M. Ing. / Digital Surface Models (DSM) are widely used in the earth sciences for research, visu- alizations, construction etc. In order to generate a DSM for a speci c area, specialized equipment and personnel are always required which leads to a costly and time consuming exercise. Image processing has become a viable processing technique to generate terrain models since the improvements of hardware provided adequate processing power to complete such a task. Digital Surface Models (DSM) can be generated from stereo imagery, usually obtained from a remote sensing platform. The core component of a DSM generating system is the image matching algorithm. Even though there are a variety of algorithms to date which can generate DSMs, it is a computationally complex calculation and does tend to take some time to complete. In order to achieve faster DSMs, an investigation into an alternative processing platform for the generation of terrain models has been done. The Graphics Processing Unit (GPU) is usually used in the gaming industry to manipulate display data and then render it to a computer screen. The architecture is designed to manipulate large amounts of oating point data. The scientic community has begun using the GPU processing power available for technical computing, hence the term, General Purpose computing on a Graphics Processing Unit (GPGPU). The GPU is investigated as alternative processing platform for the image matching procedure since the processing capability of the GPU is so much higher than the CPU but only for a conditioned set of input data. A matching algorithm, derived from the GC3 algorithm has been implemented on both a CPU platform and a GPU platform in order to investigate the viability of a GPU processing alternative. The algorithm makes use of a Normalized Cross Correlation similarity measurement and the geometry of the image acquisition contained in the sensor model to obtain conjugate point matches in the two source images. The results of the investigation indicated an improvement of up to 70% on the processing time required to generate a DSM. The improvements varied from 70% to some cases where the GPU has taken longer to generate the DSM. The accuracy of the automatic DSM generating system could not be clearly determined since only poor quality reference data was available. It is however shown the DSMs generated using both the CPU and GPU platforms relate to the reference data and correlate to each other. The discrepancies between the CPU and the GPU results are low enough to prove the GPU processing is bene cial with neglible drawbacks in terms of accuracy. The GPU will definitely provide superior processing capabilites for DSM generation above a CPU implementation if a matching algorithm is speci cally designed to cater for the bene ts and limitations of the GPU.

The Ireland´s recovery from the crisis that broke in the Irish economy was fast comparing to other eurozone nations so-called PIIGS. Therefore, the thesis identify sources and turning points that generate the inclusive growth of the Irish economy. Economic growth comes from the accumulation of labour and capital inputs combined with improvements in the productivity of labour associated with technological progress. There are clear signals that all these factors contribute to the economy growth in Ireland. Ireland benefits from large inflows of foreign direct investment that helps to spread technological progress, know-how into the country. This has resulted in export of hi-tech goods and services. Labour force in Ireland are skilled individuals. In addition, both, labour force and labour market in Ireland are highly adaptable to change. Above mentioned drivers and others are fundamental to economic growth. Overall, Ireland´s economy is reasonably well established and it has made significant progress in many areas that contrast with southern economies in PIIGS group.

We consider right modules over a ring, as models of a first order theory. We explorethe definable sets and the definable bijections between them. We employ the notionsof Euler characteristic and Grothendieck ring for a first order structure, introduced byJ. Krajicek and T. Scanlon in [24]. The Grothendieck ring is an algebraic structurethat captures certain properties of a model and its category of definable sets.If M is a module over a product of rings A and B, then M has a decomposition into a direct sum of an A-module and a B-module. Theorem 3.5.1 states that then the Grothendieck ring of M is the tensor product of the Grothendieck rings of the summands.Theorem 4.3.1 states that the Grothendieck ring of every infinite module over afield or skew field is isomorphic to Z[X].Proposition 5.2.4 states that for an elementary extension of models of anytheory, the elementary embedding induces an embedding of the corresponding Grothendieck rings. Theorem 5.3.1 is that for an elementary embedding of modules, we have the stronger result that the embedding induces an isomorphism of Grothendieck rings.We define a model-theoretic Grothendieck ring of the category Mod-R and explorethe relationship between this ring and the Grothendieck rings of general right R-modules. The category of pp-imaginaries, shown by K. Burke in [7] to be equivalentto the subcategory of finitely presented functors in (mod-R; Ab), provides a functorial approach to studying the generators of theGrothendieck rings of R-modules. It is shown in Theorem 6.3.5 that whenever R andS are Morita equivalent rings, the rings Grothendieck rings of the module categories Mod-R and Mod-S are isomorphic.Combining results from previous chapters, we derive Theorem 7.2.1 saying that theGrothendieck ring of any module over a semisimple ring is isomorphic to a polynomialring Z[X1,...,Xn] for some n.

No description available.

In this dissertation we study closure properties of pointclasses, scales on sets of reals and the models L[T2n], which are very natural canonical inner models of ZFC. We first characterize projective-like hierarchies by their associated ordinals. This solves a conjecture of Steel and a conjecture of Kechris, Solovay, and Steel. The solution to the first conjecture allows us in particular to reprove a strong partition property result on the ordinal of a Steel pointclass and derive a new boundedness principle which could be useful in the study of the cardinal structure of L(R). We then develop new methods which produce lightface scales on certain sets of reals. The methods are inspired by Jackson’s proof of the Kechris-Martin theorem. We then generalize the Kechris-Martin Theorem to all the Π12n+1 pointclasses using Jackson’s theory of descriptions. This in turns allows us to characterize the sets of reals of a certain initial segment of the models L[T2n]. We then use this characterization and the generalization of Kechris-Martin theorem to show that the L[T2n] are unique. This generalizes previous work of Hjorth. We then characterize the L[T2n] in term of inner models theory, showing that they actually are constructible models over direct limit of mice with Woodin cardinals, a counterpart to Steel’s result that the L[T2n+1] are extender models, and finally show that the generalized contiuum hypothesis holds in these models, solving a conjecture of Woodin.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第23402号 / 理博第4737号 / 新制||理||1679(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 照井 一成, 教授 牧野 和久, 教授 長谷川 真人 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

In this thesis we aim to build algebraic models in computer using machine learning methods and in particular neural networks. We start with a set of axioms that describe functions, constants and relations and use them to train neural networks approximating them. Every element is represented as a real vector, so that neural networks can operate on them. We also explore and compare different representations. The main focus in this thesis are groups. We train neural representations for cyclic (the simplest) and symmetric (the most complex) groups. Another part of this thesis are experiments with extending such trained models by introducing new "algebraic" elements, not unlike the classic extension of rational numbers Q[ √ 2]. 1

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第21123号 / 工博第4487号 / 新制||工||1697(附属図書館) / 京都大学大学院工学研究科分子工学専攻 / (主査)教授 佐藤 啓文, 教授 関 修平, 教授 山本 量一 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

No description available.

<div>We further the research in o-minimal topology by studying in full generality definable topological spaces in o-minimal structures. These are topological spaces $(X, \tau)$, where $X$ is a definable set in an o-minimal structure and the topology $\tau$ has a basis that is (uniformly) definable. Examples include the canonical o-minimal "euclidean" topology, “definable spaces” in the sense of van den Dries [17], definable metric spaces [49], as well as generalizations of classical non-metrizable topological spaces such as the Split Interval and the Alexandrov Double Circle.</div><div><br></div><div>We develop a usable topological framework in our setting by introducing definable analogues of classical topological properties such as separability, compactness and metrizability. We characterize these notions, showing in particular that, whenever the underlying o-minimal structure expands $(\mathbb{R},<)$, definable separability and compactness are equivalent to their classical counterparts, and a similar weaker result for definable metrizability. We prove the equivalence of definable compactness and various other properties in terms of definable curves and types. We show that definable topological spaces in o-minimal expansions of ordered groups and fields have properties akin to first countability. Along the way we study o-minimal definable directed sets and types. We prove a density result for o-minimal types, and provide an elementary proof within o-minimality of a statement related to the known connection between dividing and definable types in o-minimal theories.</div><div><br></div><div>We prove classification and universality results for one-dimensional definable topological spaces, showing that these can be largely described in terms of a few canonical examples. We derive in particular that the three element basis conjecture of Gruenhage [25] holds for all infinite Hausdorff definable topological spaces in o-minimal structures expanding $(\mathbb{R},<)$, i.e. any such space has a definable copy of an interval with the euclidean, discrete or lower limit topology.</div><div><br></div><div>A definable topological space is affine if it is definably homeomorphic to a euclidean space. We prove affineness results in o-minimal expansions of ordered fields. This includes a result for Hausdorff one-dimensional definable topological spaces. We give two new proofs of an affineness theorem of Walsberg [49] for definable metric spaces. We also prove an affineness result for definable topological spaces of any dimension that are Tychonoff in a definable</div><div>sense, and derive that a large class of locally affine definable topological spaces are affine.</div>