ДОСТАТНІСТЬ ПРОЕКЦІЙНИХ ЗОБРАЖЕНЬ 1-БАГАТОВИДІВ n-ПРОСТОРІВ СТАНУ ТЕХНІЧНИХ СИСТЕМ

The boundless possibilities of modern information technologies, in particular, scientific computer graphics, provide the necessary computer tools for the implementation of models. The influence of the information environment indicates ways to improve the representation models of processes with a minimal, but sufficiently complete representation of the interrelations of parameters. Processes in technical systems are given by the integral curves of state spaces as multi-spatial curve lines of multidimensional Euclidean spaces, projecting of which by means of IT technologies is possible in two- and three-dimensional coordinate planes. One of the ways of their image and research is the use of geometric modeling tools with the opportunities of multidimensional applied geometry.The results of a study of a sufficient number of image completeness of integral curves and phase trajectories of state spaces as models of processes of multiparameter technical systems by means of multidimensional applied geometry are presented. The conditions for the image of multidimensional curves on planes of different dimension of complex drawings of multidimensional Euclidean spaces are justified. The possibility of computer visualization with a minimal number of projections of curved lines into linear coordinate two- and three-dimensional subspaces is shown. Sufficient conditions for the formation of projections of curves in two- and three-dimensional planes of projections of multidimensional state spaces and phase spaces of technical systems are substantiated.It is established on the example of the space E4 that during the formation of multi-space curve lines it is possible to use only the interconnections of two parameters in two-dimensional coordinate planes. A sufficient minimum number of such interrelations is shown. The projection of a four-spatial curve into a subspace of lower measurements has determined a sufficient minimum number of such projections in a subspace of identical measurements and combinations of subspaces of various measurements.Приведені результати дослідження достатнього числа зображень інтегральних кривих і фазових траєкторій просторів стану як моделей процесів багатопараметричних технічних систем засобами прикладної багатовимірної геометрії. Обґрунтовані умови зображення багатопросторових кривих у площинах різної вимірності комплексних креслеників багатовимірних евклідових просторів. Показана можливість комп’ютерної візуалізації мінімальним числом проекцій кривих ліній у лінійні координатні дво- і тривимірні підпростори. Обґрунтовані достатні умови формування проекцій кривих у дво- і тривимірні площини проекцій багатовимірних просторів стану і фазових просторів технічних систем

Real-time modelling and interpolation of spatio-temporal marine pollution

Due to the complexity of the interactions involved in various dynamic systems, known physical, biological or chemical laws cannot adequately describe the dynamics behind these processes. The study of these systems thus depends on measurements often taken at various discrete spatial locations through time by noisy sensors. For this reason, scientists often necessitate interpolative, visualisation and analytical tools to deal with the large volumes of data common to these systems. The starting point of this study is the seminal research by C. Shannon on sampling and reconstruction theory and its various extensions. Based on recent work on the reconstruction of stochastic processes, this paper develops a novel real-time estimation method for non- stationary stochastic spatio-temporal behaviour based on the Integro-Di erence Equation (IDE). This meth- odology is applied to collected marine pollution data from a Norwegian fjord. Comparison of the results obtained by the proposed method with interpolators from state-of-the-art Geographical Information System (GIS) packages will show, that signifi cantly superior results are obtained by including the temporal evolution in the spatial interpolations.peer-reviewe

Scaling Flow Path Processes to Fluvial Landscapes: An Integrated Field and Model Assessment of Temperature and Dissolved Oxygen Dynamics in a River-Floodplain-Aquifer System

Biogeochemical cycling within river ecosystems is strongly influenced by geomorphic and hydrologic dynamics. To scale point observations of temperature and dissolved oxygen (DO) to a hydrologically complex and dynamic three-dimensional river-floodplain-aquifer system, we integrated empirical models of temperature and biotic oxygen utilization with a recently published hydrogeomorphic model. The hydrogeomorphic model simulates channel flow, floodplain inundation, and surface-subsurface water exchange on the 16 km(2) Nyack Floodplain, Middle Fork Flathead River, Montana, USA. Model results were compared to observed data sets of DO to test the hypothesis that complexity in spatiotemporal patterns of biogeochemistry emerges from a comparatively simple representation of biogeochemical processes operating within a multidimensional hydrologic system. The model explained 58% of the variance in 820 DO measurements that spanned the study site longitudinally, laterally, vertically, and across river discharge conditions and seasons. We also used model results to illustrate spatial and temporal trends of temperature and DO dynamics within the shallow alluvial aquifer, which is an extensive hyporheic zone because subsurface alluvial flow paths are recharged primarily by channel water. Our results underscore the importance of geomorphic, hydrologic, and temperature dynamics in driving river ecosystem processes, and they demonstrate how a realistic representation of a river\u27s physical template, combined with simple biogeochemical models, can explain complex patterns of solute availability

Mixed Tree and Spatial Representation of Dissimilarity Judgments

Whereas previous research has shown that either tree or spatial representations of dissimilarity judgments may be appropriate, focussing on the comparative fit at the aggregate level, we investigate whether there is heterogeneity among subjects in the extent to which their dissimilarity judgments are better represented by ultrametric tree or spatial multidimensional scaling models. We develop a mixture model for the analysis of dissimilarity data, that is formulated in a stochastic context, and entails a representation and a measurement model component. The latter involves distributional assumptions on the measurement error, and enables estimation by maximum likelihood. The representation component allows dissimilarity judgments to be represented either by a tree structure or by a spatial configuration, or a mixture of both. In order to investigate the appropriateness of tree versus spatial representations, the model is applied to twenty empirical data sets. We compare the fit of our model with that of aggregate tree and spatial models, as well as with mixtures of pure trees and mixtures of pure spaces, respectively. We formulate some empirical generalizations on the relative importance of tree versus spatial structures in representing dissimilarity judgments at the individual level.Multidimensional scaling;tree models;mixture models;dissimilarity judgments

Identifying residential sub-markets using intra-urban migrations: the case of study of Barcelona’s neighborhoods

The dynamic evolution of the real estate market, as well as the sophistications of the interactions of the actors involved in it have caused that, contrary to classical economic theory, the real estate market is increasingly being thought of as a set of submarkets. This is because, among other things, the modeling of a segmented housing market allows, on the one hand, to design housing policies that are better adapted to the needs of the population, but on the other hand, it allows the generation of both marketing and supply strategies Oriented to specific population sectors. Such strategies in theory should behave as options with relatively low uncertainty, thus representing an attractive offer to all market players. However, in praxis, the segmentation of the real estate market is usually modeled on the offer. It is therefore that this paper proposes a modeling from observed preferences3 seen through intraurban migrations. In particular, it is proposed to model the market through the interaction value of Coombes, scaling the results in order to visualize the resulting submarket structure from the construction of a PAM (Partitioning Algorithm Medoids).Peer ReviewedPostprint (published version