When large areas of forest are modelled, spatial detail can create excessively large databases and adversely affect the processing time. Spatial generalization can be an efficient means of aggregating polygons into blocks in strategic forest planning models. In this study, a sensitivity analysis on spatial generalization was conducted to examine the trade-off between accuracy and spatial resolution to meet the objectives of strategic planning. Five scenarios were designed by generalizing forest cover polygons into the uniform hexagon block sizes of 5, 10, 20, 50 and 100 ha. To quantitatively assess accuracy, deviations caused by spatial generalization were calculated by criteria for hexagon scenarios relative to the base case. Criteria include model inputs (area of natural disturbance type and ungulate winter range) and outputs (harvest volume, growing stock and seral stage distribution). In general, deviations in all criteria increased with the block size. Spatial resolution was also evaluated by the database size and simulation runtime. A negative relationship was observed between spatial resolution and the block size. The trade-off analysis between accuracy and spatial resolution indicated that using the smallest block size of 5 ha creates more detail than necessary. Although scenarios with the block sizes of 50 and 100 ha reduced spatial resolution significantly, the maximum deviations relative to the base case were as high as 14% and 17% in growing stock, 12% and 12% in seral stage distribution, and 6% and 21% in ungulate winter range, respectively. For this study, the preferred block size is in the range of 10-20 ha, however, in general, the preferred block size will vary depending on the importance of each criterion used in the trade-off analysis.

When large areas of forest are modelled, spatial detail can create excessively large databases and adversely affect the processing time. Spatial generalization can be an efficient means of aggregating polygons into blocks in strategic forest planning models. In this study, a sensitivity analysis on spatial generalization was conducted to examine the trade-off between accuracy and spatial resolution to meet the objectives of strategic planning. Five scenarios were designed by generalizing forest cover polygons into the uniform hexagon block sizes of 5, 10, 20, 50 and 100 ha. To quantitatively assess accuracy, deviations caused by spatial generalization were calculated by criteria for hexagon scenarios relative to the base case. Criteria include model inputs (area of natural disturbance type and ungulate winter range) and outputs (harvest volume, growing stock and seral stage distribution). In general, deviations in all criteria increased with the block size. Spatial resolution was also evaluated by the database size and simulation runtime. A negative relationship was observed between spatial resolution and the block size. The trade-off analysis between accuracy and spatial resolution indicated that using the smallest block size of 5 ha creates more detail than necessary. Although scenarios with the block sizes of 50 and 100 ha reduced spatial resolution significantly, the maximum deviations relative to the base case were as high as 14% and 17% in growing stock, 12% and 12% in seral stage distribution, and 6% and 21% in ungulate winter range, respectively. For this study, the preferred block size is in the range of 10-20 ha, however, in general, the preferred block size will vary depending on the importance of each criterion used in the trade-off analysis.

When large areas of forest are modelled, spatial detail can create excessively large databases and adversely affect the processing time. Spatial generalization can be an efficient means of aggregating polygons into blocks in strategic forest planning models. In this study, a sensitivity analysis on spatial generalization was conducted to examine the trade-off between accuracy and spatial resolution to meet the objectives of strategic planning. Five scenarios were designed by generalizing forest cover polygons into the uniform hexagon block sizes of 5, 10, 20, 50 and 100 ha. To quantitatively assess accuracy, deviations caused by spatial generalization were calculated by criteria for hexagon scenarios relative to the base case. Criteria include model inputs (area of natural disturbance type and ungulate winter range) and outputs (harvest volume, growing stock and seral stage distribution). In general, deviations in all criteria increased with the block size. Spatial resolution was also evaluated by the database size and simulation runtime. A negative relationship was observed between spatial resolution and the block size. The trade-off analysis between accuracy and spatial resolution indicated that using the smallest block size of 5 ha creates more detail than necessary. Although scenarios with the block sizes of 50 and 100 ha reduced spatial resolution significantly, the maximum deviations relative to the base case were as high as 14% and 17% in growing stock, 12% and 12% in seral stage distribution, and 6% and 21% in ungulate winter range, respectively. For this study, the preferred block size is in the range of 10-20 ha, however, in general, the preferred block size will vary depending on the importance of each criterion used in the trade-off analysis. / Forestry, Faculty of / Graduate

Lorsque le système nerveux central est exposé à une nouvelle association visuoproprioceptive, l’adaptation de la carte visuomotrice est nécessaire afin d’exécuter des mouvements précis. L’efficacité de ces processus adaptatifs correspond aussi à la capacité à les transférer dans des contextes différents de l’apprentissage de cette nouvelle association, par exemple dans de nouvelles régions de l’espace extrapersonnel (généralisation spatiale). Comme le contexte exerce une influence considérable sur les processus adaptatifs, les composantes multidimensionnelles de la tâche et de la perturbation pourraient constituer des éléments affectant considérablement l’adaptation et la généralisation spatiale. Ce mémoire présente une étude exploratoire de l’adaptation à une perturbation triaxiale, introduite graduellement, réalisée dans un environnement virtuel tridimensionnel et sa généralisation spatiale. Nos résultats suggèrent que les trois axes de l’espace présentent des différences importantes quant aux processus adaptatifs qui les sous-tendent. L’axe vertical présente à la fois une plus grande variabilité et de plus grandes erreurs spatiales au cours de l’adaptation comparativement à l’axe sagittal et à l’axe horizontal, tandis que l’axe sagittal présente une plus grande variabilité que l’axe horizontal. Ces différences persistent lors de l’effet consécutif, l’axe vertical affichant une désadaptation importante. Le test de généralisation spatiale montre une généralisation à l’ensemble des cibles, cependant, la généralisation semble plus faible le long de l’axe vertical. Ces résultats suggèrent que l’adaptation à une translation tridimensionnelle se généralise à travers l’espace le long des trois axes de l’espace et renforcent l’idée que le système nerveux central utilise une stratégie de décomposition modulaire des composantes de l’espace tridimensionnel. / We explored visuomotor adaptation and spatial generalization in the context of three-dimensional reaching movements performed in a virtual reality environment using a learning paradigm composed of four phases: pre-exposure, baseline, learning, and post-exposure (aftereffect and generalization). Subjects started by performing five reaching movements to six 3D memorized target locations without visual feedback (pre-exposure). Next, subjects performed twelve reaching movements to the learning target with veridical visual feedback (baseline). Immediately after, the 3D visuomotor dissociation (horizontal, vertical and sagittal translations) between actual hand motions and visual feedback of hand motions in the 3D virtual environment was gradually introduced (learning phase). Finally, subjects aimed at the pre-exposure and baseline targets without visual feedback (post-exposure). Although subjects were unaware of the visuomotor perturbation, they showed movement adaptation for each component of the triaxial perturbation, but they displayed reduced adaptation rate along the vertical axis. Subjects persisted in applying the new visuomotor association when the perturbation was removed, but the magnitude of this post-exposure shift was lower along the vertical axis. Similar trends were observed for movement aimed at pre-exposure targets. Furthermore, these post-exposure shifts were, on average, greater along the horizontal and sagittal axes relative to the vertical axis. These results suggest that the visuomotor map may be more adaptable to shifts in the horizontal and sagittal directions, than to shifts in the vertical direction. This finding supports the idea that the brain may employ a modular decomposition strategy during learning to simplify complex multidimensional visuomotor tasks.

TITLE Spatial generalizations of the properties of the triangle AUTHOR Jirˇı' Sřubarˇ SUPERVISOR Prof. RNDr. Adolf Karger, DrSc. DEPARTMENT Department of mathematics education ABSTRACT The present thesis describes various interesting properties of a triangle. The aim is to find and prove similar properties of its spatial generalization - a tetrahedron. Even though both synthetic and computational methods are used for proving spatial relations, synthetic approach is preferred whenever possible. The thesis is divided into two parts. In the first part, the properties of the tetrahedron analogous to the centroid and the orthocenter of the triangle are described. Also, conditions on the existence of the orthocenter of the tetrahedron are derived. Moreover, for tetrahedrons without an orthocenter, the so-called Monge point is introduced as its generalization. In the second part of the thesis, some further properties of the triangle are studied - - the Simson line, the de Longchamps point, the nine-point circle, the Euler line, the Lemoine point, the isodynamic points, the Lemoine axis and the Brocard axis. As the main contribution of the present thesis we define and prove the existence of spatial analogues of the above mentioned properties for the tetrahedron - the de Longchamps point, the twelve-point and...