The aim of this paper is to outline a position concerning the unity of knowledge and to provide a model for the relationship between reality and knowledge. This paper is based on remarks made by E.W. Beth in his Foundations of Mathematics, in which he claims a new version of realism is needed. This realism would hold that man is acquainted with four aspects of reality and that the various aspects should be considered complementary. More specifically Beth states: In my opinion, man has on account of his own life experience an immediate and authentic contact with various spheres (perhaps it would be better to say, zones, or aspects) of reality, some of which may be enumerated; physical reality - the world of matter -, social reality - the world of men -, subjective reality - the world of mind -, logical reality - the world of reason or discourse - , in which mathematical entites participate. It seems reasonable however tentatively to consider the various spheres of reality as complementary. . . . (Beth, 1959, pp. 644-645) I will be using the principle of complementarity in its general form to argue for a certain type of unity of knowledge. In the introduction I discuss the general need for unity of knowledge. Attempts at unity in atomic physics are examined in Chapter I, in particular the role of complementarity in unifying the theory of Quantum Mechanics. Chapter II treats complementarity as a thema in Hoi ton's sense, "an unverifiable, unfalsifiable and yet not quite arbitrary hypothesis" that is crucial to the development of knowledge (Hoiton, 1973, pp. 185-192). Chapter II also examines applications of complementarity in contexts other than atomic physics. Having shown the principle in use in different contexts I proceed in Chapter III to develop my main thesis -that the principle of complementarity represents a new model of explanation. When applied to the problem of the unity of knowledge, the principle would suggest the view that knowledge is a description of projections of the actual state, reality, on the observer. This view is compatible with a new version of realism. Complementarity, together with modest realism, modest foundational ism and a prospective conception of truth can be used to provide the outline of an alternative to foundational ism and coherentism. Chapter IV discusses complementarity in relation to other metaphysical and epistemological approaches to the monism-pluralism issue. Chapter V discusses the possibility of a realistic interpretation of knowledge in the special case of science. I conclude with a summary of the argument in this paper. / Arts, Faculty of / Philosophy, Department of / Graduate

The thesis consists of five chapters. The first of them contains introduction. Chapter 2 considers a broad class of two player symmetric games, which display a fundamental non-concavity when actions of both players are about to be the same. This implies that no symmetric equilibrium is possible. We distinguish different properties of the payoff functions, like strategic substitutes, complements and quasi-concavity, which are not necessarily imposed globally on the joint action space. For each of these cases we provide conditions to secure the existence of exclusively asymmetric equilibria. Moreover we consider the case of convex payoff functions. A number of applications from industrial organization and applied microeconomics literature are provided. In Chapter 3 we generalize to the extent possible the known results for the case of games with one-dimensional action sets to the general case of games with strategic complemantarities with action spaces that are complete lattices. One key issue addressed is the extent to which all equilibria tend to be symmetric for the general case of multi-dimensional (i.e. only partially ordered) strategy spaces. We find that the scope for asymmetric equilibrium behavior is definitely broader than in the one-dimensional case, though still quite limited. Another key question investigated here is whether asymmetric pure strategy Nash equilibria are always Pareto dominated by symmetric pure strategy Nash equilibria. While this need not hold in general for games with strategic complementarities, we identify different sufficient conditions that guarantee that such dominance holds. In Chapter 4 we deal with the effects of market transparency on prices in the Bertrand duopoly model. The analysis is intuitive and simple when we consider two types of strategic interaction between firms in an industry - strategic complementarities and substitutabilities. We present also traditional comparative statics analyses, demanding additionally some other regularity conditions, to cover those problems, when neither of these situations is the case. In the first case, the results are close to conventional wisdom, especially, when in the same time products are substitutes. Namely, equilibrium prices and profits are always decreasing in transparency level, while the consumer's surplus is increasing. For a special case when supermodularity holds, but products are not substitutes, the result on profits is not valid anymore. Considering price competition with strategic substitutes, an ambiguity in the direction of change of prices appears. This leads to ambiguity concerning equilibrium profits and surplus changes caused by increasing transparency. In Chapter 5 we provide general conditions for Cournot oligopoly with product differentiation to have monotonic reaction correspondences. We give a proof for the conditions stated by Vives (1999). Moreover we elaborate more general requirements. They allow for identifying increasing best responses even in case inverse demand is submodular, and similarly, decreasing best responses in case of supermodular inverse demand. Examples illustrating the scope of applicability of these results are provided.

In this paper, we introduce a new class of general-ized co-complementarity problems in Banach spaces. An iterative algorithm for finding approximate solutions of these problems is considered. Some convergence results for this iterative algorithm are derived and several existence results are obtained.

Thesis--University of Wisconsin--Madison. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 135-139).

The work presented in this thesis is a collection of four different research projects, conducted at the intersection between academic and industrial fields, and related to the restructuring of the electricity industry. Many models have been proposed to organise restructured electricity systems. We first propose a unified mathematical framework for expressing them, using variational inequalities. This allows the use of existence and uniqueness theorems, but also leads to models that can be solved by existing numerical algorithms. In the second part, we present a model of the European Commission proposals on cross-border trade, in particular access to the network and congestion issues. The model allows for various domestic regulation of the national non-eligible market, and different forms of competition in the eligible market. We illustrate this flexibility on a stylised example, and identify policy issues to be studied in a more realistic case study. The third contribution elaborates on the modelling of imperfect competition on electricity markets, more specifically the integration of imperfect competition behaviours in power models, through conjectural variations. We propose a consistent estimation procedure. Finally, a model of the EU Emission Trading Scheme, limiting the total CO2 emissions, is proposed. We illustrate the effect of some basic economic assumptions on the investment and generation mix, and how these assumptions impact the permit price and affect profitability. The novel part is in the way allocation mechanisms for subsequent commitment periods can potentially distort the behaviour of CO2 emitting agents.

Doctor Legum - LLD / The principle of complementarity forms the basis upon which the International Criminal Court (ICC) exercises its jurisdiction. This principle of international law first appears in the Preamble to the Rome Statute and then the admissibility provisions under Article 17 of the Rome Statute, which outline that the Court will declare a case inadmissible where it is being investigated or prosecuted by a state which has jurisdiction over it; unless the state is unwilling or unable to genuinely carry out the investigation or prosecution. Alternatively where the case has been investigated by a state which has jurisdiction over it and the state has decided not to prosecute the person concerned, unless the decision resulted from the unwillingness or inability of the state to genuinely prosecute. This principle implies that the ICC is a court of last resort and will therefore not intervene in a case where the state of commission is either able or willing genuinely to investigate and prosecute perpetrators of grave crimes. It is common cause that Africa has been the staging area of mass atrocities for decades. The indictment of Kenyan president Uhuru Kenyatta’s’ and his deputy William Ruto, Hissene Habre case, and the indictment and issuance of an arrest warrant against the Sudanese President Omar El-Bashir are instructive in this regard. The ICC’S actions created the perception of bias, injustice and inequity. This prompted a sharp reaction from African states, which threated a mass withdrawal from the Rome Statute in 2013. The one positive spin off from the AU reaction was the expansion of the jurisdiction of the merged court to include a criminal chamber in 2014, thus creating Africa’s first international criminal court, the African Criminal Court (ACC). This development was the result of the discontent and frustration of the African continent towards the work of the ICC, which was perceived as focusing only on African cases, whilst ignoring the litany of cases coming from other regions of the world.

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.

The goal of electric circuit simulation is to describe the flow of electricity throughout an electric circuit. Simulating the behavior of the circuit can not only help improve the design and efficiency of electronics, but also save time and money used in physically making the circuit. Circuit simulation has been an ongoing problem due to the difficult equations that model circuit components. In this thesis we develop a mathematical model for simulating dynamic electric circuits with ideal diodes. We build our model to include key electrical components like power sources, resistors, inductors, and capacitors. We then extend our model to include ideal diodes. Diodes are special electrical elements in that they only allow current to flow in one direction. We present numerical methods for simulating electrical networks with resistors, capacitors, inductors, and diodes using a complementarity approach. These methods have both high order of accuracy and work directly with the network description of the circuit.

Within the last decade, the importance of flexibility and efficiency has increased in the manufacturing sector. The rising level of uncertainty in consumer preferences has caused many organizations to aggressively search for cost reductions and other sources of competitive advantage. This fact has resulted in an increased implementation of advanced manufacturing technologies (AMT). A number of studies propose that the implementation of AMT must be accompanied by a shift in supporting organizational practices to realize the greatest performance enhancement. As yet, the complementarities between organizational policies and AMT have not been determined. Using assumptions about complementarities in manufacturing made by Milgrom and Roberts (1995) in conjunction with a comprehensive AMT survey (Survey of Advanced Technology in Canadian Manufacturing-1998) a model of manufacturing plant productivity was developed. Constrained regression analysis reveals that the use of AMT, as well as various organizational policies, depends both on the size of the plant as well as the industry in which it operates. Factor analysis of the over 70 variables found that regardless of the nature of the variable (business strategy, source of implementation support, AMT, etc. ), all design elements factored together. The factor analysis also shows that large firms who use AMT also have many design technologies. This result differs for smaller firms where the use of AMT is highly correlated with perceived benefits of the technology and a large number of sources of implementation support. The analysis also supports the distinction of high technology (highly innovative) industries and low technology (low levels of innovation) industries since electronics, chemicals and automotive have a large percentage of plants with all of the model factors whereas the textile, non-metal and lumber industries have very few plants with all of the model factors. The results show that there are important differences that should be considered when creating policies to encourage innovation and the use of AMT for the various manufacturing industries and plant sizes.

Within the last decade, the importance of flexibility and efficiency has increased in the manufacturing sector. The rising level of uncertainty in consumer preferences has caused many organizations to aggressively search for cost reductions and other sources of competitive advantage. This fact has resulted in an increased implementation of advanced manufacturing technologies (AMT). A number of studies propose that the implementation of AMT must be accompanied by a shift in supporting organizational practices to realize the greatest performance enhancement. As yet, the complementarities between organizational policies and AMT have not been determined. Using assumptions about complementarities in manufacturing made by Milgrom and Roberts (1995) in conjunction with a comprehensive AMT survey (Survey of Advanced Technology in Canadian Manufacturing-1998) a model of manufacturing plant productivity was developed. Constrained regression analysis reveals that the use of AMT, as well as various organizational policies, depends both on the size of the plant as well as the industry in which it operates. Factor analysis of the over 70 variables found that regardless of the nature of the variable (business strategy, source of implementation support, AMT, etc. ), all design elements factored together. The factor analysis also shows that large firms who use AMT also have many design technologies. This result differs for smaller firms where the use of AMT is highly correlated with perceived benefits of the technology and a large number of sources of implementation support. The analysis also supports the distinction of high technology (highly innovative) industries and low technology (low levels of innovation) industries since electronics, chemicals and automotive have a large percentage of plants with all of the model factors whereas the textile, non-metal and lumber industries have very few plants with all of the model factors. The results show that there are important differences that should be considered when creating policies to encourage innovation and the use of AMT for the various manufacturing industries and plant sizes.