We have obtained broad-band NIR-photometry for six Galactic star clusters, M92,M15,M13, NGC1851, M71 and NGC6791, as observed with the WIRCam wide-field imager on the Canada-France-Hawaii Telescope; supplemented by images taken with HAWK-I on VLT. From the resultant (V − J)-V and (V − K)-V colour-magnitude diagrams, fiducial sequences spanning the range in metallicity, −2.4 ≤ [Fe/H] ≤+0.3, have been defined which extend from the tip of the red-giant branch to ∼ 2.5 magnitudes below the main-sequence turnoff. These fiducials provide a valuable set of empirical isochrones for the interpretation of stellar population data in the 2MASS system. From the NIR data, the reddenings of M15, M71 and NGC6791 — which have been subject to considerable controversy — were found to be E(B−V)=0.075, 0.22 and 0.155 mag respectively. Comparisons of our CMDs to Victoria isochrones that have been transformed using the MARCS model colour-Teff relations reveal that the models reproduce the giant branches of clusters more metal-rich than [Fe/H] ≈ −1.3, but they become systematically redder than the observed RGBs as the cluster metallicity decreases. These discrepancies are seen consistently in the two colours and therefore may indicate that the temperature scale of the stellar evolutionary models for giant stars at low metallicity is too cool.MARCS colour transformations were also tested using the classic Population II subdwarfs. The MARCS colours show redward offsets of ∼ 0.03 mag when compared with the observed (V − K) and (J − K) colours (assuming best estimates of Teff, log g, and [Fe/H]), and a systematic blue offset relative to the isochrone temperatures. Together with the indications from the cluster (V − K) and (V − J) CMDs, these results suggest that there is a problem with the MARCS colour transformations involving J.

Let v [greater than or equal to] k [greater than or equal to] 1 and lamda [greater than or equal to] 0 be integers and G be a graph with n vertices, m edges, and no multiple edges. A (v, k, lambda) block design is a collection Beta of k-subsets of a v-set X in which every unordered pair of elements in X is contained in exactly lambda of the subsets in Beta. A (G-decomposition, or (v, G, lambda) graph design, is a collection H1, H2, ..., Ht of subgraphs of Kv (the complete graph on v vertices) such that each edge of Kv is an edge of exactly lambda of the subgraphs Hi and each of the subgraphs Hi is isomorphic to G. A famous result by Wilson says that for a fixed graph G and integer lambda, there exists a (v, G, lambda) graph design for all sufficiently large integers v satisfying certain necessary conditions. In this thesis, we extend this result to include the case of loops in G. As a consequence, one obtains asymptotic existence of equireplicate graph designs for values of v satisfying certain necessary conditions, where a graph design is called equireplicate if each vertex of Kv occurs in the same number of subgraphs Hi of the decomposition.

Inducible defenses alter the strength of interaction in food webs. Theoretical models that incorporate their effects are therefore critical for predicting community dynamics and stability. I examined ecological effects of an inducible morphological defense in a microbial model. I first investigated the effect of genotype. number of predators, and previous exposure to predators on the speed and maximum level of defense for eight clones in three species of the ciliate Euplotes. The effectiveness of defense depends on both of these aspects of defense induction: therefore these traits should evolve in concert. The speed and maximum level of induction varied among genotypes, showing that there is genetic variance for these traits and the potential for evolutionary change under selection. Higher predator densities led to more rapid induction and higher maximum levels of defense. but previous exposure to predators had no detectable effect on either of these traits. I then used a model selection approach to determine the shape of the functional response of clones that differed in their level of defense, and to estimate and compare the model parameters attack rate and handling time. Defense decreased the attack rate of Euploes on Chlorella vulgar-is algae in one highly defended clone, but did not affect the functional response in two less defended clones. My results demonstrate that Euploes ciliates can precisely and rapidly adjust their morphological defense to the magnitude of predation risk in a way that varies among genotypes. This variation will lead to diversity in prey vulnerability to predators under natural conditions and translates to genetically-based differences in the foraging impact on resources of Euplotes. These estimates of ecological effects of induced defense in this system allow their inclusion in the development and testing of dynamic models. This in turn will inform our understanding of the influence of induced defenses and related trait-mediated indirect effects on community dynamics and stability.

The Functional Outcome Profile (FOP, Joschko & Skelton, 2003) was developed to be a broad measure of functional outcome following brain injury, unique from existing outcome measures. The purpose of this thesis was to investigate the underlying assumptions and psychometric properties of aspects of the FOP. Data from 107 brain injury survivors and 20 matched significant others were utilized. Exploratory investigations of the items, the scoring and the subscales were undertaken first, followed by investigations of the internal consistency and test-retest reliability of the outcome scores and the survivor-proxy agreement of the frequency ratings. Finally, multiple lines of evidence for the validity of the FOP were put forth based on the content, its relation to external, demographic variables and its sensitivity to change over time. In general, the FOP was found to be a reliable measure of outcome following brain injury with the subscale scores providing the most useful information. The implications for these findings are discussed.

An oxygen barometer to estimate fO2 during the crystallization of kimberlites is developed using the Fe content of perovskite (Pv), a common groundmass phase in these rocks. With increasing fO2, more Fe exists in the kimberlitic liquid as Fe3+, and thus partitions into Pv, which accepts only Fe3+ into its crystal structure. Experiments to study the partitioning of Fe3+ between Pv and kimberlite liquid were conducted on simple and complex anhydrous kimberlite bulk compositions at 100 kPa over a range temperatures (1130 - 1300°C) and of fO2's from NN0+4 to NNO-5 (NNO, nickel-nickel oxide buffer) and at Nb and REE levels of 0 to 1.5 wt% and 1500 ppm respectively. For Nb-free experiments, the Fe2O3 content of Pv increases with fO2 according to the relation (at 2σ): Fe2O3 Pv (wt%) = 0.25 (0.04) ?NNO + 1.83(0.06) For experiments doped with Nb, two universal equations for the relationship between the Fe and Nb in Pv, and fO2 were defined. Based on a slope intercept fitting method (SIM) we obtain: Log Fe (0.04)=0.058(0.004)* ?NNO + 0.26(0.02)*Log Nb - 0.91(0.03) Based on a multiple linear regression method (MLR): Fe (0.031)= 0.404(0)* NNO + 0.50(0.021)*Nb + 0.030(0.001) with uncertainties at 2o, and Nb and Fe as cation units per 3 oxygens in both equations. Over the range of conditions of our experiments, these relationships show no temperature (T) dependence and are not affected by the bulk Fe content of the kimberlite starting material. The Fe2O3 content of Pv from natural kimberlites compiled from the literature corresponds to fO2 conditions of NNO-5 to NNO+1. Data on zoned Pv from a single kimberlite, the Phoenix pipe, suggests that cores record lower fO2 than rims, NNO-1 in = cores compared to NNO+1 in rims. Within the Somerset Island cluster, Pv from six pipes display an average relative f02 of NNO-4 to NNO+I . Within individual kimberlite pipes, however, the fO2 range recorded by Pv narrows to NNO-2.6 +/- 0.6 within the Nikos 1 pipe, and NNO +1- 2 within the Zulu pipe. Within the Lac de Gras cluster, Pv from five pipes display an average relative fO2 of NNO-2.5 to NNO+6. However, within a single kimberlite, the Grizzly pipe, the fO2 range recorded by Pv narrows to NNO+/- 1. The range in fO2 recorded by Pv may result from the diversity and complexity of processes that ensue during the emplacement of kimberlite magma (crystallization, assimilation and degassing), a detailed record of which is revealed by a comprehensive study of perovskite parageneses in these complex rocks.

A sensor network is comprised of a large number of sensor nodes with limited power, which collect and process data from a target domain and transmit information back to specific sites, such as, headquarters and disaster control centers. Since the wireless communication channel shared by sensor nodes is broadcast in nature, a Medium Access Control (MAC) protocol is needed to specify how nodes share the channel, which plays a central role in the performance of a sensor network. In this thesis, we investigate the performance of randomized and time hopping Aloha MAC protocols by theoretical analysis and simulations. The first part of our research formulates the multiple access collision problem raised from the ARGOS satellite telemetry system. We analyze the factors that affect the performance of the system and derive the mathematical model. We simulate the system and generate valuable performance results for design purpose. In the second part of the thesis, we extend our research to sensor networks with Impulse Radio Ultra WideBand (IR- UWB) physical layer defined in IEEE802.15.4a. We analyze and model the time hopping Aloha MAC protocol and verify the results with simulations using NS-2 network simulator.

In preparations for the ATLAS experiment at the Large Hadron Collider at CERN, sections of the ATLAS Electromagnetic Endcap Calorimeter (EMEC) and Hadronic Endcap Calorimeter (HEC) were subjected to particle beams in the summer of 2002. The EMEC and HEC are non-compensating calorimeters with e/h > I: electromag¬netic showers will, on average; have a higher energy response than hadronic showers initiated by particles of the same energy. To reconstruct the energy of pions, the method of software compensation is investigated. Several beam energy dependent weighting schemes are studied, using calorimeter depth weights and cluster energy density weights. Finally, a beam energy independent cluster energy density weighting scheme is studied. Partial software compensation is achieved for pion energy recon¬struction, improving the energy resolution and response linearity of the calorimeters.

A generalization of the circular chromatic number to hypergraphs is devel-oped. Circular colourings of graphs and hypergraphs are first discussed and it is shown that the circular chromatic number of a graph is the same regard-less of whether the hypergraph or graph definition is used. After presenting a few basic results, some examples of circular chromatic numbers of various families of hypergraphs are given. Subsequently, the concepts of the star chromatic number and the arc chromatic number are introduced. Specif¬ically, both numbers are shown to be equivalent to the circular chromatic number. Finally the relationship between the imbalance of a hypergraph and the circular chromatic number is explored and a classical result of Minty is deduced.

The synthesis of the cyclopentadiene-fused dimethyldihydropyrene, CpDI-IP(H) 44, from DHP 31 was achieved in a seven-step synthesis in an overall yield of 7%. Deprotonation of 44 gave the Cp anion fused CpDHP anion 28. The photochromic properties of 28 were studied. It is found that 28 is photochromic and its behavior is intermediate between the parent DHP 31 and the benzannelated DHP 36. The 1H-NMR data of 28 were also analyzed and showed that the Cp anion has similar bond fixing effect on the DHP ring as benzene does, but to a lesser extent. The complexation of anion 28 to various metal centers has been investigated. While the reactions of 28 with Re(CO)5Br, (Cp*RuCl2)„ and FeC12 yielded (CpDHP)Re(CO)3 51. Cp*Ru(CpDHP) 52 and (CpDHP)2Fe 54 respectively, the reactions with Mn. Y. Yb(III) or Zr precursors either gave the starting materials back or resulted in the decomposition of 28 to unidentified products. Reaction of the protonated form CpDHP(H) 44 with Yb[N(SiMe3)2I(thf)2 afforded Yb(CpDHP)2(thf)2 57.

A k-uniform hypergraph N = (X. B) of order n is a family of k-subsets B of an n-set X. A k-uniform hypergraph 7--L = (X. B) is disjoint union-free (DUF) if all disjoint pairs of elements of B have distinct unions; that is, if for every A, B, C, D E B. A fl B = C f1 D = 0 and A U B =CUD implies {A. B} = {C, D}. DUF families of maximum size have been studied by Erdos and Fiiredi. and in the case k = 3 this maximum size has been conjectured to equal (z). In this thesis, we study DUF 3-uniform hypergraphs with the main goals of presenting evidence to support this conjecture and studying the structures that have conjectured maximum size. If each pair of distinct elements of X is covered exactly A times in B then we call N = (X, B) an (n. k. A)-design. Using a blend of graph- and design-theoretic techniques, we study the DUF (n,. 3. 3)-designs that are the conjectured unique structures having maximum size. Central results of this thesis include substantially improving lower bounds on the maximum size for a large class of n. giving conditions on pair coverage in a DUF 3-uniform hypergraph that force an (n., 3, 3)-design, and providing constructions for DUF 3-uniform hypergraphs from families of DUF hypergraphs with smaller orders. Let. N = (X, B) be a DUF k-uniform hypergraph with the property that 7-t U {E} is not DUF for any k-subset E of X not already in H. Then N is maximally DUF. We introduce the problem of finding the minimum size of maximally DUF families and provide bounds on this quantity for k = 3.