Response curves of deterministic and probabilistic cellular automata in one and two dimensions

One of the most important problems in the theory of cellular automata (CA) is determining the proportion of cells in a specific state after a given number of time iterations. We approach this problem using patterns in preimage sets - that is, the set of blocks which iterate to the desired output. This allows us to construct a response curve - a relationship between the proportion of cells in state 1 after niterations as a function of the initial proportion. We derive response curve formulae for many two-dimensional deterministic CA rules with L-neighbourhood. For all remaining rules, we find experimental response curves. We also use preimage sets to classify surjective rules. In the last part of the thesis, we consider a special class of one-dimensional probabilistic CA rules. We find response surface formula for these rules and experimental response surfaces for all remaining rules.

The Terroir of Winter Hardiness: Investigation of Winter Hardiness, Water Metrics, and Yield of Riesling and Cabernet Franc in the Niagara Region Using Geomatic Technologies

Grapevine winter hardiness is a key factor in vineyard success in many cool climate wine regions. Winter hardiness may be governed by a myriad of factors in addition to extreme weather conditions – e.g. soil factors (texture, chemical composition, moisture, drainage), vine water status, and yield– that are unique to each site. It was hypothesized that winter hardiness would be influenced by certain terroir factors , specifically that vines with low water status [more negative leaf water potential (leaf ψ)] would be more winter hardy than vines with high water status (more positive leaf ψ). Twelve different vineyard blocks (six each of Riesling and Cabernet franc) throughout the Niagara Region in Ontario, Canada were chosen. Data were collected during the growing season (soil moisture, leaf ψ), at harvest (yield components, berry composition), and during the winter (bud LT50, bud survival). Interpolation and mapping of the variables was completed using ArcGIS 10.1 (ESRI, Redlands, CA) and statistical analyses (Pearson’s correlation, principal component analysis, multilinear regression) were performed using XLSTAT. Clear spatial trends were observed in each vineyard for soil moisture, leaf ψ, yield components, berry composition, and LT50. Both leaf ψ and berry weight could predict the LT50 value, with strong positive correlations being observed between LT50 and leaf ψ values in eight of the 12 vineyard blocks. In addition, vineyards in different appellations showed many similarities (Niagara Lakeshore, Lincoln Lakeshore, Four Mile Creek, Beamsville Bench). These results suggest that there is a spatial component to winter injury, as with other aspects of terroir, in the Niagara region.