Lack of calibrated instruments and written records prior to European contact in North America has forced palaeoclimatic researchers to develop various proxies capable of reconstructing ancient environments. Stable isotope analysis of tooth enamel of large terrestrial herbivores has increasingly become a creditable method of determining the ancient environments which these large mammals occupied during life. Archaeological evidence indicates human inhabitants of the northern Great Plains relied heavily on bison procurement throughout much of the Holocene. Because of this correlation, stable isotope analysis of bison tooth enamel has the capability of informing on palaeoenvironmental conditions which these ancient cultural groups occupied for the last 10,000 years on the northern Great Plains. Decades of research has provided evidence that stable isotope analysis of tooth enamel of large bodied herbivores (e.g. bovids) has the potential to be used as a proxy for reconstructing palaeoclimate, palaeoecology, foraging strategies and herd behaviour. Oxygen (δ 18O) isotope ratios are used as a proxy to track the meteoric hydraulic cycle (i.e. precipitation), which in turn is driven by local surface temperatures. Carbon (δ13C) isotope ratios have the ability to indicate photosynthetic pathways used by plant species, thus indicating local terrestrial plant cover. Dietary intake of water (δ 18O) and food (δ13C) are associated with isotopic signals which are recorded in the tooth enamel of a bison during amelogenesis (tooth enamel formation). Once tooth enamel is formed it never remodels; therefore, isotopic ratios recovered from fossil enamel become an archive of dietary consumption. In general, δ 18O isotope ratios are used to determine surface water and surface temperature conditions, whereas δ13C isotope values are used to indicate the abundance of C3 to C4 grasses consumed during an animal’s life. This study analyzes stable isotope (δ 18O and δ13C) ratios obtained from fossil bison enamel associated with archaeological sites in the northern Great Plains (Saskatchewan) region. The purpose of this study is to create a comparative model used to indicate ancient seasonality and palaeoenvironmental conditions over a 9,000 year period in the Holocene. A total of eight archaeological sites were examined, with each site representing a distinct time period and an affiliated human culture. In addition, isotope (δ 18O and δ13C) ratios recovered from tooth enamel was compared to isotope (δD and δ13C) values previously (Leyden 2004) examined from bone collagen of bison remains from the same archaeological sites. Results of this study demonstrates that original isotopic values from consumed water (δ 18O) and food (δ13C) from archaeological bison tooth enamel reflects seasonal changes for an approximate 18 month period. Further, results from this study also indicate that several climate and plant ecology changes occurred in the Saskatoon, Saskatchewan region over the last 9,000 years. Episodes of climate warming and cooling have been inferred by changes in δ 18O ratios at different time periods of the Holocene. Similarly, significant differences are also detected in δ13C values from different archaeological sites, inferring that bison populations consumed various abundances of C4 grasses at different time periods. In addition, evidence from this study has indicated that stable isotope ratios from enamel (δ 18O) and collagen (δD) from the same archaeological site, for the purpose of inferring climate conditions, demonstrate differing data for several time periods and close correlations for others. On the contrary, δ13C from both tooth enamel and bone collagen from each archaeological site produce comparable data which were used to measure the abundance of C4 grasses consumed by bison population during particular time periods.

Ten years ago, J. Villadsen constructed the first examples of simple C*-algebras with stable rank other than one or infinity. Villadsen's examples all had a unique tracial state. It is natural to ask whether examples can be found of simple C*-algebras with higher stable rank and more than one tracial state; by building on Villadsen's construction, we describe such examples that admit arbitrary tracial state spaces.

Soient k un corps algébriquement clos de caractéristique p > 0 et C/k une courbe projective, lisse, intègre de genre g > 1 munie d'un p-groupe d'automorphismes G tel que |G| > 2p/(p-1)g. Le couple (C,G) est appelé grosse action. Si (C,G) est une grosse action, alors |G| <=4p/(p-1)^2g^2 (*). Dans cette thèse, nous étudions les répercussions arithmétiques des propriétés géométriques de grosses actions. Nous étudions d'abord l'arithmétique de l'extension de monodromie sauvage maximale de courbes sur un corps local K d'inégale caractéristique p à corps résiduel algébriquement clos, de genre arbitrairement grand ayant pour potentielle bonne réduction une grosse action satisfaisant le cas d'égalité de (*). On étudie en particulier les conducteurs de Swan attachés à ces courbes. Nous donnons ensuite les premiers exemples, à notre connaissance, de grosses actions (C,G) telles que le groupe dérivé D(G) soit non abélien. Ces courbes sont obtenues comme revêtements de S-corps de classes de rayons de P1(Fq) pour S non vide un sous-ensemble fini de P1(Fq). Enfin, on donne une méthode de calcul des S-corps de classes de Hilbert de revêtements abéliens de la droite projective d'exposant p et supersinguliers que l'on illustre pour des courbes de Deligne-Lusztig.

Reservoirs impound and store large volumes of water and flood land. The water is used for electricity generation, irrigation, industrial and municipal consumption, flood control and to improve navigation. The decomposition of flooded soil and vegetation creates greenhouse gases and thus reservoirs are a source of greenhouse gases. Reservoirs are not well studied for greenhouse gas flux from the water to the atmosphere. The FLooded Upland Dynamics EXperiment (FLUDEX) involves the creation of three experimental reservoirs in the upland boreal forest to study greenhouse gas and mercury dynamics. The balance of biological processes, decomposition, primary production, CH₄ oxidation and the nitrogen cycle in the reservoirs controls the greenhouse gas flux from the reservoir to the atmosphere. Understanding the importance and controlling factors of these processes is vital to understanding the sources and sinks of greenhouse gases within reservoirs. The carbon and oxygen dynamics near the sediment-water interface are very important to the entire reservoir because many processes occur in this area. Light and dark benthic chambers were deployed, side-by-side, to determine the benthic flux of DIC and CH₄ across the sediment-water interface and to determine the role of benthic photoautotrophs in benthic DIC, CH₄ and O₂ cycling. Benthic chambers have shown photoautotrophs use the decomposing soil, rocks and exposed bedrock as a physical substrate to colonize and the CO₂ produced by the decomposing soil as a carbon source since the delta¹³C-DIC value of the DIC added to light chambers is enriched relative to dark chambers and net photosynthesis rates are linked to community respiration. Benthic photoautotrophs consume 15-33% of the potential DIC flux into the water column. CH₄ produced by the decomposition of soils is partially oxidized by methanotrophs that use the photosynthetically produced oxygen. The delta¹³C-CH₄ values of the CH₄ added to light chambers is enriched relative to dark chambers and 15-88% of the potential CH₄ flux into the water column is oxidized. An isotope-mass budget for DIC and CH₄ is presented for each reservoir to identify the importance of processes on areservoir scale. Input of DIC to the reservoirs from overland flow can be important because concentration is greater and delta¹³C-DIC values are depleted relative to inflow from Roddy Lake. Estimates of total reservoir primary production indicate that 3-19% of the total DIC production from decomposition is removed by photoautotrophs. The carbon cycling in biofilm and the importance of periphytic primary production needs to be better understood. Dissolved delta¹³C-CH₄ values of CH₄ in reservoir outflow enriched 45-60permil, indicating that CH₄ oxidation was an important CH₄ sink within the reservoirs. Stable carbon isotope data indicates that the CH₄ in the bubbles is partially oxidized so the site of bubble formation is the upper portion of the flooded soil. The fraction of CH₄ converted to CO₂ in the FLUDEX reservoirs is similar to that of the wetland flooded for the Experimental Lakes Area Reservoir Project (ELARP). Approximately half of the dissolved CH₄ in the FLUDEX reservoirs was removedby CH₄ oxidation. The ebullitive flux of CH₄ from FLUDEX reservoirs is reduced 25-75% by CH₄ oxidation. The CH₄ flux to the atmosphere from peat surface of the ELARP reservoir became less oxidized after flooding: 91% to 85% oxidized. The floating peat islands of the ELARP reservoir were less oxidized than the peat surface. Similar to the CH₄ in the FLUDEX reservoirs, CH₄ in the ELARP peat islands was oxidized 56%. CH₄ oxidation is an important process because it reduces the global warming potential of the greenhouse gas flux since CO₂ is less radiatively active than CH₄.

A boreal forest wetland (L979) was flooded in 1993 at the Experimental Lakes Area, Ontario to imitate a hydroelectric reservoir and to study the effects of flooding on greenhouse gas production and emission. Flooding initially caused CO&#8322; and CH4 emission rates to increase and changed the wetland from a small, natural carbon sink to a large source of carbon. The increased production of greenhouse gases in the peatland also caused the majority of the peat to float to the surface creating floating peat islands, within 4 years of flooding. The floating peat islands are a larger source than the central pond of CH4 to the atmosphere due to the high water table and small oxidation zone as compared to the earlier undisturbed peatland. The floating peat islands had an average flux of 202 ± 66 mg C-CH4/m²/day comparable to rates measured in 1995. Methane flux rates are spatially and temporally variable ranging from ?117 to 3430 mg C-CH4/m²/day. The variability is partly due to episodic releases of gas bubbles and changes in overlying pressure from the water table. The development of floating peat islands created an underlying water pocket. The water pocket increased water movement between the central pond and the peatland and led to increased peat temperatures and methane oxidation, and removal of debris from the water pocket. DIC, CH4, and O&#8322; concentrations, and &#948;13C-DIC, &#948;13-CH4, and &#948;18O-O&#8322; values in the water pocket were similar to values in the central pond. Before flooding, the &#948;13C-CH4 values from the peatland ranged between ?36 and ?72? indicating that about 65 to 90% of the methane was oxidized before flooding. After flooding, the median &#948;13C-CH4 value from the floating peat islands was ?52? indicating that about 30% of the methane was oxidized before it was emitted to the atmosphere. Since the floating islands are now vegetated, photosynthesis and transport via plants allow the movement of oxygen into the peat islands Methane oxidation in the central pond was similar in 2001 and 2002. DIC and CH4 isotope mass budgets from June 3 to September 23, 2002 indicate that inputs were smaller than outputs at L979. Calculated net DIC and CH4 production in the central pond was 8490 and 432 kg C, with &#948;13C-DIC of -18. 5 ? and &#948;13C-CH4 of -32. 5?. Decomposition of peat was the source of DIC and CH4. O&#8322; saturation levels indicate that the pond is always undersaturated and that respiration dominates the system; however, the &#948;18O-O&#8322; also indicates that photosynthesis is an important process in the central pond of L979. The peat islands contributed about 90% of the total CH4 flux, whereas the open water areas contributed 10%. This indicates that formation of peat islands in a hydroelectric area can significantly affect the greenhouse gas emissions to the atmosphere. The average flux of CH4 from the entire wetland in 2002 was 202 ± 77 mg C-CH4/m²/day, equivalent to 44 ± 17 g C-CH4/m²/year (year = 220 days). This is higher than preflood values of 0. 5 g C-CH4/m²/year in 1992, and the early post-flood value of 8. 9 g C-CH4/m²/year in 1993/1994. The wetland continues to emit methane after ten years of flooding at higher than preflood rates.

The caribou (Rangifer tarandus groenlandicus) on Southampton Island, Nunavut, Canada for the years 1998-2000 and 2004, 2005, were investigated using stable isotope analysis (SIA) of carbon (d 13C) and nitrogen (d 15N). Spring signatures of rumen contents and muscle samples were correlated with standard biological measures of back fat and Riney kidney fat index. Caribou d 13C and d 15N ratios, together with detailed rumen content analysis, show that SIA data yields a time-integrated signal reflective of spatial and temporal variation in feeding ecology and as such is capable of detecting trophic interactions. Rumen content signatures provide current indication of forage selection, while muscle tissue signatures reflect bulk summer seasonal diet and in combination with rumen signatures, can help identify potential shifts in winter diet and the potential for short-term changes in caribou condition. <br /><br /> d 13C and d 15N signatures for major forage species categories were also compared to variations in rumen content and muscle signatures to investigate possible changes in forage preference. The results indicate that SIA is capable of assessing the importance of seasonal habitat use with regard to seasonal food intake. Stable isotopes analysis (SIA) was also used to investigate the effects of winter snow thickness and temperature on caribou (Rangifer tarandus), on Southampton Island. Variations found in isotope signatures of rumen content and muscle indicated that differences in winter climate conditions may affect forage selection, and impact on animal condition.

Oil sands mining operations in northeastern Alberta are rapidly expanding. Upgrading and extracting the bitumen from the sand requires large volumes of water generating large quantities of oil sands process water/materials (OSPM) which is high in organic content. Some of the major organic components found in OSPM include unrecovered bitumen, polycyclic aromatic compounds (PACs), naphthenic acids (NAs) and humic acids. Concerns of acute and chronic toxicity resulting from OSPM have led to provincial legislation preventing the discharge of OSPM into local water and mandating the reclamation of areas affected by oil sands mining. To date, OSPM is stored on lease in settling basins while the mining companies evaluate reclamation strategies. One of the reclamation strategies involves the use of wetlands constructed with differing amounts of OSPM and organic amendments such as peat. Currently, numerous wetlands, both natural and constructed, are present on oil sands leases. To determine the sustainability of these wetlands for reclamation, the assimilation and flow of carbon and nitrogen within the systems need to be defined. Stable isotope analysis can enhance this understanding. To effectively use stable isotopes in the field, there is the need to determine the changes in stable isotope values occurring from the microbial degradation of organic components such as NAs which contribute a significant portion to the dissolved organic carbon (DOC) in reclamation sites. This study examined the microbial degradation of commercial and oil sands derived NAs by oil sands derived microbial cultures. Changes in stable isotopes values in the biomass (δ13C, δ15N), DOC and dissolved inorganic carbon (DIC) (δ13C) arising from degradation of the DOC were tracked in both static and semi-continuous tests. Utilization of commercial and oil sands derived NAs resulted in minimal change of the DOC stable isotope values. The biomass was 13C enriched for both the commercial (0.3 to 2.9 per mil (‰)) and oil sands derived NAs (3.7 to 8.5 ‰) relative to the DOC stable isotope values. DIC stable isotope values showed higher variability (-5 to +5.5 ‰). The semi-continuous tests showed biomass that was 15N enriched (3.8 to 8.4 ‰) with the assimilation of ammonium. Isotope trends established in the laboratory study provide further understanding into assimilation of carbon and nitrogen compounds in the field. DOC and DIC concentration and carbon stable isotope values were determined for water sampled from 13 oil sands aquatic reclamation sites varying in age, construction and organic material. Both DOC and DIC concentrations were elevated in OSPM affected sites, by an average of 40 mg/L for DOC and 83 mg/L for DIC concentrations. DOC concentrations were also elevated by approximately 10 mg/L at high organic sites. δ13C DOC values were slightly 13C enriched in young sites: 0.6 ‰ compared to δ13C DOC values at the mature sites. Also, from June to July 13C enrichment (0.3 to 1.9 ‰) of the DOC for all sites was seen. Corresponding with the enrichment seen in the DOC, 13C depletion (-8.8 to -0.3 ‰) of the DIC was seen for most sites from June to July. The trends seen from June to July may be a result of the release of readily degradable organics from the spring thaw stimulating the microbial community. The baseline values determined for DOC and DIC may assist future field food web studies.

Nitrate (NO3) contamination in agricultural watersheds is a widespread problem that threatens local drinking supplies and downstream ecology. Dual isotopes of NO3- (d15N and d18O) have been successfully used to identify sources of NO3 contamination and nitrogen (N)-cycle processes in agricultural settings. From 1998 to 2000, tile drainage and stream waters at the Strawberry Creek Catchment were sampled for NO3- concentration and isotopes. The results suggest that tile NO3 were mainly derived from soil organic matter and manure fertilizers, and that they were not extensively altered by denitrification. NO3- concentrations and isotopes in the stream oscillated between the influence of tile inputs, during periods of higher basin discharge, and groundwater inputs, during low basin discharge. The affect of denitrification was evident in stream NO3- samples. Sources and processes of dissolved NO3- and N2O were explored using concentrations and stable isotopes during the 2007 Springmelt and 2008 mid-winter thaw events. Tiles are a source of NO3- to the stream during both events and concentrations at the outflow are above the 10 mg N/L drinking water limit during the 2008 mid-winter thaw. The stream was a source of N2O to the atmosphere during both events. d15N and d18O of N2O reveal that N2O is produced from denitrification during both events. d18O:d15N slopes measured in N2O were due to the influence of substrate consumption (tiles) and gas exchange (stream). The stable isotopes of dissolved NO3- and N2O were also characterized during non-melt conditions (October 2006 to June 2007 and Fall 2007) at the Strawberry Creek catchment. Again, the purpose was to determine the sources and processes responsible for the measured concentrations and isotopic signatures. The isotope data suggests that N2O was produced by denitrification. Furthermore, NO3- consumption and gas exchange altered the original N2O signature. Isotopic distinction between soil gas N2O and dissolved N2O is suggestive of different production mechanisms between the unsaturated and saturated zones. Since the range of dissolved N2O isotopes from the Strawberry Creek catchment are relatively constraned, definition of the local isotopic signature of secondary, agricultural N2O sources was possible.

This thesis proposes an optimization formulation to ensure accuracy and stability in the local volatility function calibration. The unknown local volatility function is represented by kernel splines. The proposed optimization formulation minimizes calibration error and an L1 norm of the vector of coefficients for the kernel splines. The L1 norm regularization forces some coefficients to be zero at the termination of optimization. The complexity of local volatility function model is determined by the number of nonzero coefficients. Thus by using a regularization parameter, the proposed formulation balances the calibration accuracy with the model complexity. In the context of the support vector regression for function based on finite observations, this corresponds to balance the generalization error with the number of support vectors. In this thesis we also propose a trust region method to determine the coefficient vector in the proposed optimization formulation. In this algorithm, the main computation of each iteration is reduced to solving a standard trust region subproblem. To deal with the non-differentiable L1 norm in the formulation, a line search technique which allows crossing nondifferentiable hyperplanes is introduced to find the minimum objective value along a direction within a trust region. With the trust region algorithm, we numerically illustrate the ability of proposed approach to reconstruct the local volatility in a synthetic local volatility market. Based on S&P 500 market index option data, we demonstrate that the calibrated local volatility surface is smooth and resembles in shape the observed implied volatility surface. Stability is illustrated by considering calibration using market option data from nearby dates.

Dissolved oxygen (DO) is one of the most important environmental factors necessary to sustain aquatic life. The Southern Grand River is characterized with extensive marshes. This study focuses on the Dunnville Marsh in the Southern Grand River. The spatial and temporal variation in dissolved oxygen was studied in the Dunnville Marsh and the Grand River over a one year cycle during 2007 to 2008. Dunnville Marsh exhibited little influence on the oxygen regime of the river. The Grand River; however, could influence the oxygen regime in the marsh during the spring when waters are high but exerts little influence during the rest of the year. There were no great differences in DO between the wetland and the river during the high water spring melt period; however notable differences occurred in the summer and fall. Oxygen stable isotopes and diel O2 measurements showed that ecological factors probably were influencing the DO cycle in Dunnville Marsh, whereas both ecological and weather factors influenced the cycle in the Grand River. Monthly δ18O-DO data from the river revealed a shift towards atmospheric equilibrium compared to the wetland. These data exhibited less photosynthetic activity in the fall and more photosynthetic activity during the summer. The wetland showed higher photosynthetic activities in the summer than the river. Nitrogen input from the agricultural areas was low at most of the time and had minimal influence on the DO in the Dunnville Marsh. Despite low nitrogen input the attenuation ability of the Dunnville Marsh was apparent, presumably due to plant uptake, especially in the northern part of the marsh. Based on the δ18O-water signature in late April (after the flood season) it appears river water extended about two-thirds along the main stream well into Dunnville Marsh. River water, probably inundates a significant part of the Dunnville Marsh in early April (flood peak), when water flow was more than 10 fold higher than later in April following the peak flood season. River water can be intruded into the marsh and brought the DO to similar saturations as in the river in spring.