Оптимальний вибір площин, на яких розміщені томограми, в комп’ютерній томографії

The solution of the problem of reconstructing the internal structure of a three-dimensional body by the known tomograms produced by a computer to-mograph using interflatation of functions and blending approximation is proposed. The known methods ofapproximating functions of one and two variables by interpolation type piecewise constant splines using means and medians are also considered. The paper presents an algorithm for optimizing the choice of the planes in which the tomogramsproduced by a computer tomograph are placed. The case is considered when all the tomograms are parallel to each other. The algorithm developeduses approximations of objects by classical piecewise constant splines. The internal structure of a three-dimensional body (density or absorption coefficient) is assumed to be given by a function of three variables of the form h(x, y, z ) = f (x)g( y, z), where g is an arbitrary function, provided that f is a monotone function on a closed segment. The method of optimal choice of the planes for placing the tomograms is implemented using MathCad computer software.Представлено розв’язок задачі відновлення внутрішньої структури тривимірного тіла за відомими томограмами, що поступають з комп’ютерного томографу, за допомогою інтерфлетації функцій та мішаної апроксимації. Розглянуто також відомі методи наближення функцій однієї та двоx змінних кусково-сталими сплайнами інтерполяційного типу, з використанням середніх та медіан. В статті пропонується алгоритм оптимізації вибору площин, на яких розміщені томограми, що поступають з комп’ютерного томографу. Розглядається випадок, коли всі томограми паралельні одна одній. Запропонований алгоритм використовує наближення об’єктів класичними кусково-сталими сплайнами. При побудові алгоритму істотно використовується припущення про те, що внутрішня структура тривимірного тіла (щільність або коефіцієнт поглинання) є функцією від трьох змінних вигляду h(x, y, z ) = f (x)g( y, z), де g – довільна функція, при умові, що f – монотонна функція на замкненому відрізку. Представлена чисельна реалізація методу оптимального вибору площин, на яких лежать томограми, в системі компʼютерної математики MathCad

COINVENT: Towards a Computational Concept Invention Theory

We aim to develop a computationally feasible, cognitively-inspired, formal model of concept invention, drawing on Fauconnier and Turner’s theory of conceptual blending, and grounding it on a sound mathematical theory of concepts. Conceptual blending, although successfully applied to describing combinational creativity in a varied number of fields, has barely been used at all for implementing creative computational systems, mainly due to the lack of sufficiently precise mathematical characterisations thereof. The model we will define will be based on Goguen’s proposal of a Unified Concept Theory, and will draw from interdisciplinary research results from cognitive science, artificial intelligence, formal methods and computational creativity. To validate our model, we will implement a proof of concept of an autonomous computational creative system that will be evaluated in two testbed scenarios: mathematical reasoning and melodic harmonisation. We envisage that the results of this project will be significant for gaining a deeper scientific understanding of creativity, for fostering the synergy between understanding and enhancing human creativity, and for developing new technologies for autonomous creative systems.The project COINVENT acknowledges the nancial support of the Future and Emerging Tech- nologies (FET) programme within the Seventh Framework Programme for Research of the Eu- ropean Commission, under FET-Open Grant number: 611553Peer Reviewe

Understanding as integration of heterogeneous representations

The search for understanding is a major aim of science. Traditionally, understanding has been undervalued in the philosophy of science because of its psychological underpinnings; nowadays, however, it is widely recognized that epistemology cannot be divorced from psychology as sharp as traditional epistemology required. This eliminates the main obstacle to give scientific understanding due attention in philosophy of science. My aim in this paper is to describe an account of scientific understanding as an emergent feature of our mastering of different (causal) explanatory frameworks that takes place through the mastering of scientific practices. Different practices lead to different kinds of representations. Such representations are often heterogeneous. The integration of such representations constitute understanding

Towards a computational- and algorithmic-level account of concept blending using analogies and amalgams

Concept blending–a cognitive process which allows for the combination of certain elements (and their relations) from originally distinct conceptual spaces into a new unified space combining these previously separate elements, and enables reasoning and inference over the combination–is taken as a key element of creative thought and combinatorial creativity. In this article, we summarise our work towards the development of a computational-level and algorithmic-level account of concept blending, combining approaches from computational analogy-making and case-based reasoning (CBR). We present the theoretical background, as well as an algorithmic proposal integrating higher-order anti-unification matching and generalisation from analogy with amalgams from CBR. The feasibility of the approach is then exemplified in two case studies