Hierarchy and Expansiveness in Two-Dimensional Subshifts of Finite Type

Subshifts are sets of configurations over an infinite grid defined by a set of forbidden patterns. In this thesis, we study two-dimensional subshifts offinite type (2D SFTs), where the underlying grid is Z2 and the set of for-bidden patterns is finite. We are mainly interested in the interplay between the computational power of 2D SFTs and their geometry, examined through the concept of expansive subdynamics. 2D SFTs with expansive directions form an interesting and natural class of subshifts that lie between dimensions 1 and 2. An SFT that has only one non-expansive direction is called extremely expansive. We prove that in many aspects, extremely expansive 2D SFTs display the totality of behaviours of general 2D SFTs. For example, we construct an aperiodic extremely expansive 2D SFT and we prove that the emptiness problem is undecidable even when restricted to the class of extremely expansive 2D SFTs. We also prove that every Medvedev class contains an extremely expansive 2D SFT and we provide a characterization of the sets of directions that can be the set of non-expansive directions of a 2D SFT. Finally, we prove that for every computable sequence of 2D SFTs with an expansive direction, there exists a universal object that simulates all of the elements of the sequence. We use the so called hierarchical, self-simulating or fixed-point method for constructing 2D SFTs which has been previously used by Ga´cs, Durand, Romashchenko and Shen.

DEVELOPMENT OF A FAIR CHARGING MODEL FOR A PUBLIC DATA CENTER

The purpose of the study was to explore how a public, IT services transferor, organization, comprised of autonomous entities, can effectively develop and organize its data center cost recovery mechanisms in a fair manner. The lack of a well-defined model for charges and a cost recovery scheme could cause various problems. For example one entity may be subsidizing the costs of another entity(s). Transfer pricing is in the best interest of each autonomous entity in a CCA. While transfer pricing plays a pivotal role in the price settings of services and intangible assets, TCE focuses on the arrangement at the boundary between entities. TCE is concerned with the costs, autonomy, and cooperation issues of an organization. The theory is concern with the factors that influence intra-firm transaction costs and attempting to manifest the problems involved in the determination of the charges or prices of the transactions. This study was carried out, as a single case study, in a public organization. The organization intended to transfer the IT services of its own affiliated public entities and was in the process of establishing a municipal-joint data center. Nine semi-structured interviews, including two pilot interviews, were conducted with the experts and managers of the case company and its affiliating entities. The purpose of these interviews was to explore the charging and pricing issues of the intra-firm transactions. In order to process and summarize the findings, this study employed qualitative techniques with the multiple methods of data collection. The study, by reviewing the TCE theory and a sample of transfer pricing literature, created an IT services pricing framework as a conceptual tool for illustrating the structure of transferring costs. Antecedents and consequences of the transfer price based on TCE were developed. An explanatory fair charging model was eventually developed and suggested. The findings of the study suggested that the Chargeback system was inappropriate scheme for an organization with affiliated autonomous entities. The main contribution of the study was the application of TP methodologies in the public sphere with no tax issues consideration.