Master of Science / Department of Statistics / Perla Reyes / Networks are defined as sets of items and their connections. Interconnected items are represented by mathematical abstractions called vertices (or nodes), and the links connecting pairs of vertices are known as edges. Networks are easily seen in everyday life: a network of friends, the Internet, metabolic or citation networks. The increase of available data and the need to analyze network have resulted in the proliferation of models for networks. However, for networks with billions of nodes and edges, computation and inference might not be achieved within a reasonable amount of time or budget. A sampling approach seems a natural choice, but traditional models assume that we can have access to the entire network. Moreover, when data is only available for a sampled sub-network conclusions tend to be extrapolated to the whole network/population without regard to sampling error. The statistical problem this report addresses is the issue of how to sample a sub-network and then draw conclusions about the whole network. Are some sampling techniques better than others? Are there more efficient ways to estimate parameters of interest? In which way can we measure how effectively my method is reproducing the original network? We explore these questions with a simulation study on Mesa High School students' friendship network. First, to assess the characteristics of the whole network, we applied the traditional exponential random graph model (ERGM) and a stochastic blockmodel to the complete population of 205 students. Then, we drew simple random and stratified samples of 41 students, applied the traditional ERGM and the stochastic blockmodel again, and defined a way to generalized the sample findings to the population friendship network of 205 students. Finally, we used the degree distribution and other network statistics to compare the true friendship network with the projected one. We achieved the following important results: 1) as expected stratified sampling outperforms simple random sampling when selecting nodes; 2) ERGM without restrictions offers a poor estimate for most of the tested parameters; and 3) the Bayesian stochastic blockmodel estimation using a strati ed sample of nodes achieves the best results.

The novel complexes [special characters omitted] and [special characters omitted] were prepared and characterized. Photoredox quantum yields for the formation of [special characters omitted] from the above compounds were measured on irradiation at 360 nm to be 0.065, 0.082, 0.0088 and 0.0040 respectively. With added thiocyanate a significant increase in ΦCo2+ occurred. This can be modeled in two ways; (i) scavenging of thiocyanate radical from an initial caged radical pair giving 6-25 ps estimates for the lifetime of the latter species; (ii) photolysis of a thiocyanate/complex ion pair, giving formation constants of 0.19, 0.09, 0.08 and 0.05 for the complexes [special characters omitted] and [special characters omitted] respectively. Subnanosecond laser flash photolysis studies showed evidence for the formation of [special characters omitted]. The effects of added electrolytes and of viscosity on the formation and decay of [special characters omitted] were also investigated. To help to distinguish between the above two mechanisms, the zero-charged novel complex [special characters omitted] (tacn = 1,4,7-triazacyclononane) was synthesized and characterized. It is thermally stable in aqueous/DMSO solution, but on irradiation at 360 nm undergoes parallel photosubstitution to form DMSO and aqua-substituted products with an overall quantum yield of 0.012. The product yields increase linearly with added thiocyanate. For a 1 M thiocyanate solution, the quantum yield for disappearance of the starting complex rose to 0.022 and a small redox yield of 0.0008 was found. Under these same conditions, ns laser flash photolysis at 355 nm revealed a transient absorption owing to [special characters omitted], which was produced with a quantum yield of 0.036. These results are interpreted in terms of scavenging of radical pair species by thiocyanate ion followed by back electron transfer to give a photosubstituted product, and a radical pair quantum yield of 0.29 and lifetime of 12 ps was derived. The emission of [special characters omitted] (where pop = μ-pyrophosphite-P,P’) can be quenched by the complexes [special characters omitted] (where X = [special characters omitted]) only in the presence of electrolytes. The salt effects have been studied using the salts MCl, M'Cl2, or [special characters omitted] (where M, M’ and R represent alkali, alkaline earth metals, and alkyl respectively, with n = 0-3), and [special characters omitted]. For 0.5 M cation concentration, second-order quenching rate constants kq lie in the range [special characters omitted]. For the different quencher complexes used, kq decreases in the order [special characters omitted]. The oxidative quenching products [special characters omitted] are observed, and their quantum yields are 0.083 and 0.027 respectively for the reaction of [special characters omitted] with [special characters omitted] and [special characters omitted] in 0.5 M KCl / pH2 solution. The quenching occurred by atom transfer (dominant) and electron transfer (minor) for quencher [special characters omitted] or [special characters omitted], while only electron transfer was observed for [special characters omitted] and [special characters omitted] quenchers. The quenching efficiency of the cobalt complexes increases with electrolyte concentration and specific cation effects are observed in the kq with the following trends Li+ < Na+ < K+ < Cs+: Mg2+ < Ca2+ < Sr2+ < Ba2+; NH4+ < MeNH3+ < Me2NH2+ < Me3NH+: Et3NH+ < Et2NH2+ < EtNH3+: n-PrNH3+ < EtNH3+ < MeNH3+. / Graduate

Submitted by Marcos Afonso Da Silva (marcos.da.silvaaf@gmail.com) on 2018-05-02T18:35:06Z No. of bitstreams: 1 silva_ma_me_rcla.pdf: 1746007 bytes, checksum: 2ae251af6bbcaa3e703be73180764ea3 (MD5) / Rejected by Adriana Aparecida Puerta null (dripuerta@rc.unesp.br), reason: Prezado Marcos, O documento "Análise complexa e aplicações" enviado para a coleção IGCE- Rio Claro foi recusado pelo(s) seguinte(s) motivo(s): - Falta a capa, que é elemento obrigatório e deve vir em primeiro lugar, antes da folha de rosto. - Falta a folha de aprovação, que deve ser solicitada à Seção de Pós-Graduação e deve ser inserida após a ficha catalográfica. O documento enviado não foi excluído. Para revisá-lo e realizar uma nova tentativa de envio, acesse: https://repositorio.unesp.br/mydspace Em caso de dúvidas entre em contato pelo email repositoriounesp@reitoria.unesp.br. Agradecemos a compreensão e aguardamos o envio do novo arquivo. Atenciosamente, Biblioteca Campus Rio Claro Repositório Institucional UNESP https://repositorio.unesp.br on 2018-05-03T16:21:47Z (GMT) / Submitted by Marcos Afonso Da Silva (marcos.da.silvaaf@gmail.com) on 2018-05-04T00:42:07Z No. of bitstreams: 1 silva_ma_me_rcla.pdf: 1807104 bytes, checksum: 5b70e3ffe1793a2b25dc37beaa31e31f (MD5) / Rejected by Adriana Aparecida Puerta null (dripuerta@rc.unesp.br), reason: Prezado Marcos, - O arquivo foi rejeitado pois, de acordo com as normas, tanto na capa quando na folha de rosto é obrigatório constar a cidade de defesa e o ano ao final da página. Exemplo: Rio Claro (e embaixo da cidade, 2018) Aguardamos o envio do novo arquivo com a correção. Atenciosamente, Biblioteca Campus Rio Claro. Repositório Institucional on 2018-05-04T13:28:00Z (GMT) / Submitted by Marcos Afonso Da Silva (marcos.da.silvaaf@gmail.com) on 2018-05-04T14:39:38Z No. of bitstreams: 1 silva_ma_me_rcla.pdf: 1749221 bytes, checksum: 91fb75a089e7b171f8516ee87703344f (MD5) / Approved for entry into archive by Adriana Aparecida Puerta null (dripuerta@rc.unesp.br) on 2018-05-04T17:56:05Z (GMT) No. of bitstreams: 1 silva_ma_me_rcla.pdf: 1689269 bytes, checksum: 5b3bb5cf57504efea17305264a03cccb (MD5) / Made available in DSpace on 2018-05-04T17:56:05Z (GMT). No. of bitstreams: 1 silva_ma_me_rcla.pdf: 1689269 bytes, checksum: 5b3bb5cf57504efea17305264a03cccb (MD5) Previous issue date: 2018-04-20 / O objetivo principal deste trabalho é desenvolver um estudo introdutório, porém detalhado, sobre Análise Complexa e algumas de suas aplicações. Apresentamos o corpo dos números complexos, exploramos as funções complexas de uma variável complexa, exibimos parte da teoria das funções analíticas e parte da teoria de integração complexa. Provamos importantes resultados, tais como o Teorema de Cauchy, o Teorema de Taylor, o Teorema dos Resíduos, entre outros igualmente relevantes. Como aplicação da teoria, destacamos a utilização do Teorema dos Resíduos para determinar a transformada inversa de Laplace de uma função F(s). / The main objective of this work is to develop an introductory but detailed study on Complex Analysis and some of its applications. We present the field of the complex numbers, explore the complex functions of a complex variable, exhibit part of the theory of analytic functions, and part of the complex integration theory. We prove important results, such as Cauchy’s Theorem, Taylor’s Theorem, Residue Theorem, among others equally relevant. As an application of the theory, we highlight the use of the Residue Theorem to determine the inverse Laplace transform of a function F(s).

This work set out to develop synthetic routes to transition metal complexes containing the ligands of general type [PPh₂(X)][PPh₂(Y)][PPh₂(Z)]CH and [PPh₂(X)][PPh₂(Y)][PPh₂(Z)]C⁻, where X, Y, Z = various combinations of O, S, Se and electron pairs. The aim would then be to fully characterise the complexes by various spectroscopic methods to determine the modes of coordination of the ligands and rationalise any dynamic processes which may be occurring in solution. Finally the complexes would be investigated in terms of chemical reactivity, especially with regards to potential catalytic activity. The synthesis and characterisation of a series of rhodium, iridium, platinum, and palladium complexes containing the phosphine chalcogenide ligands, [CH(P(S)Ph₂)₃]/[C(P(S)Ph₂)₃]⁻ and [CH (PPh₂)(P(S)Ph₂)₂]/[C(PPh₂)(P(S)Ph₂)₂]⁻, are described.The crystal structures of seven of these complexes plus that of the ligand, [CH(PPh₂)(P(S)Ph₂)₂], have been determined. These structures include [Pd(n³-C₄H₇){CH(PPh₂)(P(S)Ph₂)₂-P,S}]BF₄ 2H₂O, [Pd(n³-QH₇){CH(P(S)Ph₂)₃-S,S,S]BF4, [Rh(cod){C(P(S)Ph₂)₃-S,S}], [Ir(CO)3 {C(P(S)Ph₂)3 -S,S}], [Rh(cod){C(PPh₂(P(S)Ph₂)₂-P,S}] CH₂Cl₂. [Rhl₂CBuNC)₂ {C(PPh₂)(P(S)Ph₂)₂-P,S}], and [Ir(cod){CH(PPh₂)(P(S)Ph₂)₂-P,S}]BF₄ CH₂Cl₂, which are all discussed in detail. The [CH(P(S)Ph₂)₃] ligand coordinates in an n³ mode to metal centres. The anionic ligand [C(P(S)Ph₂)₃]⁻ coordinates to metals in an n² mode using two of its sulphur atoms, leaving a -P(S)Ph₂ group dangling. The ligand, [CH(PPh₂)(P(S)Ph₂)₂], can either coordinate in an n² P,S mode, using a phosphorus and a sulphur atom, or in an n³ P.S.S mode using a phosphorus and two sulphur atoms. The anionic ligand, [C(PPh₂)(P(S)Ph₂)₂], acts as a four electron donor, using one phosphorus and one sulphur atom, to metal centres. The reaction of [Ir(cod){C(P(S)Ph₂)₃-S,S}] with CO to give [Ir(CO)₂{C(P(S)Ph₂)₃-S,S}] is described. The reaction of [Rh(cod){C(PPh₂)(P(S)Ph₂)₂-P,S}] with tBuNC to give [Rh(tBuNC)₂{C(PPh₂)(P(S)Ph₂)₂-P,S}] is discussed. The subsequent oxidative additions of I₂ and benzyl bromide, to give isomeric mixtures of [RhI₂(tBuNC)₂{C(PPh₂)(P(S)Ph₂-P,S}] and [RhBr)(Bz)(tBuNC)₂ {C(PPh₂)(P(S)Ph₂)₂-P,S}] respectively, are also presented. The fluxional behaviours of [Pd(n³-C₄H₇){CH(PPh₂(P(S)Ph₂)₂-P,S}]BF₄, [Pd(n³-₄H₇){C(P(S)Ph₂)3-S,S}, [Pt(MeOcod){C(P(S)Ph₂)₃-S,S}], and [Rh(cod){C(P(S)Ph₂)₃}] are discussed in detail.The two -Ph₂P=S groups in the above complexes undergo a rapid intramolecular site exchange at ambient temperature in solution. Line shape analysis of variable temperature ³¹P{¹H} NMR data gives the following ΔG° for this dynamic exchange of coordinated and noncoordinated sulphur at 298 K. [Pd(n³-C₄H₇){CH(PPh₂)(P(S)Ph₂)₂-P,S)}]BF₄ 48 kJ/mol [Pd(n³-C₄H₇ ){C(P(S)Ph₂)₃-S,S}] 38 kJ/mol [Pt(MeOcod){C(P(S)Ph₂)₃-S,S}] 48 kJ/mol [Rh(cod){C(P(S)Ph₂)₃-S,S}] 46 kJ/mol / Graduate

Prof. A. Roodt

Several disequilibrium textures are found to occur within the hanging wall and footwall of the UG2 chromitite layer of the Bushveld Complex, South Africa. These textures include plagioclase chadacrysts found included within orthopyroxene and clinopyroxene as well as the orthopyroxenes exhibiting round crystal boundaries that appear to be resorbed. Textures found within the UG2 stratigraphy such as linear boundaries and 120° triple junctions at interfaces of adjacent plagioclase or pyroxene grains also suggest that recrystallization has taken place. The presence of both disequilibrium textures and recrystallization textures would suggest that a complex emplacement history has occurred. Ideally, this would be expected to be manifested by minerals of the same type but which are texturally distinct showing different composition. However this has been found not to be the case; minerals that suggest disequilibrium textures show similar compositions to the minerals which appear to have formed in equilibrium. This is also the same for recrystallized crystals which show the same compositions as crystals that have not been recrystallized. For example tabular clinopyroxene, which has a compositional range of En 44.6 to En 50.5, is indistinguishable from clinopyroxene occuring as discontinuous rims, En 44.3-48.2, and as intergranular necking connecting primocrysts of orthopyroxene ( En 44.3-50.4). Similarly, plagioclase occurring as inclusions with An 66.3-76.0 is indistinguishable from plagioclase occurring as zoned or recrystallized interstitial grains ( An 69.0- An 77.4). Compositional variation has however, been found to be controlled to an extent by stratigraphy in that minerals show different compositions within one layer to the same minerals within another layer, consistent with an evolving magma composition. It is concluded therefore that while composition is not texturally controlled it is to an extent stratigraphy controlled and that the evidence collected within the study supports two models for the formation of chromite within the Bushveld complex. The evidence is consistent with a combination of the magma mixing model and magma injection model to account for the textures and compositional variations found within the study. The evidence may also show support for models involving late modification of minerals by magmatic fluids but not as prominently as for the models mentioned above / Microsoft� Word 2010 / Adobe Acrobat 9.53 Paper Capture Plug-in

Eight rare earth complexes with bis(2-pyridylmethyl)amine (DPA) were synthesised and recrystallised, under air-sensitive or low moisture conditions. The crystal structures were successfully determined, via SC-XRD, and the asymmetric units of five complexes (1, 3, 5, 6 and 7) were submitted for DFT molecular modelling calculations, which involved geometry optimisation and frequency calculations. The neutral complexes obtained were bis(bis(2-pyridylmethyl)amine)-trichloro-lanthanum(III) [LaCl3(DPA)2] (1), bis(bis(2-pyridylmethyl)amine)-trichloro-cerium(III)) [CeCl3(DPA)2] (2), bis(μ2-chloro)-diaqua-tetrachloro-bis(bis(2-pyridylmethyl)amine)-di-praseodymium(III) [PrCl2(μ-Cl)(DPA)(OH2)]2 (3) and bis(μ2-methoxo)-bis(bis(2-pyridylmethyl)amine)- tetrachloro-di-dysprosium(III) [DyCl2(μ-OCH3)(DPA)]2 (4). The cationic complexes obtained in this study were dichloro-bis(bis(2-pyridylmethyl)amine)- neodymium(III) chloride methanol solvate [NdCl2(DPA)2]Cl·CH3OH (5), dichloro-bis(bis(2- pyridylmethyl)amine)-dysprosium(III) chloride methanol solvate [DyCl2(DPA)2]Cl·CH3OH (6), dichloro-bis(bis(2-pyridylmethyl)amine)-yttrium(III) chloride methanol solvate [YCl2(DPA)2]Cl·CH3OH (7) and dichloro-bis(bis(2-pyridylmethyl)amine)-lutetium(III) chloride methanol solvate [LuCl2(DPA)2]Cl·CH3OH (8). The ‘Quantum theory of atoms in molecules’ approach was used to investigate the electron density topology, primarily in order to investigate the hydrogen and coordination bonds for three of the eight complexes. Two of the neutral complexes contain the ‘early’ rare earth elements lanthanum and praseodymium and one cationic complex contains the ‘late’ lanthanide element dysprosium. Noncovalent interaction analysis was also performed on the aforementioned complexes in order to gain a deeper understanding of the intra-molecular stereo-electronic interactions. Spin density analysis was used to investigate the distribution of unpaired electron density at and around the metal centres of the aforementioned paramagnetic Pr- and Dy-complexes. A ligand conformation search for DPA was undertaken and 32 low energy conformers were identified and their relative energies were determined using two DFT functionals, namely M06 and M06-2X.

NADH:ubiquinone oxidoreductase (complex I) is the largest and most complicated enzyme in the mitochondrial electron transfer chain. It catalyses the oxidation of NADH and the reduction of ubiquinone, coupled to the translocation of protons across the mitochondrial inner membrane, maintaining the proton motive force used for ATP synthesis. Complex I is the least understood of the respiratory enzymes; although the mechanisms of NADH oxidation and intramolecular electron transfer are gradually becoming appreciated, the mechanisms of quinone binding and reduction and proton translocation remain unknown. Complex I dysfunction has been implicated in a wide range of pathologies including mitochondrial diseases such as Leigh's disease, as well as neurodegenerative diseases such as Alzheimer's and Parkinson's. The work described in the first part of this thesis is aimed at elucidating the structure of either a subcomplex of mitochondrial complex I, or of the intact enzyme itself. A comprehensive investigation revealed that hydrophilic subcomplexes of complex I from bovine heart mitochondria are not suitable for use as models of the intact enzyme. Attempts to prepare intact complex I of sufficient quality for structural work were successful; however, results from a large set of crystallization trials were disappointing. The second part of this thesis describes three studies of the function and mechanism of complex I from bovine heart mitochondria. First, the flavin mononucleotide, the site of NADH oxidation, was identified as the site of the 'inhibitor-insensitive' NADH:ubiquinone oxidoreduction reaction. The formation of semiquinones initiates redox cycling reactions with oxygen, producing vast amounts of reactive oxygen species; further studies revealed that other oxidants, such as paraquat, also react at the flavin site and initiate redox cycling reactions. Second, kinetic studies showed that the reaction between NADH and positively charged oxidants such as HAR (hexaammineruthenium (III)) proceeds by an unusual ternary reaction mechanism at the flavin site of complex I. Finally, double electron-electron resonance spectroscopy was used to show unambiguously that iron sulphur cluster 4Fe[TY]1 gives rise to electron paramagnetic resonance signal N4; the data provide an alternating potential energy profile for electron transfer along the cluster chain between the flavin and the quinone-binding site.

Bisphenol A (BPA) and phthalates are chemicals found in many consumer products including water bottles, food packaging and cosmetics. Previous research has shown that there is potential for these compounds to contribute to obesity. In this analysis, the Canadian Health Measures Survey was used to investigate possible associations between urinary concentrations of these compounds and measures of adiposity. BPA urine concentrations were found to decrease with age, and significant associations with BMI and waist circumference were found in linear regression in adults. No associations with measures of adiposity were found in logistic regression for adults and significant negative associations were found in children. A similar discrepancy was found for mono-(2-ethyl-5-hydroxyhexyl) phthalate and mono-(2-ethyl-5-oxohexyl) phthalate, which were significantly associated with obesity in adults, but showed several significant negative associations in children. Overall, this analysis showed that it is unlikely that BPA and phthalates are contributing to adiposity in the Canadian population.

This dissertation covers the two major parts of my PhD research on statistical physics and complex networks: i) modeling a new type of attack – localized attack, and investigating robustness of complex networks under this type of attack; ii) discovering the clustering structure in complex networks and its influence on the robustness of coupled networks. Complex networks appear in every aspect of our daily life and are widely studied in Physics, Mathematics, Biology, and Computer Science. One important property of complex networks is their robustness under attacks, which depends crucially on the nature of attacks and the structure of the networks themselves. Previous studies have focused on two types of attack: random attack and targeted attack, which, however, are insufficient to describe many real-world damages. Here we propose a new type of attack – localized attack, and study the robustness of complex networks under this type of attack, both analytically and via simulation. On the other hand, we also study the clustering structure in the network, and its influence on the robustness of a complex network system. In the first part, we propose a theoretical framework to study the robustness of complex networks under localized attack based on percolation theory and generating function method. We investigate the percolation properties, including the critical threshold of the phase transition pc and the size of the giant component P∞. We compare localized attack with random attack and find that while random regular (RR) networks are more robust against localized attack, Erd ̋os-R ́enyi (ER) networks are equally robust under both types of attacks. As for scale-free (SF) networks, their robustness depends crucially on the degree exponent λ. The simulation results show perfect agreement with theoretical predictions. We also test our model on two real-world networks: a peer-to-peer computer network and an airline network, and find that the real-world networks are much more vulnerable to localized attack compared with random attack. In the second part, we extend the tree-like generating function method to incorporating clustering structure in complex networks. We study the robustness of a complex network system, especially a network of networks (NON) with clustering structure in each network. We find that the system becomes less robust as we increase the clustering coefficient of each network. For a partially dependent network system, we also find that the influence of the clustering coefficient on network robustness decreases as we decrease the coupling strength, and the critical coupling strength qc, at which the first-order phase transition changes to second-order, increases as we increase the clustering coefficient.