Quantum of Vision

Visual inputs to artificial and biological visual systems are often quantized: cameras accumulate photons from the visual world, and the brain receives action potentials from visual sensory neurons. Collecting more information quanta leads to a longer acquisition time and better performance. In many visual tasks, collecting a small number of quanta is sufficient to solve the task well. The ability to determine the right number of quanta is pivotal in situations where visual information is costly to obtain, such as photon-starved or time-critical environments. In these situations, conventional vision systems that always collect a fixed and large amount of information are infeasible. I develop a framework that judiciously determines the number of information quanta to observe based on the cost of observation and the requirement for accuracy. The framework implements the optimal speed versus accuracy tradeoff when two assumptions are met, namely that the task is fully specified probabilistically and constant over time. I also extend the framework to address scenarios that violate the assumptions. I deploy the framework to three recognition tasks: visual search (where both assumptions are satisfied), scotopic visual recognition (where the model is not specified), and visual discrimination with unknown stimulus onset (where the model is dynamic over time). Scotopic classification experiments suggest that the framework leads to dramatic improvement in photon-efficiency compared to conventional computer vision algorithms. Human psychophysics experiments confirmed that the framework provides a parsimonious and versatile explanation for human behavior under time pressure in both static and dynamic environments.

Disorder driven transitions in non-equilibrium quantum systems

This thesis presents studies of the role of disorder in non-equilibrium quantum systems. The quantum states relevant to dynamics in these systems are very different from the ground state of the Hamiltonian. Two distinct systems are studied, (i) periodically driven Hamiltonians in two dimensions, and (ii) electrons in a one-dimensional lattice with power-law decaying hopping amplitudes. In the first system, the novel phases that are induced from the interplay of periodic driving, topology and disorder are studied. In the second system, the Anderson transition in all the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude.

In periodically driven systems the study focuses on the effect of disorder in the nature of the topology of the steady states. First, we investigate the robustness to disorder of Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are generated by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator.

Interestingly, the effects of disorder are not necessarily adverse, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). Such a state would be a dynamical realization of the topological Anderson insulator. We identify the conditions on the driving field necessary for observing such a transition. We realize such a disorder induced topological Floquet spectrum in the driven honeycomb lattice and quantum well models.

Finally, we show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.

The thesis also present the study of disordered systems using Wegner's Flow equations. The Flow Equation Method was proposed as a technique for studying excited states in an interacting system in one dimension. We apply this method to a one-dimensional tight binding problem with power-law decaying hoppings. This model presents a transition as a function of the exponent of the decay. It is shown that the the entire phase diagram, i.e. the delocalized, critical and localized phases in these systems can be studied using this technique. Based on this technique, we develop a strong-bond renormalization group that procedure where we solve the Flow Equations iteratively. This renormalization group approach provides a new framework to study the transition in this system.

Ferrous iron sensing and responding in Pseudomonas aeruginosa

Controlling iron distribution is important for all organisms, and is key in bacterial pathogenesis. It has long been understood that cystic fibrosis (CF) patient sputum contains elevated iron concentrations. However, anaerobic bacteria have been isolated from CF sputum and hypoxic zones in sputum have been measured. Because ferrous iron [Fe(II)] is stable in reducing, acidic conditions, it could exist in the CF lung. I show that a two-component system, BqsRS, specifically responds to Fe(II) in the CF pathogen, Pseudomonas aeruginosa. Concurrently, a clinical study found that Fe(II) is present in CF sputum at all stages of lung function decline. Fe(II), not Fe(III) correlates with patients in the most severe disease state. Furthermore, transcripts of the newly identified BqsRS were detected in sputum. Two component systems are the main method bacteria interact with their extracellular environment. A typical two-component system contains a sensor histidine kinase, which upon activation phosphorylates a response regulator that then acts as a transcription factor to elicit a cellular response to stimuli. To explore the mechanism of BqsRS, I describe the Fe(II)-sensing RExxE motif in the sensor BqsS and determine the consensus DNA sequence BqsR binds. With the BqsR binding sequence, I identify novel regulon members through bioinformatic and molecular biology techniques. From the predicted function of new BqsR regulon members, I find that Fe(II) elicits a response that globally protects the cells against cationic stressors, including clinically relevant antibiotics. Subsequently, I use BqsR as a case study to determine if promoter outputs can accurately be predicted based only on a deep understanding of a transcriptional activator’s operator or if a broader regulatory context is required for accurate predictions at all genomic loci. This work highlights the importance of Fe(II) as a (micro)environmental factor, even in conditions typically thought of as aerobic. Since the presence of Fe(II) can alter P. aeruginosa’s antibiotic susceptibility, combining the current strategy of targeting Fe(III) with a new approach targeting Fe(II) may help eradicate infections in the CF lung in the future.