Rationality and the Foundations of Positive Political Theory

In this paper, we discuss and debunk the four most common critiques of the rational choice research program (which we prefer to call Positive Political Theory) by explaining and advocating its foundations: the rationality assumption, component analysis (abstraction), strategic behavior, and theory building, in turn. We argue that the rationality assumption and component analysis, properly understood, can be seen to underlie all social science, despite the protestations of critics. We then discuss the two ways that PPT most clearly contributes to political science (i.e., what distinguishes it from other research programs), namely the introduction of strategic behavior (people do not just act; they interact) and PPT’s more careful attention to the theory-building step within the scientific method. We explain the roles of theory- building and of empirical “testing,” respectively, in scientific inquiry, and the criteria by which theories should and should not be judged

Formal Analysis of Geometrical Optics using Theorem Proving

Geometrical optics is a classical theory of Physics which describes the light propagation in the form of rays and beams. One of its main advantages is efficient and scalable formalism for the modeling and analysis of a variety of optical systems which are used in ubiquitous applications including telecommunication, medicine and biomedical devices. Traditionally, the modeling and analysis of optical systems have been carried out by paper-and-pencil based proofs and numerical algorithms. However, these techniques cannot provide perfectly accurate results due to the risk of human error and inherent incompleteness of numerical algorithms. In this thesis, we propose a higher-order logic theorem proving based framework to analyze optical systems. The main advantages of this framework are the expressiveness of higher-order logic and the soundness of theorem proving systems which provide unrivaled analysis accuracy. In particular, this thesis provides the higher-order logic formalization of geometrical optics including the notion of light rays, beams and optical systems. This allows us to develop a comprehensive analysis support for optical resonators, optical imaging and Quasi-optical systems. This thesis also facilitates the verification of some of the most interesting optical system properties like stability, chaotic map generation, beam transformation and mode analysis. We use this infrastructure to build a library of commonly used optical components such as lenses, mirrors and optical cavities. In order to demonstrate the effectiveness of our proposed approach, we conduct the formal analysis of some real-world optical systems, e.g., an ophthalmic device for eye, a Fabry-P\'{e}rot resonator, an optical phase-conjugated ring resonator and a receiver module of the APEX telescope. All the above mentioned work is carried out in the HOL Light theorem prover

Hilbert, completeness and geometry

This paper aims to show how the mathematical content of Hilbert's Axiom of Completeness consists in an attempt to solve the more general problem of the relationship between intuition and formalization. Hilbert found the accordance between these two sides of mathematical knowledge at a logical level, clarifying the necessary and sufficient conditions for a good formalization of geometry. We will tackle the problem of what is, for Hilbert, the definition of geometry. The solution of this problem will bring out how Hilbert's conception of mathematics is not as innovative as his conception of the axiomatic method. The role that the demonstrative tools play in Hilbert's foundational reflections will also drive us to deal with the problem of the purity of methods, explicitly addressed by Hilbert. In this respect Hilbert's position is very innovative and deeply linked to his modern conception of the axiomatic method. In the end we will show that the role played by the Axiom of Completeness for geometry is the same as the Axiom of Induction for arithmetic and of Church-Turing thesis for computability theory. We end this paper arguing that set theory is the right context in which applying the axiomatic method to mathematics and we postpone to a sequel of this work the attempt to offer a solution similar to Hilbert's for the completeness of set theory

How Do Established Firms Produce Breakthrough Innovations? Managerial Identity‐Dissemination Discourse and the Creation of Novel Product‐Market Solutions

Despite the legacy of experience, some established firms are able to avoid a mindset, behaviors, and routines that can be expected to lead them down paths of local search and incremental product innovations of ever‐declining value. Indeed, established firms are often adept at introducing successful path‐breaking innovations. To explain this apparent paradox, this article draws on the organizational identity literature to present a model that ascribes breakthrough innovations by established firms to managerial identity‐dissemination discourse (MIDD). MIDD is argued to provide a sense‐giving framework, which fosters an understanding of the firm as a nexus of values around which the firm can be continuously rediscovered and reconstituted in new ways. By exposing the firm as an idea that can assume fresh forms in terms of product‐market combinations, MIDD stimulates and coordinates creative endeavor, thus increasing the disposition to produce breakthrough innovations. The model also suggests that the impact of MIDD is likely to depend on transformational leadership and the level of centralization and formalization in the company. The results of a cross‐sectional empirical study provide support for the model. In contrast to the focus of earlier research on behavioral and structural explanations for breakthroughs by established firms, this article advances understanding by offering a cognitive explanation. In doing so, the article highlights that creativity and innovation in firms are mentally located in an interpretive schema of the firm's identity, which has important implications in relation to organizing for breakthroughs. The article discusses these implications with particular reference to the use of multifunctional teams and advanced information and communication technologies for facilitating breakthroughs

Linear superposition as a core theorem of quantum empiricism

Clarifying the nature of the quantum state $|\Psi\rangle$ is at the root of the problems with insight into (counterintuitive) quantum postulates. We provide a direct-and math-axiom free-empirical derivation of this object as an element of a vector space. Establishing the linearity of this structure-quantum superposition-is based on a set-theoretic creation of ensemble formations and invokes the following three principia: $(\textsf{I})$ quantum statics, $(\textsf{II})$ doctrine of a number in the physical theory, and $(\textsf{III})$ mathematization of matching the two observations with each other; quantum invariance. All of the constructs rest upon a formalization of the minimal experimental entity: observed micro-event, detector click. This is sufficient for producing the $\mathbb C$-numbers, axioms of linear vector space (superposition principle), statistical mixtures of states, eigenstates and their spectra, and non-commutativity of observables. No use is required of the concept of time. As a result, the foundations of theory are liberated to a significant extent from the issues associated with physical interpretations, philosophical exegeses, and mathematical reconstruction of the entire quantum edifice.Comment: No figures. 64 pages; 68 pages(+4), overall substantial improvements; 70 pages(+2), further improvement

Disentangling the role of management control systems for product and process innovation in different contexts

This paper studies the relationship between the use of management control systems and different types of innovation (product and process), taking into account innovation contexts (high-tech versus low-tech sectors). We develop and test our hypotheses based on a large sample of Spanish manufacturing firms and find that input controls have a positive association only with process innovation in both innovation contexts. Behavior controls have similar effects on both types of innovation outcomes for high-tech firms, while they have stronger positive associations with process than with product innovation for low-tech firms. Output controls are equally relevant for product and process innovation in both contexts.This work was supported by the Spanish Ministry of Economics and Competitiveness [grant number ECO2013-45864-P]; the Community of Madrid and the European Social Fund [grant number S2015/HUM-3417] and [INNCOMCON-CM]; and Ramon Areces Foundation [grant number What Triggers Innovation?]; FEDER [grant number UNC315-EE-3636]

Abstracts of Ph.D. theses in mathematics

summary:Čihák, Michael: Teaching probability at secondary schools using computers. Pavlíková, Pavla: Life and work of Miloš Kössler. Bárta, Tomáš: Integrodifferential equations in Banach spaces Beneš, Michal: Asymptotic behavior of the regular orbits of strongly continuous semigroup Pavlica, David: On convex functions, dc-functions and boundary structure of convex sets. Henclová, Alena: Duality in multistage stochastic programming and its application to arbitrage theory. Polívka, Jan: Stochastic programming approach to asset-liability management. Rychtář, Jan: Some problems in rotund renormings of Banach spaces and in operator theory. Jeřábek, Emil: Weak pigeonehole principle and randomized computation. Kupčáková, Marie: Geometry as creation. Kundrátová, Karolína: Comparative analysis of geometric software packages based on solving selected problems. Bejček, Michal: Numerical methods for solving compressible flow problems. Ernestová, Martina: Systems of algebraic equations and their solution in antiquity and the middle ages. Příhoda, Pavel: Decompositions of modules. Jarolímková, Tereza: Valuation of life insurance using diffusion model of interest rate. Fajfrová, Lucie: Equilibrium behaviour of zero range processes on binary tree. Marek, Tomáš: Random coefficient moving average models