populations for the applications of synthetic biology and lab-on-a-chip systems. The realization of molecular communication systems necessitates analysis and design of the communication channel, where the information carrying molecular signal is transported from the transmitter to the receiver. In this thesis, significant progress towards the use of microfluidic channels to interconnect molecular transmitter and receiver pairs is presented. System-theoretic analysis of the microfluidic channels are performed, and a finite-impulse response filter is designed using microfluidic channels. The spectral density of the propagation noise is studied and the additive white Gaussian noise channel model is developed. Memory due to inter-diffusion of the transmitted molecular signals is also modeled. Furthermore, the interference modeling is performed for multiple transmitters and its impact on the communication capacity is shown. Finally, the efficient sampling of the signal transduction by engineered bacterial receivers connected to a microfluidic channel is investigated for the detection of the pulse-amplitude modulated molecular signals. This work lays the foundation for molecular communication over microfluidic channels that will enable interconnection of engineered molecular machines.