Equitable romantic relationships are relationships in which partners perceive that they are giving benefits to their partner that equal the benefits they receive from their partner (e.g., Walster, Traupmann, & Walster, 1978), and such relationships promote commitment (Rusbult, 1980). But do equity considerations influence observers’ impressions of a romantic couple? In the present study, I tested this possibility by examining observers’ impressions of romantic partners who were mismatched in physical attractiveness (i.e., one partner will be more physically attractive than the other). In this situation, heterosexual observers instinctually categorize the opposite-sex member of the couple as a potential mate and the same-sex member of the couple as a competitor for the potential mate’s affection (e.g., Buss & Dedden, 1990; Fisher & Cox, 2009). Furthermore, observers also conclude that a potential mate who is more attractive than his or her current partner (i.e., the competitor) is not committed to his or her current relationship (Stinson & Reddoch, unpublished data). Thus, when evaluating a romantic couple, I hypothesize that observers’ will demonstrate mating-motivated biased perceptions of potential mates and competitors when the mate is more attractive than the competitor, because such more-attractive potential mates will be perceived as romantically “available.” Participants viewed photos of dating couples who matched in attractiveness, or viewed photos of dating couples where the mate was more attractive or less attractive than the competitor. Participants then rated the potential mates’ and competitors’ status-resources (SR; Fletcher et al., 1999). Results supported my theory of mating-motivated person-perception: Observers derogated the SRs of competitors who were paired with a more attractive (and romantically available) potential mate. / Graduate / 0623 / 0451 / c.joordens@gmail.com

This work explores the interaction of electromagnetic radiation with periodic metal-dielectric composite materials. In particular, the majority of the studies explore the role of evanescent diffraction in the regime where the wavelength of the incident radiation is of the order of the period of the array just below the onset of diffraction. The underlying aim of the thesis is to build on the current knowledge and gain deeper understanding into the causal mechanism of the electromagnetic response of these periodic materials. Developments in metamaterial research have led to a resurgance of interest in the use of periodic metallic surface to control the transmission of electromagnetic radiation. The response of these surfaces can be `tuned' to provide the required response simply by altering the geometric parameters of the material. Numerical modelling techniques are often used to predict the response of such structures. However, the aim of this work is to gain a deeper understanding of the reasons for the response and therefore an analytical modal matching method has been used. The modal matching method provides the opportunity to extract greater understanding of the resonant phenomena by linking them to specific mathematical terms in the analytical formulation. The modal matching technique is initially used to study the response from a single layer bigrating comprising a square array of square holes in a PEC sheet and its complementary system of a square array of square PEC patches. The importance of evanescent diffraction in both resonant phenomena and tunneling responses is discussed and it is shown that complete transmission (reflection) is supported by these structures even for very high (low) metal occupancy. This technique is extended and adapted to describe a variety of structures in chapters 5 and 6, exploring how resonant excitation of surface waves via evanescent diffraction leads to highly interesting electromagnetic responses. In chapter 7, alternating multilayer stacks of two different subwavelength meshes provide an observable one-dimensional topological mode in a physical system for particular mesh configurations.

In multi-tier cellular networks, user performance is largely a ected by the varying transmit powers, distances, and non-uniform tra c loads of di erent base stations (BSs) in both the downlink (DL) and uplink (UL) directions of transmission. In presence of such heterogeneity, decoupled UL-DL user association (DUDe), which allows users to associate with di erent BSs for UL and DL transmissions, can be used to optimize network performance. Again, in-band full-duplex (FD) communi- cation is considered as a promising technique to improve the spectral e ciency of future multi-tier fth generation (5G) cellular networks. Nonetheless, due to severe UL-to-DL and DL-to-UL interference issues arising due to FD communications, the performance gains of DUDe in FD multi-tier networks are inconspicuous. To this end, this thesis develops a comprehensive framework to analyze the usefulness of DUDe in a full-duplex multi-tier cellular network. We rst formulate a joint UL and DL user association problem (with the provision of decoupled association) that maximizes the sum-rate for UL and DL transmission of all users. Since the formulated problem is a mixed-integer non-linear programming (MINLP) problem, we invoke approxi- mations and binary constraint relaxations to convert the problem into a Geometric Programming (GP) problem that is solved using Karush-Kuhn-Tucker (KKT) opti- mality conditions. Given the centralized nature and complexity of the GP problem, the solution of which serves as the upper bound for any sub-optimal solution, we formulate a distributed two-sided iterative matching game and develop a solution to obtain the solution of the game. In this game, the users and BSs rank one another using preference metrics that are subject to the externalities (i.e., dynamic interfer- ence conditions). The solution of the game is guaranteed to converge and provides Pareto-e cient stable associations. Finally, we derive e cient light-weight versions of the iterative matching solution, i.e., non-iterative matching and sequential UL-DL matching algorithms. The performances of all the solutions are critically evaluated in terms of aggregate UL and DL rates of all users, the number of unassociated users, and the number of coupled/decoupled associations. Simulation results demonstrate the e cacy of the proposed algorithms over the centralized GP solution as well as traditional coupled and decoupled user association schemes. / October 2016

Doctor of Philosophy / Department of Mechanical and Nuclear Engineering / Warren N. White / There are a number of different types of mechanical systems which can be termed as underactuated. The degrees of freedom (DOF) of a system are defined by the system’s number of independent movements. Underactuated mechanical systems have fewer actuators than DOF. Some examples such as satellites, air craft, overhead crane loads, and missiles have at least one unactuated DOF. The work presented here develops a nonlinear control law for the asymptotic stabilization of underactuated systems. This is accomplished by finding the solution of matching conditions that arise from Lyapunov’s second method, analogous to the dissipation of energy. The direct Lyapunov approach (DLA) offers a wide range of applications for underactuated systems due to the fact that the algebraic equations, ordinary differential equations, and partial differential equations stemming from the matching conditions are more tractable than those appearing in other approaches. Two lemmas of White et al. (2007) are applied for the positive definiteness and symmetry condition of the KD matrix which is used to define an analogous kinetic energy for the system. The defined KD matrix and the Lyapunov candidate function are developed to ensure stability. The KD matrix is analogous to the mass matrix of the dynamic system. The candidate Lyapunov function, involving the analogous kinetic energy and an undefined potential of the generalized position coordinates, is presented. By computing the time derivative of the Lyapunov candidate function, three equations called matching conditions emerge and parts of their solution provide the nonlinear control law that stabilizes the system. This dissertation presents the derivation of the DLA, provides a new method to solve the first matching condition (FMC), and shows the tools for the control law design. The stability is achieved from the proper shape of the potential, the positive definiteness of the KD matrix, and the non-positive rate of change of the Lyapunov function. The ball and beam, the inverted pendulum cart, and, a more complicated system, the ball and arc are presented to demonstrate the importance of the results because the methods to solve the matching equations, emerging from the system examples, are simple and easier. The presented controller design formulation satisfies the FMC exactly without introducing control law terms that are quadratic in the velocities or approximations. This methodology allows the development of the first nonlinear stabilizing control law for the ball and arc system, a simple and effective formulation to find a control law for the inverted pendulum cart, and a stabilizing control of the ball and beam apparatus without the necessity of approximations to solve the FMC. To illustrate the formulation, the derivation is performed using the symbolic manipulation program Maple and it is simulated in the Matlab/Simulink environment. The dissertation on the solvability of the first matching condition for stabilization is organized into six different chapters. The introduction of the problem and the previous approaches are presented in Chapter 1. Techniques for solving of the first matching condition, as well as the limitations, are provided in Chapter 2. The application of this general strategy to the ball and beam system appears in Chapter 3. Chapter 4 and 5 present the application of the method to the ball and arc apparatus and to the inverted pendulum cart, respectively. The difficulties for each application are also presented. Particularly, Chapter 5 shows the application of the produced material to obtain an easier formulation for the inverted pendulum cart compared to previous published controller examples. Finally, some conclusions and recommendations for future work are presented.

Thesis advisor: Utku Unver / This dissertation consists of two chapters. The first chapter: Dynamic reserves in matching markets with contracts. In this paper we study a matching problem where agents care not only about the institution they are assigned to but also about the contractual terms of their assignment so that they have preferences over institution-contractual term pairs. Each institution has a target distribution of its slots reserved for different contractual terms. If there is less demand for some groups of slots, then the institution is given opportunity to redistribute unassigned slots over other groups. The choice function we construct takes the capacity of each group of seats to be a function of number of vacant seats of groups considered earlier. We advocate the use of a cumulative offer mechanism (COM) with overall choice functions designed for institutions that allow capacity transfer across different groups of seats as an allocation rule. In applications such as engineering school admissions in India, cadet-branch matching problems at the USMA and ROTC where students are ranked according to test scores (and for each group of seats, corresponding choice functions are induced by them), we show that the COM with a monotonic capacity transfer scheme produces stable outcomes, is strategy proof, and respect improvements in test scores. Allowing capacity redistribution increases efficiency. The outcome of the COM with monotone capacity transfer scheme Pareto dominates the outcome of the COM with no capacity transfer. The second chapter: On relationships between substitutes conditions. In the matching with contracts literature, three well-known conditions on choice functions (from stronger to weaker)- substitutability, unilateral substitutability (US) and bilateral substitutability (BS) have proven to be critical. This paper aims to deepen our understanding of them by separately axiomatizing the gap between the BS and the other two. We first introduce a new “doctor separability” (DS) condition and show that BS, DS and irrelevance of rejected contracts (IRC) are equivalent to IRC and US. Due to Hatfield and Kojima (2010) and Aygün and Sönmez (2012), it is known that US, “Pareto separability” (PS), and IRC are equivalent to substitutability and IRC. This, along with our result, implies that BS, DS, PS, and IRC are equivalent to substitutability and IRC. All of these results are given without IRC whenever hospital choices are induced from preferences. / Thesis (PhD) — Boston College, 2015. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.

Thesis advisor: Utku Unver / This dissertation is composed of three essays in microeconomic theory. The first and second essays are in the theory of matching, with hierarchical organizations and complementarities being their respective topic. The third essay is in on electoral competition and political polarization as a result of manipulation of public opinion through social influence networks. Hierarchies are a common organizational structure in institutions. In the first essay, I offer an explanation of this fact from a matching-theoretic perspective, which emphasizes the importance of stable outcomes for the persistence of organizational structures. I study the matching of individuals (talents) via contracts with institutions, which are aggregate market actors, each composed of decision makers (divisions) enjoined by an institutional governance structure. Conflicts over contracts between divisions of an institution are resolved by the institutional governance structure, whereas conflicts between divisions across institutions are resolved by talents' preferences. Stable market outcomes exist whenever institutional governance is hierarchical and divisions consider contracts to be bilaterally substitutable. In contrast, when governance in institutions is non-hierarchical, stable outcomes may not exist. Since market stability does not provide an impetus for reorganization, the persistence of markets with hierarchical institutions can thus be rationalized. Hierarchies in institutions also have the attractive incentive property that in a take-it-or-leave-it bargaining game with talents making offers to institutions, the choice problem for divisions is straightforward and realized market outcomes are pairwise stable, and stable when divisions have substitutable preferences. Complementarity has proved to be a challenge for matching theory, because the core and group stable matchings may fail to exist. Less well understood is the more basic notion of pairwise stability. In a second essay, I define a class of complementarity, asymmetric complements, and show that pairwise stable matchings are guaranteed to exist in matching markets where no firm considers workers to be asymmetric complements. The lattice structure of the pairwise stable matchings, familiar from the matching theory with substitutes, does not survive in this more general domain. The simultaneous-offer and sequential-offer versions of the worker-proposing deferred acceptance algorithm can produce different matchings when workers are not necessarily substitutable. If no firm considers workers to be imperfect complements, then the simultaneous-offer version produces a pairwise stable matching, but this is not necessarily true otherwise. If no firm considers workers to be asymmetric complements, a weaker restriction than no imperfect complements, then the sequential-offer version produces a pairwise stable matching, though the matching produced is order-dependent. In a third essay, I examine electoral competition in which two candidates compete through policy and persuasion, and using a tractable two-dimensional framework with social learning provide an explanation for increasing political polarization. Voters and candidates have policy preferences that depend upon the state of the world, which is known to candidates but not known to voters, and are connected through a social influence network that determines through a learning process the final opinion of voters, where the voters' initial opinions and the persuasion efforts of the candidates affect final opinions, and so voting behavior. Equilibrium level of polarization in policy and opinion (of both party and population) increases when persuasion costs decrease. An increase in homophily increases the equilibrium level of policy polarization and population opinion polarization. These comparative static results help explain the increased polarization in both the policy and opinion dimensions in the United States. / Thesis (PhD) — Boston College, 2013. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.

Apresentamos a teoria sobre mercados de dois lados, centralizados e descentralizados, para analisar o mercado de admissão de estudantes aos Centros de Pós-graduação em Economia no Brasil ao longo dos últimos 15 anos. Iniciamos descrevendo a história da organização deste mercado até a época atual. As falhas do sistema descentralizado e as hipóteses sobre o insucesso do procedimento centralizado de 1997 são discutidas. Observações empíricas são utilizadas para propor um modelo teórico que represente aproximadamente o atual mecanismo descentralizado e explique a aparente duradoura aplicação desse mecanismo. Por fim, tecemos considerações a respeito das possibilidades de aprimoramento deste mercado com modificações do mecanismo existente. / We present the theory of two-sided matching markets, with centralized and decentralized mechanisms, in order to analyze a Brazilian market in which graduated students seek positions in postgraduate programs in economics. We first describe the institutional history of this market. The failures of the decentralized procedure and the hypothesis about the failure of the 1997 centralized mechanism are discussed. Empirical observations are used to propose a theoretical model that represents the actual decentralized matching procedure of the market. Based in this model we explain the apparent long-lasting use of this decentralized mechanism. Finally, we make considerations about the possibilities of developments in this market by modifying the mechanism used today.

Correlation-based translated-feature finding techniques are fast and effective in identifying targets in test images despite unknown translation. Information involving both translation and in-plane orientation of targets, however, is important in many industrial machine vision applications such as manufacturing and quality assurance. A traditional correlation based technique that expands the search criteria to include in-plane orientation is based upon use of a bank of filters that each implement a feature finding operation for one rotation of the target. This computational complexity of this approach is inversely proportional to the resolution of the orientation estimate. This thesis develops a correlation based method for translation and in-plane orientation feature finding that requires only two underlying correlation filter operations. A composite filter is constructed from a specially arranged and complex weighted sum of the set of the translated exemplar filters contained the usual filter bank. The arrangement allows for robust peak location detection yielding the target position and the multiplier angle that is extracted from the amplitude of the peak output response supplys an orientation estimate. A demonstration system using two such filters in an iterative fashion to counteract different sources of interference produced results accurate to plus or minus 1 degree 100 times faster than the traditional system.

In this thesis, we present novel methodology for emulating and calibrating computer models with high-dimensional output. Computer models for complex physical systems, such as climate, are typically expensive and time-consuming to run. Due to this inability to run computer models efficiently, statistical models ('emulators') are used as fast approximations of the computer model, fitted based on a small number of runs of the expensive model, allowing more of the input parameter space to be explored. Common choices for emulators are regressions and Gaussian processes. The input parameters of the computer model that lead to output most consistent with the observations of the real-world system are generally unknown, hence computer models require careful tuning. Bayesian calibration and history matching are two methods that can be combined with emulators to search for the best input parameter setting of the computer model (calibration), or remove regions of parameter space unlikely to give output consistent with the observations, if the computer model were to be run at these settings (history matching). When calibrating computer models, it has been argued that fitting regression emulators is sufficient, due to the large, sparsely-sampled input space. We examine this for a range of examples with different features and input dimensions, and find that fitting a correlated residual term in the emulator is beneficial, in terms of more accurately removing regions of the input space, and identifying parameter settings that give output consistent with the observations. We demonstrate and advocate for multi-wave history matching followed by calibration for tuning. In order to emulate computer models with large spatial output, projection onto a low-dimensional basis is commonly used. The standard accepted method for selecting a basis is to use n runs of the computer model to compute principal components via the singular value decomposition (the SVD basis), with the coefficients given by this projection emulated. We show that when the n runs used to define the basis do not contain important patterns found in the real-world observations of the spatial field, linear combinations of the SVD basis vectors will not generally be able to represent these observations. Therefore, the results of a calibration exercise are meaningless, as we converge to incorrect parameter settings, likely assigning zero posterior probability to the correct region of input space. We show that the inadequacy of the SVD basis is very common and present in every climate model field we looked at. We develop a method for combining important patterns from the observations with signal from the model runs, developing a calibration-optimal rotation of the SVD basis that allows a search of the output space for fields consistent with the observations. We illustrate this method by performing two iterations of history matching on a climate model, CanAM4. We develop a method for beginning to assess model discrepancy for climate models, where modellers would first like to see whether the model can achieve certain accuracy, before allowing specific model structural errors to be accounted for. We show that calibrating using the basis coefficients often leads to poor results, with fields consistent with the observations ruled out in history matching. We develop a method for adjusting for basis projection when history matching, so that an efficient and more accurate implausibility bound can be derived that is consistent with history matching using the computationally prohibitive spatial field.

This dissertation analyzes problems related to matching in general networks and decision under uncertainty. Chapter 1 introduces the framework of convex matching games. Chapter 2 discusses three distinct applications of the framework. Chapter 3 develops a new test of choice models with expected utility. In Chapter 1, I use Scarf's lemma to show that given a convexity structure that I introduce, the core of a matching game is always nonempty, and the framework I introduce can accommodate general contracting networks, multilateral contracts, and complementary preferences. In Chapter 2, I provide three applications to show how the convexity structure is satisfied in different contexts by different assumptions. In the first application, I show that in large economies, the convexity structure is satisfied if the set of participants in each contract is small compared to the overall economy. The second application considers finite economies, and I show that the convexity structure is satisfied if all agents have convex, but not necessarily substitutable, preferences. The third application considers a large-firm, many-to-one matching market with peer preferences, and I show that the convexity structure is satisfied under convexity of preferences and a competition aversion restriction on workers' preferences over colleagues. In Chapter 3, I show that some form of cyclic choice pattern across distinct information scenarios should be regarded as inconsistent with a utility function that is linear in beliefs.