A computer-algebraic approach to the study of the symmetry properties of molecules and clusters

This thesis work is dedicated to use the computer-algebraic approach for dealing with the group symmetries and studying the symmetry properties of molecules and clusters. The Maple package Bethe, created to extract and manipulate the group-theoretical data and to simplify some of the symmetry applications, is introduced. First of all the advantages of using Bethe to generate the group theoretical data are demonstrated. In the current version, the data of 72 frequently applied point groups can be used, together with the data for all of the corresponding double groups. The emphasize of this work is placed to the applications of this package in physics of molecules and clusters. Apart from the analysis of the spectral activity of molecules with point-group symmetry, it is demonstrated how Bethe can be used to understand the field splitting in crystals or to construct the corresponding wave functions. Several examples are worked out to display (some of) the present features of the Bethe program. While we cannot show all the details explicitly, these examples certainly demonstrate the great potential in applying computer algebraic techniques to study the symmetry properties of molecules and clusters. A special attention is placed in this thesis work on the flexibility of the Bethe package, which makes it possible to implement another applications of symmetry. This implementation is very reasonable, because some of the most complicated steps of the possible future applications are already realized within the Bethe. For instance, the vibrational coordinates in terms of the internal displacement vectors for the Wilson's method and the same coordinates in terms of cartesian displacement vectors as well as the Clebsch-Gordan coefficients for the Jahn-Teller problem are generated in the present version of the program. For the Jahn-Teller problem, moreover, use of the computer-algebraic tool seems to be even inevitable, because this problem demands an analytical access to the adiabatic potential and, therefore, can not be realized by the numerical algorithm. However, the ability of the Bethe package is not exhausted by applications, mentioned in this thesis work. There are various directions in which the Bethe program could be developed in the future. Apart from (i) studying of the magnetic properties of materials and (ii) optical transitions, interest can be pointed out for (iii) the vibronic spectroscopy, and many others. Implementation of these applications into the package can make Bethe a much more powerful tool.

Theory for Optical Absorption in Small Clusters: Dependence on Atomic Structure and Cluster Size

We present a theory which permits for the first time a detailed analysis of the dependence of the absorption spectrum on atomic structure and cluster size. Thus, we determine the development of the collective excitations in small clusters and show that their broadening depends sensitively on the tomic structure, in particular at the surface. Results for Hg_n^+ clusters show that the plasmon energy is close to its jellium value in the case of spherical-like structures, but is in general between w_p/ \wurzel{3} and w_p/ \wurzel{2} for compact clusters. A particular success of our theory is the identification of the excitations contributing to the absorption peaks.

Theoretical study of magnetism, structure and chemical order in transition-metal alloy clusters

Research on transition-metal nanoalloy clusters composed of a few atoms is fascinating by their unusual properties due to the interplay among the structure, chemical order and magnetism. Such nanoalloy clusters, can be used to construct nanometer devices for technological applications by manipulating their remarkable magnetic, chemical and optical properties. Determining the nanoscopic features exhibited by the magnetic alloy clusters signifies the need for a systematic global and local exploration of their potential-energy surface in order to identify all the relevant energetically low-lying magnetic isomers. In this thesis the sampling of the potential-energy surface has been performed by employing the state-of-the-art spin-polarized density-functional theory in combination with graph theory and the basin-hopping global optimization techniques. This combination is vital for a quantitative analysis of the quantum mechanical energetics. The first approach, i.e., spin-polarized density-functional theory together with the graph theory method, is applied to study the Fe$_m$Rh$_n$ and Co$_m$Pd$_n$ clusters having $N = m+n \leq 8$ atoms. We carried out a thorough and systematic sampling of the potential-energy surface by taking into account all possible initial cluster topologies, all different distributions of the two kinds of atoms within the cluster, the entire concentration range between the pure limits, and different initial magnetic configurations such as ferro- and anti-ferromagnetic coupling. The remarkable magnetic properties shown by FeRh and CoPd nanoclusters are attributed to the extremely reduced coordination number together with the charge transfer from 3$d$ to 4$d$ elements. The second approach, i.e., spin-polarized density-functional theory together with the basin-hopping method is applied to study the small Fe$_6$, Fe$_3$Rh$_3$ and Rh$_6$ and the larger Fe$_{13}$, Fe$_6$Rh$_7$ and Rh$_{13}$ clusters as illustrative benchmark systems. This method is able to identify the true ground-state structures of Fe$_6$ and Fe$_3$Rh$_3$ which were not obtained by using the first approach. However, both approaches predict a similar cluster for the ground-state of Rh$_6$. Moreover, the computational time taken by this approach is found to be significantly lower than the first approach. The ground-state structure of Fe$_{13}$ cluster is found to be an icosahedral structure, whereas Rh$_{13}$ and Fe$_6$Rh$_7$ isomers relax into cage-like and layered-like structures, respectively. All the clusters display a remarkable variety of structural and magnetic behaviors. It is observed that the isomers having similar shape with small distortion with respect to each other can exhibit quite different magnetic moments. This has been interpreted as a probable artifact of spin-rotational symmetry breaking introduced by the spin-polarized GGA. The possibility of combining the spin-polarized density-functional theory with some other global optimization techniques such as minima-hopping method could be the next step in this direction. This combination is expected to be an ideal sampling approach having the advantage of avoiding efficiently the search over irrelevant regions of the potential energy surface.

Porter’s model and exports in Colombia: analysis of two profitable products

Tanto las industrias legales como ilegales tienen líderez y gerentes. Estas personas al mando deben hacer decisiones estrategicas con el fin de asegurar la rentabilidad de sus negocios. La manera en que ellos toman estas decisiones y las consecuencias de estas mismas son las preguntas que este documento pretende resolver. Haciendo una aplicación general del modelo de Michael Porter, este documento analiza y describe brevemente la configuración de ambos mercados (legal e illegal): es decir las maneras de hacer negocios, las tácticas utilizadas para negociar con los proveedores y compradores, las estrategias para resaltar los beneficios de sus productos frente a los sustitutos, y en general las acciones realizadas para competir, obtener un posicionamiento y porción en el mercado total. El objetivo de este documento no es exaltar las estrategias de los líderes en las industrias ilegales, sino resaltar aquello que los directivos en las industrias legales podrían hacer mejor para mejorar el nombre de los productos colombianos en el exterior.

Los clusters como mecanismo para la generación de economías a escala en el sector de medicamentos de alto costo en Colombia

La presente investigación tiene por objeto considerar los cluster en la industria farmacéutica Colombiana, como un mecanismo para la disminución de los sobrecostos de los medicamentos, que han impactado de forma importante, entre otras causas, al sistema de salud, con unos recobros (por concepto de medicamentos No POS) que superan el billón de pesos, situación que dada la crisis que enfrenta al respecto, el Estado Colombiano, ha propuesto una quinta reforma que cursa actualmente en el Congreso de la República. Se trata de una investigación cualitativa tipo estudio de caso, en la que se presenta el modelo Colombiano de Salud y las cifras de recobros de las Empresas Prestadoras de Servicios de Salud (EPS), cantidad que representó el 0.4% del PIB (Producto Interno Bruto) en el 2009. Para tal fin se analizará el comportamiento de los recobros durante el año 2012, en cuarenta y una (41) EPS reconocidas del sector. Subsecuentemente se estudian las diferentes estrategias para la generación de economías de escala y dentro de ellas, los clusters como un posible modelo a seguir hacia la disminución de estos costos en salud, se analizan sus componentes y su posible constitución dentro del entorno Colombiano. Al final del estudio se establece como conclusión, que existen suficiente evidencia para apoyar la implementación de un cluster farmacéutico dentro del territorio Colombiano.

Counterpoise-corrected geometries and harmonic frequencies of N-body clusters: application to (HF)n (n=3,4)

A study was conducted on the methods of basis set superposition error (BSSE)-free geometry optimization and frequency calculations in clusters larger than a dimer. In particular, three different counterpoise schemes were critically examined. It was shown that the counterpoise-corrected supermolecule energy can be easily obtained in all the cases by using the many-body partitioning of energy

Analysis of chemical bonding and aromaticity from electronic delocalization descriptors

Interactions between electrons determine the structure and properties of matter from molecules to solids. Therefore, the understanding of the electronic structure of molecules will enable us to extract relevant chemical information. In the first part of this thesis, we focus our attention on the analysis of chemical bonding by means of the Electron Localization Function (ELF) and the Domain-Averaged Fermi Hole analysis (DAFH). In the second part, we assess the performance of some indicators of aromaticity by analyzing their advantages and drawbacks. We propose a series of tests based on well-known aromaticity trends that can be applied to evaluate the aromaticity of current and future indicators of aromaticity in both organic and inorganic species. Moreover, we investigate the nature of electron delocalization in both aromatic and antiaromatic systems in the light of Hückel’s (4n + 2) rule. Finally, we analyze the phenomenon of multiple aromaticity in all-metal clusters.

Bayesian analysis of an inverse Gaussian correlated frailty model

In survival analysis frailty is often used to model heterogeneity between individuals or correlation within clusters. Typically frailty is taken to be a continuous random effect, yielding a continuous mixture distribution for survival times. A Bayesian analysis of a correlated frailty model is discussed in the context of inverse Gaussian frailty. An MCMC approach is adopted and the deviance information criterion is used to compare models. As an illustration of the approach a bivariate data set of corneal graft survival times is analysed. (C) 2006 Elsevier B.V. All rights reserved.

A comparison of three different models for estimating relative risk in meta-analysis of clinical trials under unobserved heterogeneity

We focus on the comparison of three statistical models used to estimate the treatment effect in metaanalysis when individually pooled data are available. The models are two conventional models, namely a multi-level and a model based upon an approximate likelihood, and a newly developed model, the profile likelihood model which might be viewed as an extension of the Mantel-Haenszel approach. To exemplify these methods, we use results from a meta-analysis of 22 trials to prevent respiratory tract infections. We show that by using the multi-level approach, in the case of baseline heterogeneity, the number of clusters or components is considerably over-estimated. The approximate and profile likelihood method showed nearly the same pattern for the treatment effect distribution. To provide more evidence two simulation studies are accomplished. The profile likelihood can be considered as a clear alternative to the approximate likelihood model. In the case of strong baseline heterogeneity, the profile likelihood method shows superior behaviour when compared with the multi-level model. Copyright (C) 2006 John Wiley & Sons, Ltd.

GeneMCL in microarray analysis

Accurately and reliably identifying the actual number of clusters present with a dataset of gene expression profiles, when no additional information on cluster structure is available, is a problem addressed by few algorithms. GeneMCL transforms microarray analysis data into a graph consisting of nodes connected by edges, where the nodes represent genes, and the edges represent the similarity in expression of those genes, as given by a proximity measurement. This measurement is taken to be the Pearson correlation coefficient combined with a local non-linear rescaling step. The resulting graph is input to the Markov Cluster (MCL) algorithm, which is an elegant, deterministic, non-specific and scalable method, which models stochastic flow through the graph. The algorithm is inherently affected by any cluster structure present, and rapidly decomposes a graph into cohesive clusters. The potential of the GeneMCL algorithm is demonstrated with a 5730 gene subset (IGS) of the Van't Veer breast cancer database, for which the clusterings are shown to reflect underlying biological mechanisms. (c) 2005 Elsevier Ltd. All rights reserved.

Analysis of the sulfate-reducing bacterial and methanogenic archaeal populations in contrasting Antarctic sediments

The distribution and activity of communities of sulfate-reducing bacteria (SRB) and methanogenic archaea in two contrasting Antarctic sediments were investigated. Methanogenesis dominated in freshwater Lake Heywood, while sulfate reduction dominated in marine Shallow Bay. Slurry experiments indicated that 90% of the methanogenesis in Lake Heywood was acetoclastic. This finding was supported by the limited diversity of clones detected in a Lake Heywood archaeal clone library, in which most clones were closely related to the obligate acetate-utilizing Methanosaeta concilii. The Shallow Bay archaeal clone library contained clones related to the C-1-utilizing Methanolobus and Methanococcoides and the H-2-utilizing Methanogenium. Oligonucleotide probing of RNA extracted directly from sediment indicated that archaea represented 34% of the total prokaryotic signal in Lake Heywood and that Methanosaeta was a major component (13.2%) of this signal. Archaea represented only 0.2% of the total prokaryotic signal in RNA extracted from Shallow Bay sediments. In the Shallow Bay bacterial clone library, 10.3% of the clones were SRB-like, related to Desulfotalea/Desulforhopalus, Desulfofaba, Desulfosarcina, and Desulfobacter as well as to the sulfur and metal oxidizers comprising the Desulfuromonas cluster. Oligonucleotide probes for specific SRB clusters indicated that SRB represented 14.7% of the total prokaryotic signal, with Desulfotalea/Desulforhopalus being the dominant SRB group (10.7% of the total prokaryotic signal) in the Shallow Bay sediments; these results support previous results obtained for Arctic sediments. Methanosaeta and Desulfotalea/Desulforhopalus appear to be important in Lake Heywood and Shallow Bay, respectively, and may be globally important in permanently low-temperature sediments.

A novel cation induced polymeric chain in Na-8[{Cu(gly)(2)}(2)]{H-2(H2W12O42)}] center dot 24H(2)O: hydrothermal synthesis, spectroscopic characterization and X-ray structure analysis

A novel bis(glycinato) copper(II) paradodecatungstate Na-8[{Cu(gly)(2)}(2)]-{H-2(H2W12O42)}] center dot 24H(2)O (1) has been synthesized under hydrothermal conditions. The crystal structure of 1 reveals an infinite one-dimensional chain along the [100] direction and is built from paradodecatungstate (H2W12O42)(10-) clusters joined through [Cu(gly)(2)] moieties. Parallel chains are interlinked by NaO6 octahedra to generate a two-dimensional network.

Comparative genome analysis provides insights into the evolution and adaptation of Pseudomonas syringae pv. aesculi on Aesculus hippocastanum.

A recently emerging bleeding canker disease, caused by Pseudomonas syringae pathovar aesculi (Pae), is threatening European horse chestnut in northwest Europe. Very little is known about the origin and biology of this new disease. We used the nucleotide sequences of seven commonly used marker genes to investigate the phylogeny of three strains isolated recently from bleeding stem cankers on European horse chestnut in Britain (E-Pae). On the basis of these sequences alone, the E-Pae strains were identical to the Pae type-strain (I-Pae), isolated from leaf spots on Indian horse chestnut in India in 1969. The phylogenetic analyses also showed that Pae belongs to a distinct clade of P. syringae pathovars adapted to woody hosts. We generated genome-wide Illumina sequence data from the three E-Pae strains and one strain of I-Pae. Comparative genomic analyses revealed pathovar-specific genomic regions in Pae potentially implicated in virulence on a tree host, including genes for the catabolism of plant-derived aromatic compounds and enterobactin synthesis. Several gene clusters displayed intra-pathovar variation, including those encoding type IV secretion, a novel fatty acid biosynthesis pathway and a sucrose uptake pathway. Rates of single nucleotide polymorphisms in the four Pae genomes indicate that the three E-Pae strains diverged from each other much more recently than they diverged from I-Pae. The very low genetic diversity among the three geographically distinct E-Pae strains suggests that they originate from a single, recent introduction into Britain, thus highlighting the serious environmental risks posed by the spread of an exotic plant pathogenic bacterium to a new geographic location. The genomic regions in Pae that are absent from other P. syringae pathovars that infect herbaceous hosts may represent candidate genetic adaptations to infection of the woody parts of the tree.

A structural analysis of M protein in coronavirus assembly and morphology

The M protein of coronavirus plays a central role in virus assembly, turning cellular membranes into workshops where virus and host factors come together to make new virus particles. We investigated how M structure and organization is related to virus shape and size using cryo-electron microscopy, tomography and statistical analysis. We present evidence that suggests M can adopt two conformations and that membrane curvature is regulated by one M conformer. Elongated M protein is associated with rigidity, clusters of spikes and a relatively narrow range of membrane curvature. In contrast, compact M protein is associated with flexibility and low spike density. Analysis of several types of virus-like particles and virions revealed that S protein, N protein and genomic RNA each help to regulate virion size and variation, presumably through interactions with M. These findings provide insight into how M protein functions to promote virus assembly.

The use of trajectory cluster analysis to interpret trace gas measurements at Mace Head, Ireland

A first step in interpreting the wide variation in trace gas concentrations measured over time at a given site is to classify the data according to the prevailing weather conditions. In order to classify measurements made during two intensive field campaigns at Mace Head, on the west coast of Ireland, an objective method of assigning data to different weather types has been developed. Air-mass back trajectories calculated using winds from ECMWF analyses, arriving at the site in 1995–1997, were allocated to clusters based on a statistical analysis of the latitude, longitude and pressure of the trajectory at 12 h intervals over 5 days. The robustness of the analysis was assessed by using an ensemble of back trajectories calculated for four points around Mace Head. Separate analyses were made for each of the 3 years, and for four 3-month periods. The use of these clusters in classifying ground-based ozone measurements at Mace Head is described, including the need to exclude data which have been influenced by local perturbations to the regional flow pattern, for example, by sea breezes. Even with a limited data set, based on 2 months of intensive field measurements in 1996 and 1997, there are statistically significant differences in ozone concentrations in air from the different clusters. The limitations of this type of analysis for classification and interpretation of ground-based chemistry measurements are discussed.