The normal co-ordinate analysis, vibrational spectra and theoretical infrared intensities of some thiocarbonyl halide molecules /

TITLE: The normal co-ordinate analysis, vibrational spectra and theoretical infrared intensities of some thiocarbonyl halides. AUTHOR: J. L. Brema SUPERVISOR: Dr. D. C. Moule NUMBER OF PAGES: 89 ABSTRACT: The vibrational assignment of the five-in-plane fundamental modes of CSClBr has been made on the basis of infrared gas phase and liquid Raman spectral analyses to supplement our earlier vibrational studies. Even though the one out-of-plane fundamental was not observed spectroscopically an attempt has been made to predict its frequency. The vibrational spectra contained impurity bands and the CSClBr assignment was made only after a thorough analysis of the impurities themselves. A normal co-ordinate analysis calculation was performed assuming a Urey-Bradley force field. This calculation yielded the fundamental frequencies in good agreement with those observed after refinement of the originally transferred force constants. The theoretical frequencies are the eigenvalues of the secular equation and the calculation also gave the corresponding eigenvectors in the form of the very important LLj matrix. The [l] matrix is the transfoirmation between internal co-ordinates and normal co-ordinates and it is essential for Franck-Condon calculations on electronically excited molecules and for infrared Integrated band intensity studies. Using a self-consistent molecular orbital calculation termed "complete neglect of differential overlap" (CNDO/2) , theoretical values of equilibrium bond lengths and angleswere calcuted for a series of carbonyl and thlocarbonyl molecules. From these calculations valence force field force constants were also determined but with limited success. With the CNIX)/2 method theoretical dipole moment derivatives with respect to symmetrized internal co-ordinates were calculated and the results should be useful in a correlation with experimentally determined values.

Structural analysis of the Paint Lake Deformation Zone, Northern Ontario /

The Paint Lake Deformation Zone (PLDZ), located within the Superior Province of Canada, demarcates a major structural and lithological break between the Onaman-Tashota Terrane to the north and the Beardmore-Geraldton Belt to the south. The PLDZ is an east-west trending lineament, approximately 50 km in length and up to 1 km in width, comprised of an early ductile component termed the Paint Lake Shear Zone and a late brittle component known as the Paint Lake Fault. Structures associated with PLDZ development including S-, C- and C'-fabrics, stretching lineations, slickensides, C-C' intersection lineations, Z-folds and kinkbands indicate that simple shear deformation dominated during a NW-SE compressional event. Movement along the PLDZ was in a dextral sense consisting of an early differential motion with southside- down and a later strike-slip motion. Although the locus of the PLDZ may in part be lithologically controlled, mylonitization which accompanied shear zone development is not dependent on the lithological type. Conglomerate, intermediate and mafic volcanic units exhibit similar mesoscopic and microscopic structures where transected by the PLDZ. Field mapping, supported by thin section analysis, defines five strain domains increasing in intensity of deformation from shear zone boundary to centre. A change in the dominant microstructural deformation mechanism from dislocation creep to diffusion creep is observed with increasing strain during mylonitization. C'-fabric development is temporally associated with this change. A decrease in the angular relationship between C- and C'-fabrics is observed upon attaining maximum strain intensity. Strain profiling of the PLDZ demonstrates the presence of an outer primary strain gradient which exhibits a simple profile and an inner secondary strain gradient which exhibits a more complex profile. Regionally metamorphosed lithologies of lower greenschist facies outside the PLDZ were subjected to retrograde metamorphism during deformation within the PLDZ.

Functional analysis and treatment of OCD-related behaviour in a child with Autism Spectrum Disorder

Research indicates that Obsessive-Compulsive Disorder (OCD; DSM-IV-TR, American Psychiatric Association, 2000) is the second most frequent disorder to coincide with Autism Spectrum Disorder (ASD; Leyfer et aI., 2006). Excessive collecting and hoarding are also frequently reported in children with ASD (Berjerot, 2007). Although functional analysis (Iwata, Dorsey, Slifer, Bauman, & Richman, 1982/1994) has successfully identified maintaining variables for repetitive behaviours such as of bizarre vocalizations (e.g., Wilder, Masuda, O'Connor, & Baham, 2001), tics (e.g., Scotti, Schulman, & Hojnacki, 1994), and habit disorders (e.g., Woods & Miltenberger, 1996), extant literature ofOCD and functional analysis methodology is scarce (May et aI., 2008). The current studies utilized functional analysis methodology to identify the types of operant functions associated with the OCD-related hoarding behaviour of a child with ASD and examined the efficacy of function-based intervention. Results supported hypotheses of automatic and socially mediated positive reinforcement. A corresponding function-based treatment plan incorporated antecedent strategies and differential reinforcement (Deitz, 1977; Lindberg, Iwata, Kahng, and DeLeon, 1999; Reynolds, 1961). Reductions in problem behaviour were evidenced through use of a multiple baseline across behaviours design and maintained during two-month follow-up. Decreases in symptom severity were also discerned through subjective measures of treatment effectiveness.

Electrophysiological constituents of the P100 and N170 ERP complex: De-constructing of face processing using independent component analysis and robust estimation.

The initial timing of face-specific effects in event-related potentials (ERPs) is a point of contention in face processing research. Although effects during the time of the N170 are robust in the literature, inconsistent effects during the time of the P100 challenge the interpretation of the N170 as being the initial face-specific ERP effect. The interpretation of the early P100 effects are often attributed to low-level differences between face stimuli and a host of other image categories. Research using sophisticated controls for low-level stimulus characteristics (Rousselet, Husk, Bennett, & Sekuler, 2008) report robust face effects starting at around 130 ms following stimulus onset. The present study examines the independent components (ICs) of the P100 and N170 complex in the context of a minimally controlled low-level stimulus set and a clear P100 effect for faces versus houses at the scalp. Results indicate that four ICs account for the ERPs to faces and houses in the first 200ms following stimulus onset. The IC that accounts for the majority of the scalp N170 (icNla) begins dissociating stimulus conditions at approximately 130 ms, closely replicating the scalp results of Rousselet et al. (2008). The scalp effects at the time of the P100 are accounted for by two constituent ICs (icP1a and icP1b). The IC that projects the greatest voltage at the scalp during the P100 (icP1a) shows a face-minus-house effect over the period of the P100 that is less robust than the N 170 effect of icN 1 a when measured as the average of single subject differential activation robustness. The second constituent process of the P100 (icP1b), although projecting a smaller voltage to the scalp than icP1a, shows a more robust effect for the face-minus-house contrast starting prior to 100 ms following stimulus onset. Further, the effect expressed by icP1 b takes the form of a larger negative projection to medial occipital sites for houses over faces partially canceling the larger projection of icP1a, thereby enhancing the face positivity at this time. These findings have three main implications for ERP research on face processing: First, the ICs that constitute the face-minus-house P100 effect are independent from the ICs that constitute the N170 effect. This suggests that the P100 effect and the N170 effect are anatomically independent. Second, the timing of the N170 effect can be recovered from scalp ERPs that have spatio-temporally overlapping effects possibly associated with low-level stimulus characteristics. This unmixing of the EEG signals may reduce the need for highly constrained stimulus sets, a characteristic that is not always desirable for a topic that is highly coupled to ecological validity. Third, by unmixing the constituent processes of the EEG signals new analysis strategies are made available. In particular the exploration of the relationship between cortical processes over the period of the P100 and N170 ERP complex (and beyond) may provide previously unaccessible answers to questions such as: Is the face effect a special relationship between low-level and high-level processes along the visual stream?

Clustering algorithms and shape factor methods to discriminate among small GTPase phenotypes using DIC image analysis.

Naïvement perçu, le processus d’évolution est une succession d’événements de duplication et de mutations graduelles dans le génome qui mènent à des changements dans les fonctions et les interactions du protéome. La famille des hydrolases de guanosine triphosphate (GTPases) similaire à Ras constitue un bon modèle de travail afin de comprendre ce phénomène fondamental, car cette famille de protéines contient un nombre limité d’éléments qui diffèrent en fonctionnalité et en interactions. Globalement, nous désirons comprendre comment les mutations singulières au niveau des GTPases affectent la morphologie des cellules ainsi que leur degré d’impact sur les populations asynchrones. Mon travail de maîtrise vise à classifier de manière significative différents phénotypes de la levure Saccaromyces cerevisiae via l’analyse de plusieurs critères morphologiques de souches exprimant des GTPases mutées et natives. Notre approche à base de microscopie et d’analyses bioinformatique des images DIC (microscopie d’interférence différentielle de contraste) permet de distinguer les phénotypes propres aux cellules natives et aux mutants. L’emploi de cette méthode a permis une détection automatisée et une caractérisation des phénotypes mutants associés à la sur-expression de GTPases constitutivement actives. Les mutants de GTPases constitutivement actifs Cdc42 Q61L, Rho5 Q91H, Ras1 Q68L et Rsr1 G12V ont été analysés avec succès. En effet, l’implémentation de différents algorithmes de partitionnement, permet d’analyser des données qui combinent les mesures morphologiques de population native et mutantes. Nos résultats démontrent que l’algorithme Fuzzy C-Means performe un partitionnement efficace des cellules natives ou mutantes, où les différents types de cellules sont classifiés en fonction de plusieurs facteurs de formes cellulaires obtenus à partir des images DIC. Cette analyse démontre que les mutations Cdc42 Q61L, Rho5 Q91H, Ras1 Q68L et Rsr1 G12V induisent respectivement des phénotypes amorphe, allongé, rond et large qui sont représentés par des vecteurs de facteurs de forme distincts. Ces distinctions sont observées avec différentes proportions (morphologie mutante / morphologie native) dans les populations de mutants. Le développement de nouvelles méthodes automatisées d’analyse morphologique des cellules natives et mutantes s’avère extrêmement utile pour l’étude de la famille des GTPases ainsi que des résidus spécifiques qui dictent leurs fonctions et réseau d’interaction. Nous pouvons maintenant envisager de produire des mutants de GTPases qui inversent leur fonction en ciblant des résidus divergents. La substitution fonctionnelle est ensuite détectée au niveau morphologique grâce à notre nouvelle stratégie quantitative. Ce type d’analyse peut également être transposé à d’autres familles de protéines et contribuer de manière significative au domaine de la biologie évolutive.

Differential regulation of early response genes by fibroblast growth factor (FGF) 8 and FGF18 in bovine granulosa cells in vitro

Les « Facteurs de croissance des fibroblastes» (FGF) agissent comme des régulateurs locaux sur la qualité des follicules et sont connus pour promouvoir la prolifération des cellules de granulosa, réduire l’apoptose et la stéroïdogenèse. Parmi la sous-famille FGF8, FGF18 est une exception puisqu’il semblerait avoir une fonction pro-apoptotique alors que FGF8 n’a pas été jusqu’à présent rapporté comme altérant la viabilité des cellules de la granulosa. Ces deux ligands ont un mode d’activation similaire et il pourrait être proposé que toute la sous-famille FGF8 ait la même réponse. L’objectif de cette étude était de déterminer si FGF8 et FGF18 activaient la même réponse précoce de gènes dans des cultures de granulosa bovine. Pour répondre à cette question, nous avons cultivé des cellules de la granulosa dans du milieu de culture sans sérum pendant 5 jours. Le jour 5, les cellules ont été traitées avec FGF8 ou FGF18. Nous avons eu recours à une approche de « puce à ADN » afin d’identifier la réponse précoce de gènes induite par FGF8 et FGF18, et les données ont été confirmées par des PCRs en temps réel lors d’une expérience in vitro où les cellules de granulosa ont été traitées avec FGF8 et FGF18 pendant différents temps. L’analyse du puce à ADN a identifié 12 gènes surexprimés par FGF8, incluant SPRY2, NR4A1, XIRP1, BAMBI, EGR1, FOS et FOSL1. A l’inverse, FGF18 n’a régulé aucun gène de manière significative. Les analyses de PCR ont confirmé l’augmentation d’ARNm codant pour EGR1, EGR3, FOS, XIRP1, FOSL1, SPRY2, NR4A1 et BAMBI après 2 h de traitement. FGF18 a entrainé seulement une augmentation de l’expression de EGR1 après 2 h de traitement parmi tous les gènes testés. Ces résultats démontrent donc que FGF8 et FGF18, malgré leur similarité dans le mode d’activation de leurs récepteurs, agissent sur les cellules de la granulosa via différentes voies de signalisation. FGF8 et FGF18, sont donc tous les deux capables de stimuler l’expression de EGR1, mais les voies de signalisation induites par la suite divergent.

Invariant discretizations of partial differential equations

Un algorithme permettant de discrétiser les équations aux dérivées partielles (EDP) tout en préservant leurs symétries de Lie est élaboré. Ceci est rendu possible grâce à l'utilisation de dérivées partielles discrètes se transformant comme les dérivées partielles continues sous l'action de groupes de Lie locaux. Dans les applications, beaucoup d'EDP sont invariantes sous l'action de transformations ponctuelles de Lie de dimension infinie qui font partie de ce que l'on désigne comme des pseudo-groupes de Lie. Afin d'étendre la méthode de discrétisation préservant les symétries à ces équations, une discrétisation des pseudo-groupes est proposée. Cette discrétisation a pour effet de transformer les symétries ponctuelles en symétries généralisées dans l'espace discret. Des schémas invariants sont ensuite créés pour un certain nombre d'EDP. Dans tous les cas, des tests numériques montrent que les schémas invariants approximent mieux leur équivalent continu que les différences finies standard.

ANALYSIS, MODIFICATION, AND EVALUATION OF THE COLD FLOW PROPERTIES OF VEGETABLE OILS AS BASE OIL FOR INDUSTRIAL LUBRICANTS

Poor cold flow properties of vegetable oils are a major problem preventing the usage of many abundantly available vegetable oils as base stocks for industrial lubricants. The major objective of this research is to improve the cold flow properties of vegetable oils by various techniques like additive addition and different chemical modification processes. Conventional procedure for determining pour point is ASTM D97 method. ASTM D97 method is time consuming and reproducibility of pour point temperatures is poor between laboratories. Differential Scanning Calorimetry (DSC) is a fast, accurate and reproducible method to analyze the thermal activities during cooling/heating of oil. In this work coconut oil has been chosen as representative vegetable oil for the analysis and improvement cold flow properties since it is abundantly available in the tropics and has a very high pour point of 24 °C. DSC is used for the analysis of unmodified and modified vegetable oil. The modified oils (with acceptable pour points) were then subjected to different tests for the valuation of important lubricant properties such as viscometric, tribological (friction and wear properties), oxidative and corrosion properties.A commercial polymethacrylate based PPD was added in different percentages and the pour points were determined in each case. Styrenated phenol(SP) was added in different concentration to coconut oil and each solution was subjected to ASTM D97 test and analysis by DSC. Refined coconut oil and other oils like castor oil, sunflower oil and keranja oil were mixed in different proportions and interesterification procedure was carried out. Interesterification of coconut oil with other vegetable oils was not found to be effective in lowering the pour point of coconut oil as the reduction attained was only to the extent of 2 to 3 °C.Chemical modification by acid catalysed condensation reaction with coconut oil castor oil mixture resulted in significant reduction of pour point (from 24 ºC to -3 ºC). Instead of using triacylglycerols, when their fatty acid derivatives (lauric acid- the major fatty acid content of coconut oil and oleic acid- the major fatty acid constituents of monoand poly- unsaturated vegetable oils like olive oil, sunflower oil etc.) were used for the synthesis , the pour point could be brought down to -42 ºC. FTIR and NMR spectroscopy confirmed the ester structure of the product which is fundamental to the biodegradability of vegetable oils. The tribological performance of the synthesised product with a suitable AW/EP additive was comparable to the commercial SAE20W30 oil. The viscometric properties (viscosity and viscosity index) were also (with out additives) comparable to commercial lubricants. The TGA experiment confirmed the better oxidative performance of the product compared to vegetable oils. The sample passed corrosion test as per ASTM D130 method.

Field Equilibrium Finite Elements for Structural Analysis

Many finite elements used in structural analysis possess deficiencies like shear locking, incompressibility locking, poor stress predictions within the element domain, violent stress oscillation, poor convergence etc. An approach that can probably overcome many of these problems would be to consider elements in which the assumed displacement functions satisfy the equations of stress field equilibrium. In this method, the finite element will not only have nodal equilibrium of forces, but also have inner stress field equilibrium. The displacement interpolation functions inside each individual element are truncated polynomial solutions of differential equations. Such elements are likely to give better solutions than the existing elements.In this thesis, a new family of finite elements in which the assumed displacement function satisfies the differential equations of stress field equilibrium is proposed. A general procedure for constructing the displacement functions and use of these functions in the generation of elemental stiffness matrices has been developed. The approach to develop field equilibrium elements is quite general and various elements to analyse different types of structures can be formulated from corresponding stress field equilibrium equations. Using this procedure, a nine node quadrilateral element SFCNQ for plane stress analysis, a sixteen node solid element SFCSS for three dimensional stress analysis and a four node quadrilateral element SFCFP for plate bending problems have been formulated.For implementing these elements, computer programs based on modular concepts have been developed. Numerical investigations on the performance of these elements have been carried out through standard test problems for validation purpose. Comparisons involving theoretical closed form solutions as well as results obtained with existing finite elements have also been made. It is found that the new elements perform well in all the situations considered. Solutions in all the cases converge correctly to the exact values. In many cases, convergence is faster when compared with other existing finite elements. The behaviour of field consistent elements would definitely generate a great deal of interest amongst the users of the finite elements.

Analysis discrete function theory

There is a recent trend to describe physical phenomena without the use of infinitesimals or infinites. This has been accomplished replacing differential calculus by the finite difference theory. Discrete function theory was first introduced in l94l. This theory is concerned with a study of functions defined on a discrete set of points in the complex plane. The theory was extensively developed for functions defined on a Gaussian lattice. In 1972 a very suitable lattice H: {Ci qmxO,I qnyo), X0) 0, X3) 0, O < q < l, m, n 5 Z} was found and discrete analytic function theory was developed. Very recently some work has been done in discrete monodiffric function theory for functions defined on H. The theory of pseudoanalytic functions is a generalisation of the theory of analytic functions. When the generator becomes the identity, ie., (l, i) the theory of pseudoanalytic functions reduces to the theory of analytic functions. Theugh the theory of pseudoanalytic functions plays an important role in analysis, no discrete theory is available in literature. This thesis is an attempt in that direction. A discrete pseudoanalytic theory is derived for functions defined on H.

Differential induction, isolation, physicochemical and molecular characterization of temperate phages of environmental Vibrio cholerae as evidence of phage mediated Horizontal Gene Transfer

The resurgence of the enteric pathogen Vibrio cholerae, the causative organism of epidemic cholera, remains a major health problem in many developing countries like India. The southern Indian state of Kerala is endemic to cholera. The outbreaks of cholera follow a seasonal pattern in regions of endemicity. Marine aquaculture settings and mangrove environments of Kerala serve as reservoirs for V. cholerae. The non-O1/non-O139 environmental isolates of V. cholerae with incomplete ‘virulence casette’ are to be dealt with caution as they constitute a major reservoir of diverse virulence genes in the marine environment and play a crucial role in pathogenicity and horizontal gene transfer. The genes coding cholera toxin are borne on, and can be infectiously transmitted by CTXΦ, a filamentous lysogenic vibriophages. Temperate phages can provide crucial virulence and fitness factors affecting cell metabolism, bacterial adhesion, colonization, immunity, antibiotic resistance and serum resistance. The present study was an attempt to screen the marine environments like aquafarms and mangroves of coastal areas of Alappuzha and Cochin, Kerala for the presence of lysogenic V. cholerae, to study their pathogenicity and also gene transfer potential. Phenotypic and molecular methods were used for identification of isolates as V. cholerae. The thirty one isolates which were Gram negative, oxidase positive, fermentative, with or without gas production on MOF media and which showed yellow coloured colonies on TCBS (Thiosulfate Citrate Bile salt Sucrose) agar were segregated as vibrios. Twenty two environmental V. cholerae strains of both O1 and non- O1/non-O139 serogroups on induction with mitomycin C showed the presence of lysogenic phages. They produced characteristic turbid plaques in double agar overlay assay using the indicator strain V. cholerae El Tor MAK 757. PCR based molecular typing with primers targeting specific conserved sequences in the bacterial genome, demonstrated genetic diversity among these lysogen containing non-O1 V. cholerae . Polymerase chain reaction was also employed as a rapid screening method to verify the presence of 9 virulence genes namely, ctxA, ctxB, ace, hlyA, toxR, zot,tcpA, ninT and nanH, using gene specific primers. The presence of tcpA gene in ALPVC3 was alarming, as it indicates the possibility of an epidemic by accepting the cholera. Differential induction studies used ΦALPVC3, ΦALPVC11, ΦALPVC12 and ΦEKM14, underlining the possibility of prophage induction in natural ecosystems, due to abiotic factors like antibiotics, pollutants, temperature and UV. The efficiency of induction of prophages varied considerably in response to the different induction agents. The growth curve of lysogenic V. cholerae used in the study drastically varied in the presence of strong prophage inducers like antibiotics and UV. Bacterial cell lysis was directly proportional to increase in phage number due to induction. Morphological characterization of vibriophages by Transmission Electron Microscopy revealed hexagonal heads for all the four phages. Vibriophage ΦALPVC3 exhibited isometric and contractile tails characteristic of family Myoviridae, while phages ΦALPVC11 and ΦALPVC12 demonstrated the typical hexagonal head and non-contractile tail of family Siphoviridae. ΦEKM14, the podophage was distinguished by short non-contractile tail and icosahedral head. This work demonstrated that environmental parameters can influence the viability and cell adsorption rates of V. cholerae phages. Adsorption studies showed 100% adsorption of ΦALPVC3 ΦALPVC11, ΦALPVC12 and ΦEKM14 after 25, 30, 40 and 35 minutes respectively. Exposure to high temperatures ranging from 50ºC to 100ºC drastically reduced phage viability. The optimum concentration of NaCl required for survival of vibriophages except ΦEKM14 was 0.5 M and that for ΦEKM14 was 1M NaCl. Survival of phage particles was maximum at pH 7-8. V. cholerae is assumed to have existed long before their human host and so the pathogenic clones may have evolved from aquatic forms which later colonized the human intestine by progressive acquisition of genes. This is supported by the fact that the vast majority of V. cholerae strains are still part of the natural aquatic environment. CTXΦ has played a critical role in the evolution of the pathogenicity of V. cholerae as it can transmit the ctxAB gene. The unusual transformation of V. cholerae strains associated with epidemics and the emergence of V. cholera O139 demonstrates the evolutionary success of the organism in attaining greater fitness. Genetic changes in pathogenic V. cholerae constitute a natural process for developing immunity within an endemically infected population. The alternative hosts and lysogenic environmental V. cholerae strains may potentially act as cofactors in promoting cholera phage ‘‘blooms’’ within aquatic environments, thereby influencing transmission of phage sensitive, pathogenic V. cholerae strains by aquatic vehicles. Differential induction of the phages is a clear indication of the impact of environmental pollution and global changes on phage induction. The development of molecular biology techniques offered an accessible gateway for investigating the molecular events leading to genetic diversity in the marine environment. Using nucleic acids as targets, the methods of fingerprinting like ERIC PCR and BOX PCR, revealed that the marine environment harbours potentially pathogenic group of bacteria with genetic diversity. The distribution of virulence associated genes in the environmental isolates of V. cholerae provides tangible material for further investigation. Nucleotide and protein sequence analysis alongwith protein structure prediction aids in better understanding of the variation inalleles of same gene in different ecological niche and its impact on the protein structure for attaining greater fitness of pathogens. The evidences of the co-evolution of virulence genes in toxigenic V. cholerae O1 from different lineages of environmental non-O1 strains is alarming. Transduction studies would indicate that the phenomenon of acquisition of these virulence genes by lateral gene transfer, although rare, is not quite uncommon amongst non-O1/non-O139 V. cholerae and it has a key role in diversification. All these considerations justify the need for an integrated approach towards the development of an effective surveillance system to monitor evolution of V. cholerae strains with epidemic potential. Results presented in this study, if considered together with the mechanism proposed as above, would strongly suggest that the bacteriophage also intervenes as a variable in shaping the cholera bacterium, which cannot be ignored and hinting at imminent future epidemics.

On Vessiot's Theory of Partial Differential Equations

The object of research presented here is Vessiot's theory of partial differential equations: for a given differential equation one constructs a distribution both tangential to the differential equation and contained within the contact distribution of the jet bundle. Then within it, one seeks n-dimensional subdistributions which are transversal to the base manifold, the integral distributions. These consist of integral elements, and these again shall be adapted so that they make a subdistribution which closes under the Lie-bracket. This then is called a flat Vessiot connection. Solutions to the differential equation may be regarded as integral manifolds of these distributions. In the first part of the thesis, I give a survey of the present state of the formal theory of partial differential equations: one regards differential equations as fibred submanifolds in a suitable jet bundle and considers formal integrability and the stronger notion of involutivity of differential equations for analyzing their solvability. An arbitrary system may (locally) be represented in reduced Cartan normal form. This leads to a natural description of its geometric symbol. The Vessiot distribution now can be split into the direct sum of the symbol and a horizontal complement (which is not unique). The n-dimensional subdistributions which close under the Lie bracket and are transversal to the base manifold are the sought tangential approximations for the solutions of the differential equation. It is now possible to show their existence by analyzing the structure equations. Vessiot's theory is now based on a rigorous foundation. Furthermore, the relation between Vessiot's approach and the crucial notions of the formal theory (like formal integrability and involutivity of differential equations) is clarified. The possible obstructions to involution of a differential equation are deduced explicitly. In the second part of the thesis it is shown that Vessiot's approach for the construction of the wanted distributions step by step succeeds if, and only if, the given system is involutive. Firstly, an existence theorem for integral distributions is proven. Then an existence theorem for flat Vessiot connections is shown. The differential-geometric structure of the basic systems is analyzed and simplified, as compared to those of other approaches, in particular the structure equations which are considered for the proofs of the existence theorems: here, they are a set of linear equations and an involutive system of differential equations. The definition of integral elements given here links Vessiot theory and the dual Cartan-Kähler theory of exterior systems. The analysis of the structure equations not only yields theoretical insight but also produces an algorithm which can be used to derive the coefficients of the vector fields, which span the integral distributions, explicitly. Therefore implementing the algorithm in the computer algebra system MuPAD now is possible.

Analysis and Control of Robot Manipulators with Kinematic Redundancy

A closed-form solution formula for the kinematic control of manipulators with redundancy is derived, using the Lagrangian multiplier method. Differential relationship equivalent to the Resolved Motion Method has been also derived. The proposed method is proved to provide with the exact equilibrium state for the Resolved Motion Method. This exactness in the proposed method fixes the repeatability problem in the Resolved Motion Method, and establishes a fixed transformation from workspace to the joint space. Also the method, owing to the exactness, is demonstrated to give more accurate trajectories than the Resolved Motion Method. In addition, a new performance measure for redundancy control has been developed. This measure, if used with kinematic control methods, helps achieve dexterous movements including singularity avoidance. Compared to other measures such as the manipulability measure and the condition number, this measure tends to give superior performances in terms of preserving the repeatability property and providing with smoother joint velocity trajectories. Using the fixed transformation property, Taylor's Bounded Deviation Paths Algorithm has been extended to the redundant manipulators.

Differential effects of insulin signaling on individual carbon fluxes for fatty acid synthesis in brown adipocytes

Considering the major role of insulin signaling on fatty acid synthesis via stimulation of lipogenic enzymes, differential effects of insulin signaling on individual carbon fluxes for fatty acid synthesis have been investigated by comparing the individual lipogenic fluxes in WT and IRS-1 knockout (IRS-1 KO) brown adipocytes. Results from experiments on WT and IRS-1 KO cells incubated with [5-¹³C] glutamine were consistent with the existence of reductive carboxylation pathway. Analysis of isotopomer distribution of nine metabolites related to the lipogenic routes from glucose and glutamine in IRS-1 KO cells using [U-¹³C] glutamine as compared to that in WT cells indicated that flux through reductive carboxylation pathway was diminished while flux through conventional TCA cycle was stimulated due to absence of insulin signaling in IRS-1 KO cells. This observation was confirmed by quantitative estimation of individual lipogenic fluxes in IRS-1 KO cells and their comparison with fluxes in WT cells. Thus, these results suggest that glutamine’s substantial contribution to fatty acid synthesis can be directly manipulated by controlling the flux through reductive carboxylation of alpha-ketoglutarate to citrate using hormone (insulin).

INFO6003 (2013) Differential Privacy -- Overview Paper

Cynthia Dwork: A Firm Foundation for Private Data Analysis Required reading