On the geometry of the spin-statistics connection in quantum mechanics

The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishabilty and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be interpreted as the spaces of sections of certain flat vector bundles over Q. With this technique, various results pertaining to the problem of quantum indistinguishability are reproduced in a clear and systematic way. Our method is also used in order to give a global formulation of the BR construction. As a result of this analysis, it is found that the single-valuedness condition of BR is inconsistent. Additionally, a proposal aiming at establishing the Fermi-Bose alternative, within our approach, is made.

Synthesis, characterization and chemical modification of a cationic polyelectrolyte poly(methylene amine)

Polyamine polymers have attracted attention due to their ability to demonstrate pH dependent cationic nature and presence of highly reactive pendant amino groups. These amino groups make them suitable for a host of applications through cross-linking and derivatization. As a result the end use application of a polyamine is largely driven by the number of amino groups and the way they are attached to the polymer backbone. Thus, this piece of work describes the synthesis and investigation of properties of a novel aliphatic polyamine, poly(methylene amine); that carries maximum number of amino group on its backbone. The target polymer, poly(methylene amine); was synthesized via two major steps viz.1.synthesis of precursor polymers of poly(methylene amine) and 2. Hydrolysis of the precursor polymers to obtain poly(methylene amine). The precursor polymers poly (1,3-diacetylimidazole-2-one)(6) and poly(1,3-diformyldihydroimidazol-2-one)(7) were synthesized via radical polymerization of their respective monomers. The monomers were polymerized in bulk as well as in solution at different reaction conditions. The maximum molecular weights were achieved by polymerizing the monomers in bulk (Mn = 6.5 x 104 g/mol and Mw = 2.13 x 105 g/mol) of 6. The precursor polymers were hydrolyzed under strong reaction conditions in ethanol in presence of NaOH, LiCl at 170°C to yield poly(methylene amine). The process of hydrolysis was monitored by IR spectroscopy. The solution properties of poly(methylene amine) and its hydrochloride were investigated by viscosimetry and light scattering. The reduced viscosity of poly (methylene amine) hydrochloride as a function of polymer concentration demonstrated a behavior typical of cationic polyelectrolyte. With decrease in polymer concentration the reduced viscosity of poly(methylene amine) hydrochloride increased gradually. The dynamic light scattering studies also revealed behaviors of a polyelectrolyte. Poly(methylene amine) was reacted with electrophiles to yield novel materials. While the attachment of alkyl group onto the nitrogen would increase nucleophilicity, it would also impose steric hindrance. As a result the degree of substitution on poly(methylene amine) would be governed by both the factors. Therefore, few model reactions with electrophiles were performed on polvinylamine under similar reaction conditions in order to make a comparative evaluation. It was found that under similar reaction conditions the degree of substitution was higher in case of polyvinylamine in comparison with poly (methylene amine).This shows that the steric hindrance outweighs nucleophilicity while deciding degree of substitution of electrophiles on poly(methylene amine). The modification was further extended to its use as an initiator for ring opening polymerization of benzyloxy protected N-carboxyanhydride of z-Lysine. The resulting polymer had an interesting brush like architecture. The solid state morphology of this polymer was investigated by SAXS. The 2D-WAXS diffractograms revealed hexagonal morphology of peptide segments without formation of alpha helices.

In vivo consequences of AML1-ETO fusion protein expression for hematopoiesis

The t(8;21) (q22;q22) translocation fusing the ETO (also known as MTG8) gene on human chromosome 8 with the AML1 (also called Runx1 or CBFα) gene on chromosome 21 is one of the most common genetic aberrations found in acute myeloid leukemia (AML). This chromosomal translocation occurs in 12 % of de novo AML cases and in up to 40 % of the AML-M2 subtype of the French-American-British classification. To date, the in vivo function of aberrant AML1-ETO fusion protein expression has been investigated by several groups. However, in these studies, controversial results were reported and some key issues remain unknown. Importantly, the consequences of aberrant AML1-ETO expression for self-renewing hematopoietic stem cells (HSCs), multipotent hematopoietic progenitors (MPPs) and lineage-restricted precursors are not known. rn The aim of this thesis was to develop a novel experimental AML1-ETO in vivo model that (i) overcomes the current lack of insight into the pre-leukemic condition of t(8;21)-associated AML, (ii) clarifies the in vivo consequences of AML1-ETO for HSCs, MPPs, progenitors and more mature blood cells and (iii) generates an improved mouse model suitable for mirroring the human condition. For this purpose, a conditional tet on/off mouse model expressing the AML1-ETO fusion protein from the ROSA26 (R26) locus was generated. rn Aberrant AML1-ETO activation in compound ROSA26/tetOAML1-ETO (R26/AE) mice caused high rates of mortality, an overall disruption of hematopoietic organs and a profound alteration of hematopoiesis. However, since the generalized activity of the R26 locus did not recapitulate the leukemic condition found in human patients, it was important to restrict AML1-ETO expression to blood cell lineages. Therefore, bone marrow cells from non-induced R26/AE mice were adoptively transplanted into sublethal irradiated RAG2-/- recipient mice. First signs of phenotypical differences between AML1-ETO-expressing and control mice were observed after eight to nine months of transgene induction. AML1-ETO-expressing mice showed profound changes in hematopoietic organs accompanied by manifest extramedullary hematopoiesis. In addition, a block in early erythropoiesis, B- and T-cell maturation was observed and granulopoiesis was significantly enhanced. Most interestingly, conditional activation of AML1-ETO in chimeric mice did not increase HSCs, MPPs, common lymphoid precursors (CLPs), common myeloid progenitors (CMPs) and megakaryocyte-erythrocyte progenitors (MEPs) but promoted the selective amplification of granulocyte-macrophage progenitors (GMPs). rn The results of this thesis provide clear experimental evidence how aberrant AML1-ETO modulates the developmental properties of normal hematopoiesis and establishes for the first time that AML1-ETO does not increase HSCs, MPPs and common lineage-restricted progenitor pools but specifically amplifies GMPs. The here presented mouse model not only clarifies the role of aberrant AML1-ETO for shaping hematopoietic development but in addition has strong implications for future therapeutic strategies and will be an excellent pre-clinical tool for developing and testing new approaches to treat and eventually cure AML.rn

Sustainable improvement of water networks : to achieve best decisions for rehabilitation plans using advanced GIS and statistical techniques

Many of developing countries are facing crisis in water management due to increasing of population, water scarcity, water contaminations and effects of world economic crisis. Water distribution systems in developing countries are facing many challenges of efficient repair and rehabilitation since the information of water network is very limited, which makes the rehabilitation assessment plans very difficult. Sufficient information with high technology in developed countries makes the assessment for rehabilitation easy. Developing countries have many difficulties to assess the water network causing system failure, deterioration of mains and bad water quality in the network due to pipe corrosion and deterioration. The limited information brought into focus the urgent need to develop economical assessment for rehabilitation of water distribution systems adapted to water utilities. Gaza Strip is subject to a first case study, suffering from severe shortage in the water supply and environmental problems and contamination of underground water resources. This research focuses on improvement of water supply network to reduce the water losses in water network based on limited database using techniques of ArcGIS and commercial water network software (WaterCAD). A new approach for rehabilitation water pipes has been presented in Gaza city case study. Integrated rehabilitation assessment model has been developed for rehabilitation water pipes including three components; hydraulic assessment model, Physical assessment model and Structural assessment model. WaterCAD model has been developed with integrated in ArcGIS to produce the hydraulic assessment model for water network. The model have been designed based on pipe condition assessment with 100 score points as a maximum points for pipe condition. As results from this model, we can indicate that 40% of water pipeline have score points less than 50 points and about 10% of total pipes length have less than 30 score points. By using this model, the rehabilitation plans for each region in Gaza city can be achieved based on available budget and condition of pipes. The second case study is Kuala Lumpur Case from semi-developed countries, which has been used to develop an approach to improve the water network under crucial conditions using, advanced statistical and GIS techniques. Kuala Lumpur (KL) has water losses about 40% and high failure rate, which make severe problem. This case can represent cases in South Asia countries. Kuala Lumpur faced big challenges to reduce the water losses in water network during last 5 years. One of these challenges is high deterioration of asbestos cement (AC) pipes. They need to replace more than 6500 km of AC pipes, which need a huge budget to be achieved. Asbestos cement is subject to deterioration due to various chemical processes that either leach out the cement material or penetrate the concrete to form products that weaken the cement matrix. This case presents an approach for geo-statistical model for modelling pipe failures in a water distribution network. Database of Syabas Company (Kuala Lumpur water company) has been used in developing the model. The statistical models have been calibrated, verified and used to predict failures for both networks and individual pipes. The mathematical formulation developed for failure frequency in Kuala Lumpur was based on different pipeline characteristics, reflecting several factors such as pipe diameter, length, pressure and failure history. Generalized linear model have been applied to predict pipe failures based on District Meter Zone (DMZ) and individual pipe levels. Based on Kuala Lumpur case study, several outputs and implications have been achieved. Correlations between spatial and temporal intervals of pipe failures also have been done using ArcGIS software. Water Pipe Assessment Model (WPAM) has been developed using the analysis of historical pipe failure in Kuala Lumpur which prioritizing the pipe rehabilitation candidates based on ranking system. Frankfurt Water Network in Germany is the third main case study. This case makes an overview for Survival analysis and neural network methods used in water network. Rehabilitation strategies of water pipes have been developed for Frankfurt water network in cooperation with Mainova (Frankfurt Water Company). This thesis also presents a methodology of technical condition assessment of plastic pipes based on simple analysis. This thesis aims to make contribution to improve the prediction of pipe failures in water networks using Geographic Information System (GIS) and Decision Support System (DSS). The output from the technical condition assessment model can be used to estimate future budget needs for rehabilitation and to define pipes with high priority for replacement based on poor condition. rn