I. Quantal effects in biochemical cooperativity and a proposed mechanism for the differentiation of calcium signaling in synaptic plasticity. II. Evolutionary algorithms for the optimization of methods in computational chemistry

In Part 1 of this thesis, we propose that biochemical cooperativity is a fundamentally non-ideal process. We show quantal effects underlying biochemical cooperativity and highlight apparent ergodic breaking at small volumes. The apparent ergodic breaking manifests itself in a divergence of deterministic and stochastic models. We further predict that this divergence of deterministic and stochastic results is a failure of the deterministic methods rather than an issue of stochastic simulations.

Ergodic breaking at small volumes may allow these molecular complexes to function as switches to a greater degree than has previously been shown. We propose that this ergodic breaking is a phenomenon that the synapse might exploit to differentiate Ca$^{2+}$ signaling that would lead to either the strengthening or weakening of a synapse. Techniques such as lattice-based statistics and rule-based modeling are tools that allow us to directly confront this non-ideality. A natural next step to understanding the chemical physics that underlies these processes is to consider \textit{in silico} specifically atomistic simulation methods that might augment our modeling efforts.

In the second part of this thesis, we use evolutionary algorithms to optimize \textit{in silico} methods that might be used to describe biochemical processes at the subcellular and molecular levels. While we have applied evolutionary algorithms to several methods, this thesis will focus on the optimization of charge equilibration methods. Accurate charges are essential to understanding the electrostatic interactions that are involved in ligand binding, as frequently discussed in the first part of this thesis.

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.

Development and Detailed Characterization of Innovative, High-Performance Membrane Materials for CO2 Capture Processes

The scope of this dissertation is to study the transport phenomena of small molecules in polymers and membranes for gas separation applications, with particular attention to energy efficiency and environmental sustainability. This work seeks to contribute to the development of new competitive selective materials through the characterization of novel organic polymers such as CANALs and ROMPs, as well as through the combination of selective materials obtaining mixed matrix membranes (MMMs), to make membrane technologies competitive with the traditional ones. Kinetic and thermodynamic aspects of the transport properties were investigated in ideal and non-ideal scenarios, such as mixed-gas experiments. The information we gathered contributed to the development of the fundamental understanding related to phenomenon like CO2-induced plasticization and physical aging. Among the most significant results, ZIF-8/PPO MMMs provided materials whose permeability and selectivity were higher than those of the pure materials for He/CO2 separation. The CANALs featured norbornyl benzocyclobutene backbone and thereby introduced a third typology of ladder polymers in the gas separation field, expanding the structural diversity of microporous materials. CANALs have a completely hydrocarbon-based and non-polar rigid backbone, which makes them an ideal model system to investigate structure-property correlations. ROMPs were synthesized by means of the ring opening metathesis living polymerization, which allowed the formation of bottlebrush polymers. CF3-ROMP reveled to be ultrapermeable to CO2, with unprecedented plasticization resistance properties. Mixed-gas experiments in glassy polymer showed that solubility-selectivity controls the separation efficiency of materials in multicomponent conditions. Finally, it was determined that plasticization pressure in not an intrinsic property of a material and does not represent a state of the system, but rather comes from the contribution of solubility coefficient and diffusivity coefficient in the framework of the solution-diffusion model.

Unsupervised reinforcement learning via state entropy maximization

Reinforcement Learning (RL) provides a powerful framework to address sequential decision-making problems in which the transition dynamics is unknown or too complex to be represented. The RL approach is based on speculating what is the best decision to make given sample estimates obtained from previous interactions, a recipe that led to several breakthroughs in various domains, ranging from game playing to robotics. Despite their success, current RL methods hardly generalize from one task to another, and achieving the kind of generalization obtained through unsupervised pre-training in non-sequential problems seems unthinkable. Unsupervised RL has recently emerged as a way to improve generalization of RL methods. Just as its non-sequential counterpart, the unsupervised RL framework comprises two phases: An unsupervised pre-training phase, in which the agent interacts with the environment without external feedback, and a supervised fine-tuning phase, in which the agent aims to efficiently solve a task in the same environment by exploiting the knowledge acquired during pre-training. In this thesis, we study unsupervised RL via state entropy maximization, in which the agent makes use of the unsupervised interactions to pre-train a policy that maximizes the entropy of its induced state distribution. First, we provide a theoretical characterization of the learning problem by considering a convex RL formulation that subsumes state entropy maximization. Our analysis shows that maximizing the state entropy in finite trials is inherently harder than RL. Then, we study the state entropy maximization problem from an optimization perspective. Especially, we show that the primal formulation of the corresponding optimization problem can be (approximately) addressed through tractable linear programs. Finally, we provide the first practical methodologies for state entropy maximization in complex domains, both when the pre-training takes place in a single environment as well as multiple environments.

Undergraduate teaching of ideal and real fluid flows: The value of real-world experimental projects

This study describes the pedagogical impact of real-world experimental projects undertaken as part of an advanced undergraduate Fluid Mechanics subject at an Australian university. The projects have been organised to complement traditional lectures and introduce students to the challenges of professional design, physical modelling, data collection and analysis. The physical model studies combine experimental, analytical and numerical work in order to develop students’ abilities to tackle real-world problems. A first study illustrates the differences between ideal and real fluid flow force predictions based upon model tests of buildings in a large size wind tunnel used for research and professional testing. A second study introduces the complexity arising from unsteady non-uniform wave loading on a sheltered pile. The teaching initiative is supported by feedback from undergraduate students. The pedagogy of the course and projects is discussed with reference to experiential, project-based and collaborative learning. The practical work complements traditional lectures and tutorials, and provides opportunities which cannot be learnt in the classroom, real or virtual. Student feedback demonstrates a strong interest for the project phases of the course. This was associated with greater motivation for the course, leading in turn to lower failure rates. In terms of learning outcomes, the primary aim is to enable students to deliver a professional report as the final product, where physical model data are compared to ideal-fluid flow calculations and real-fluid flow analyses. Thus the students are exposed to a professional design approach involving a high level of expertise in fluid mechanics, with sufficient academic guidance to achieve carefully defined learning goals, while retaining sufficient flexibility for students to construct there own learning goals. The overall pedagogy is a blend of problem-based and project-based learning, which reflects academic research and professional practice. The assessment is a mix of peer-assessed oral presentations and written reports that aims to maximise student reflection and development. Student feedback indicated a strong motivation for courses that include a well-designed project component.

A non-extensive maximum entropy based regulations method for bad conditioned inverse problems

A regularization method based on the non-extensive maximum entropy principle is devised. Special emphasis is given to the q=1/2 case. We show that, when the residual principle is considered as constraint, the q=1/2 generalized distribution of Tsallis yields a regularized solution for bad-conditioned problems. The so devised regularized distribution is endowed with a component which corresponds to the well known regularized solution of Tikhonov (1977).

Agency problems with non-smooth decision profiles: the case of monopoly under product quality

A method for dealing with monotonicity constraints in optimal control problems is used to generalize some results in the context of monopoly theory, also extending the generalization to a large family of principal-agent programs. Our main conclusion is that many results on diverse economic topics, achieved under assumptions of continuity and piecewise differentiability in connection with the endogenous variables of the problem, still remain valid after replacing such assumptions by two minimal requirements.

La multiculturalité, la communauté et les femmes non-conventionnelles dans The Diviners de Margaret Laurence et O Pioneers! de Willa Cather

Résumé Ce mémoire traite des enjeux multiculturels du tournant du vingtième siècle en Amérique du Nord, des problématiques de la communauté de face-à-face ainsi que de la non-conventionalité des protagonistes féminins présents dans The Diviners (1974) de Margaret Laurence et O Pioneers! (1913) de Willa Cather. Cette étude a pour objectif de faire des liens entre ces deux œuvres qui ont été écrites par des auteures féminines, qui mettent en scène des femmes fortes et émancipées dans des petites communautés multiculturelles de l’Ouest. Cette étude traitera également des différences entre les deux romans, soit l’époque et le contexte. Cette étude s’intéressera, en premier lieu, aux différents enjeux de la multiculturalité et analysera les deux romans à la lumière de concepts tels le Melting pot, l’assimilation et l’interculturalité. Cette étude s’intéressera ensuite aux problématiques de la communauté de face-à-face. Elle aura pour objectif de déconstruire l’idéal type de la communauté de face-à-face et de démontrer comment frictions et rejets font partie du quotidien des personnages des deux romans. En dernier lieu, cette étude s’intéressera à la non-conventionalité des personnages féminins principaux. En effet, chacune à leur manière, les protagonistes fracassent les stéréotypes féminins de leur milieu et de leur époque afin de s’émanciper.

Insertion socioprofessionnelle des sortants de la formation agricole non formelle sur le marché de l’emploi au Burkina Faso et importance accordée à la production céréalière : cas des sortants du centre de promotion rurale de Goundi

L'étude combine les méthodes qualitative et qualitative à travers l’utilisation du questionnaire et du canevas d’entrevue. Elle s’appuie sur un cadre conceptuel élaboré à partir de revue de littérature et de concepts clefs tels que : le capital social, le capital humain, l’identité personnelle, l’identité professionnelle et la socialisation, Les résultats déterminent le profil d’un céréalier indiquant son attachement aux valeurs professionnelles liées au transfert de ses connaissances, à la modernisation de l’exploitation, à la recherche de l’amélioration du rendement et à l’utilisation d’outils modernes.

Studies on magnetic monopole solutions of non-abelian gauge theories and related problems

In 1931 Dirac studied the motion of an electron in the field of a magnetic monopole and found that the quantization of electric charge can be explained by postulating the mere existence of a magnetic monopole. Since 1974 there has been a resurgence of interest in magnetic monopole due to the work of ‘t’ Hooft and Polyakov who independently observed that monopoles can exist as finite energy topologically stable solutions to certain spontaneously broken gauge theories. The thesis, “Studies on Magnetic Monopole Solutions of Non-abelian Gauge Theories and Related Problems”, reports a systematic investigation of classical solutions of non-abelian gauge theories with special emphasis on magnetic monopoles and dyons which possess both electric and magnetic charges. The formation of bound states of a dyon with fermions and bosons is also studied in detail. The thesis opens with an account of a new derivation of a relationship between the magnetic charge of a dyon and the topology of the gauge fields associated with it. Although this formula has been reported earlier in the literature, the present method has two distinct advantages. In the first place, it does not depend either on the mechanism of symmetry breaking or on the nature of the residual symmetry group. Secondly, the results can be generalized to finite temperature monopoles.

Applying Jackson’s methodological ideal-types: problems of differentiation and classification

In The Conduct of Inquiry in International Relations, Patrick Jackson situates methodologies in International Relations in relation to their underlying philosophical assumptions. One of his aims is to map International Relations debates in a way that ‘capture[s] current controversies’ (p. 40). This ambition is overstated: whilst Jackson’s typology is useful as a clarificatory tool, (re)classifying existing scholarship in International Relations is more problematic. One problem with Jackson’s approach is that he tends to run together the philosophical assumptions which decisively differentiate his methodologies (by stipulating a distinctive warrant for knowledge claims) and the explanatory strategies that are employed to generate such knowledge claims, suggesting that the latter are entailed by the former. In fact, the explanatory strategies which Jackson associates with each methodology reflect conventional practice in International Relations just as much as they reflect philosophical assumptions. This makes it more difficult to identify each methodology at work than Jackson implies. I illustrate this point through a critical analysis of Jackson’s controversial reclassification of Waltz as an analyticist, showing that whilst Jackson’s typology helps to expose inconsistencies in Waltz’s approach, it does not fully support the proposed reclassification. The conventional aspect of methodologies in International Relations also raises questions about the limits of Jackson’s ‘engaged pluralism’.

A general lagrangian approach for non-concave moral hazard problems

We establish a general Lagrangian for the moral hazard problem which generalizes the well known first order approach (FOA). It requires that besides the multiplier of the first order condition, there exist multipliers for the second order condition and for the binding actions of the incentive compatibility constraint. Some examples show that our approach can be useful to treat the finite and infinite state space cases. One of the examples is solved by the second order approach. We also compare our Lagrangian with 1\1irrlees'.