The ability to make sense of the complex sea of ever-changing molecules in the environment is one of the cell's most remarkable abilities. The molecular mechanisms by which these external cues are processed are well understood for many individual signaling pathways. However, fundamental questions for cell biology remain about how the collection of all such pathways within a cell—the signaling network—correctly responds to many inputs it receives. This dissertation focuses not only on determining the detailed biochemical mechanisms that resolve the complexities and ambiguities of individual cell signaling networks, but also on how these networks can change or grow to accommodate new pathways during evolution. To this end, reconstituted signaling networks are developed to probe the behavior of signaling systems under different environmental conditions or network compositions, as well as to rigorously compare evolutionarily related systems. Two different ambiguous network structures from model systems are explored from this perspective: overlapping signaling pathways arising from duplication/divergence events, derived from fungal ERK kinase signaling; and central signaling nodes that respond to multiple inputs and fan out to many possible outputs, derived from small Ras GTPase signaling. In the former case, allosteric dependencies on pathway-specific scaffold proteins were found to distinguish evolutionarily related molecules from one another and facilitate the use of homologous molecules in distinct signaling pathways. These allosteric dependencies appear to have evolved by exploitation of pre-existing differences in the conformational landscapes of otherwise-equivalent redundant signaling molecules. In the latter case, the behavior of Ras systems was explored in a multi-turnover in vitro setting for the first time. This revealed that Ras systems could transmit both sustained and transient signals and that the concentration and identity of signaling components strongly impacted the timing, duration, shape and amplitude of the output. Moreover, the extent to which oncogenic mutations in Ras distorted outputs was highly dependent on this underlying network configuration. Together, these studies demonstrate the utility of examining signaling systems not only from their current configuration, but the paths that led to that configuration during evolution, and the paths that might be taken through perturbation in the future.

Combustion in scramjet engines is faced with the limitation of brief residence time in the combustion chamber, requiring fuel and preheated air streams to mix and ignite in a matter of milliseconds. Accurate predictions of autoignition times are needed to design reliable supersonic combustion chambers. Most efforts in estimating non-premixed autoignition times have been de- voted to hydrogen-air mixtures. The present work addresses hydrocarbon-air combustion, which is of interest for future scramjet engines.

Computation of ignition in supersonic flows requires adequate characterization of ignition ix

chemistry and description of the flow, both of which are derived in this work. In particular, we have shown that activation energy asymptotics combined with a previously derived reduced chemical kinetic mechanism provides analytic predictions of autoignition times in homogeneous systems. Results are compared with data from shock tube experiments, and previous expressions which employ a fuel depletion criterion.

Ignition in scramjet engines has a strong dependence on temperature, which is found by perturbing the chemically frozen mixing layer solution. The frozen solution is obtained here, accounting for effects of viscous dissipation between the fuel and air streams. We investigate variations of thermodynamic and transport properties, and compare these to simplified mixing layers which neglect these variations. Numerically integrating the mixing layer problem reveals a nonmonotonic temperature profile, with a peak occurring inside the shear layer for sufficiently high Mach numbers.

These results will be essential in computation of ignition distances in supersonic combus- tion chambers.

An integer sequence {a n } is called polynomially recursive, or P-recursive, if it satisfies a nontrivial linear recurrence relation of the form

q_0(n)a_n + q_1(n)a_{n−1} + . . . + q_k(n)a_{n−k} = 0 ,

for some q_i(x) ∈ Z[x], 0 ≤ i ≤ k. The study of P-recursive sequences plays a major role in modern Enumerative and Asymptotic Combinatorics. P-recursive sequences have D-finite (also called holonomic) generating functions.

This dissertation is on the application of automata theory to the analysis of P-recursive integer sequences, and is broken into three self-contained chapters. Chapters 1 and 2 contain negative results, simulating Turing machines within combinatorial structures to show these structures are not counted by a P-recursive sequence. In Chapter 1, we answer a question of Maxim Kontsevich by showing [1]u_n is not always P-recursive when u ∈ Z[GL(k, Z)]. In Chapter 2, we disprove the celebrated Noonan-Zeilberger conjecture by showing that pattern avoidance is not P-recursive. These two chapters give the first results that disprove P-recursiveness using automata theory. Historically, results of this form have been mostly proven using analysis of the asymptotics.

Chapter 3 gives a full analysis of the class of integer sequences counting irrational tilings of a constant height strip. This class is a subset of P-recursive sequences, and we prove the equivalence of three definitions of this class: counting functions of irrational tilings, binomial multisums, and diagonals of N-rational generating functions. In this analysis, we count paths through a labelled graph in a way that is equivalent to counting strings accepted by a given deterministic finite automaton where each letter appears n times.

The scholarly study of punk is a growing interdisciplinary field. Within that already specialized group, research into punk pedagogy is emerging as a vital component of punk scholarship. However, no study in punk pedagogy has narrowed its scope to any one influential punk band to determine what constitutes its punk pedagogy. This dissertation weaves diverse disciplines together to elucidate the hidden curriculum of the progressive Canadian punk band, Propagandhi.

An understanding of Propagandhi’s punk pedagogy is formulated through textual analysis of the band’s lyrics, a sonic investigation of their music, interviews with the band, and surveys of Propagandhi fans, all informed and supported by an auto-ethnographic fan and learner experience of the researcher. As self-proclaimed “failures in school,” it is incredible that Propagandhi succeed in doing what so many schools wish to do: create critically engaged students embarking on a journey of becoming global citizens. Resolving how this could be the case brings many fields of study to task. What is the hidden curriculum woven into Propagandhi’s body of work that has effectively changed so many lives across the globe? Are they simply embodying a critical pedagogy, or have they crafted an approach unique to their brand of punk rock? Furthermore, this dissertation legitimizes the hidden curriculum found within informal educational settings. Propagandhi, ultimately, are able to strike a balance between reasonable critical thought and inquiry as outlined by Neil Postman’s theories on education, while Propagandhi also focus on changing social issues that are relevant and crucial to a free society. Propagandhi show that pain and hope can both be utilized as fuel for creative production.

Electronic excited states play two central roles in molecular chemistry: drivers of chemical change and reporters through spectroscopic measurements. While electronic ground states are theoretically well understood, excited states, and particularly excited states beyond the ground state linear response regime, require special treatment for both understanding of chemical phenomena and ab initio spectral predictions. In this work, we investigate tailoring state-specific electronic structure methodology to accurately predict X-ray absorption excitation energies both of closed shell and electronically excited molecules. X-ray absorption probes inner-shell core electrons and has become an powerful tool for studying chemical dynamics in time-resolved experiments. Many complications arise when describing the electronic structure of core-excited states, the most important of which is properly contracting the valence orbitals about the post-excitation core hole. We approach these challenges numerous ways. First, we utilize the latest advances in excited-state specific Quantum Monte Carlo (QMC) to calculate highly accurate, systematically improvable excitation energy predictions for small closed shell molecules, seeking to addresses whether QMC can serve in it's traditional role as a benchmark theoretical tool to test more approximate theories against. We then investigate how statistical uncertainty within QMC optimization can impact seemingly converged results when the wavefunction parameterization contains redundant parameters. Next, we address the accuracy of excited state mean field theory and it's perturbative extensions (ESMF and ESMP2) as a low cost alternative tool for predicting core excitation energies. Finally, we theoretically predict the time-resolved XAS spectra of the diradical photochemical ring opening of the furanone molecule. Through this work, we infer a novel spin-induced selection rule for core-to-unoccupied excitations of diradicals which should aid in the interpretation of time-resolved XAS experiments.

Introduction: Ferric derisomaltose is the newest available parenteral iron formulation. Studies have demonstrated a good safety profile with improved tolerability compared to alternative parenteral iron formulations. To date there have been no reported acute, life-threatening cardiac events associated with ferric derisomaltose.

Case Report: An 86-year-old male who had previously tolerated routine iron infusions received a first dose of ferric derisomaltose at an outpatient infusion clinic. Six minutes into the infusion the patient became unresponsive with no palpable pulse. Return of spontaneous circulation was achieved after two minutes of chest compressions. Electrocardiogram showed complete heart block requiring transcutaneous pacing and vasopressor administration. The patient was transferred to the emergency department for stabilization and then admitted to the cardiac intensive care unit. During admission, the patient received a dual-chamber, permanent pacemaker without complication and was ultimately discharged.

Conclusion: It may be reasonable to consider parenteral iron as a toxicological etiology for patients presenting with complete heart block temporally associated with parenteral iron administration, particularly in patients with underlying conduction abnormalities.