Conditional compositional biplots: theory and application

The biplot has proved to be a powerful descriptive and analytical tool in many areas of applications of statistics. For compositional data the necessary theoretical adaptation has been provided, with illustrative applications, by Aitchison (1990) and Aitchison and Greenacre (2002). These papers were restricted to the interpretation of simple compositional data sets. In many situations the problem has to be described in some form of conditional modelling. For example, in a clinical trial where interest is in how patients’ steroid metabolite compositions may change as a result of different treatment regimes, interest is in relating the compositions after treatment to the compositions before treatment and the nature of the treatments applied. To study this through a biplot technique requires the development of some form of conditional compositional biplot. This is the purpose of this paper. We choose as a motivating application an analysis of the 1992 US President ial Election, where interest may be in how the three-part composition, the percentage division among the three candidates - Bush, Clinton and Perot - of the presidential vote in each state, depends on the ethnic composition and on the urban-rural composition of the state. The methodology of conditional compositional biplots is first developed and a detailed interpretation of the 1992 US Presidential Election provided. We use a second application involving the conditional variability of tektite mineral compositions with respect to major oxide compositions to demonstrate some hazards of simplistic interpretation of biplots. Finally we conjecture on further possible applications of conditional compositional biplots

Fronts from complex two-dimensional dispersal kernels: theory and application to Reid's paradox

Bimodal dispersal probability distributions with characteristic distances differing by several orders of magnitude have been derived and favorably compared to observations by Nathan [Nature (London) 418, 409 (2002)]. For such bimodal kernels, we show that two-dimensional molecular dynamics computer simulations are unable to yield accurate front speeds. Analytically, the usual continuous-space random walks (CSRWs) are applied to two dimensions. We also introduce discrete-space random walks and use them to check the CSRW results (because of the inefficiency of the numerical simulations). The physical results reported are shown to predict front speeds high enough to possibly explain Reid's paradox of rapid tree migration. We also show that, for a time-ordered evolution equation, fronts are always slower in two dimensions than in one dimension and that this difference is important both for unimodal and for bimodal kernels

Front spreading in population dynamic models. Theory and application to the Neolithic transition

This thesis presents population dynamics models that can be applied to predict the rate of spread of the Neolithic transition (change from hunter-gathering to farming economics) across the European continent, which took place about 9000 to 5000 years ago. The first models in this thesis provide predictions at a continental scale. We develop population dynamics models with explicit kernels and apply realistic data. We also derive a new time-delayed reaction-diffusion equation which yields speeds about a 10% slower than previous models. We also deal with a regional variability: the slowdown of the Neolithic front when reaching the North of Europe. We develop simple reaction-diffusion models that can predict the measured speeds in terms of the non-homogeneous distribution of pre-Neolithic (Mesolithic) population in Europe, which were present in higher densities at the North of the continent. Such models can explain the observed speeds.

Development, implementation and application of electronic structural descriptors to the analysis of the chemical bonding, aromaticity and chemical reactivity

En la literatura sobre mecànica quàntica és freqüent trobar descriptors basats en la densitat de parells o la densitat electrònica, amb un èxit divers segons les aplicacions que atenyin. Per tal de que tingui sentit químic un descriptor ha de donar la definició d'un àtom en una molècula, o ésser capaç d'identificar regions de l'espai molecular associades amb algun concepte químic (com pot ser un parell solitari o zona d'enllaç, entre d'altres). En aquesta línia, s'han proposat diversos esquemes de partició: la teoria d'àtoms en molècules (AIM), la funció de localització electrònica (ELF), les cel·les de Voroni, els àtoms de Hirshfeld, els àtoms difusos, etc. L'objectiu d'aquesta tesi és explorar descriptors de la densitat basats en particions de l'espai molecular del tipus AIM, ELF o àtoms difusos, analitzar els descriptors existents amb diferents nivells de teoria, proposar nous descriptors d'aromaticitat, així com estudiar l'habilitat de totes aquestes eines per discernir entre diferents mecanismes de reacció.

Implementation and application of basis set superposition error-correction schemes to the theoretical modeling of weak intermolecular interactions

This thesis deals with the so-called Basis Set Superposition Error (BSSE) from both a methodological and a practical point of view. The purpose of the present thesis is twofold: (a) to contribute step ahead in the correct characterization of weakly bound complexes and, (b) to shed light the understanding of the actual implications of the basis set extension effects in the ab intio calculations and contribute to the BSSE debate. The existing BSSE-correction procedures are deeply analyzed, compared, validated and, if necessary, improved. A new interpretation of the counterpoise (CP) method is used in order to define counterpoise-corrected descriptions of the molecular complexes. This novel point of view allows for a study of the BSSE-effects not only in the interaction energy but also on the potential energy surface and, in general, in any property derived from the molecular energy and its derivatives A program has been developed for the calculation of CP-corrected geometry optimizations and vibrational frequencies, also using several counterpoise schemes for the case of molecular clusters. The method has also been implemented in Gaussian98 revA10 package. The Chemical Hamiltonian Approach (CHA) methodology has been also implemented at the RHF and UHF levels of theory for an arbitrary number interacting systems using an algorithm based on block-diagonal matrices. Along with the methodological development, the effects of the BSSE on the properties of molecular complexes have been discussed in detail. The CP and CHA methodologies are used for the determination of BSSE-corrected molecular complexes properties related to the Potential Energy Surfaces and molecular wavefunction, respectively. First, the behaviour of both BSSE-correction schemes are systematically compared at different levels of theory and basis sets for a number of hydrogen-bonded complexes. The Complete Basis Set (CBS) limit of both uncorrected and CP-corrected molecular properties like stabilization energies and intermolecular distances has also been determined, showing the capital importance of the BSSE correction. Several controversial topics of the BSSE correction are addressed as well. The application of the counterpoise method is applied to internal rotational barriers. The importance of the nuclear relaxation term is also pointed out. The viability of the CP method for dealing with charged complexes and the BSSE effects on the double-well PES blue-shifted hydrogen bonds is also studied in detail. In the case of the molecular clusters the effect of high-order BSSE effects introduced with the hierarchical counterpoise scheme is also determined. The effect of the BSSE on the electron density-related properties is also addressed. The first-order electron density obtained with the CHA/F and CHA/DFT methodologies was used to assess, both graphically and numerically, the redistribution of the charge density upon BSSE-correction. Several tools like the Atoms in Molecules topologycal analysis, density difference maps, Quantum Molecular Similarity, and Chemical Energy Component Analysis were used to deeply analyze, for the first time, the BSSE effects on the electron density of several hydrogen bonded complexes of increasing size. The indirect effect of the BSSE on intermolecular perturbation theory results is also pointed out It is shown that for a BSSE-free SAPT study of hydrogen fluoride clusters, the use of a counterpoise-corrected PES is essential in order to determine the proper molecular geometry to perform the SAPT analysis.

Selected configuration interaction with truncation energy error and application to the Ne atom

Selected configuration interaction (SCI) for atomic and molecular electronic structure calculations is reformulated in a general framework encompassing all CI methods. The linked cluster expansion is used as an intermediate device to approximate CI coefficients BK of disconnected configurations (those that can be expressed as products of combinations of singly and doubly excited ones) in terms of CI coefficients of lower-excited configurations where each K is a linear combination of configuration-state-functions (CSFs) over all degenerate elements of K. Disconnected configurations up to sextuply excited ones are selected by Brown's energy formula, ΔEK=(E-HKK)BK2/(1-BK2), with BK determined from coefficients of singly and doubly excited configurations. The truncation energy error from disconnected configurations, Δdis, is approximated by the sum of ΔEKS of all discarded Ks. The remaining (connected) configurations are selected by thresholds based on natural orbital concepts. Given a model CI space M, a usual upper bound ES is computed by CI in a selected space S, and EM=E S+ΔEdis+δE, where δE is a residual error which can be calculated by well-defined sensitivity analyses. An SCI calculation on Ne ground state featuring 1077 orbitals is presented. Convergence to within near spectroscopic accuracy (0.5 cm-1) is achieved in a model space M of 1.4× 109 CSFs (1.1 × 1012 determinants) containing up to quadruply excited CSFs. Accurate energy contributions of quintuples and sextuples in a model space of 6.5 × 1012 CSFs are obtained. The impact of SCI on various orbital methods is discussed. Since ΔEdis can readily be calculated for very large basis sets without the need of a CI calculation, it can be used to estimate the orbital basis incompleteness error. A method for precise and efficient evaluation of ES is taken up in a companion paper

Case-Crossover Analysis of Air Pollution Health Effects: A Systematic Review of Methodology and Application

Case-crossover is one of the most used designs for analyzing the health-related effects of air pollution. Nevertheless, no one has reviewed its application and methodology in this context. Objective: We conducted a systematic review of case-crossover (CCO) designs used to study the relationship between air pollution and morbidity and mortality, from the standpoint of methodology and application.Data sources and extraction: A search was made of the MEDLINE and EMBASE databases.Reports were classified as methodologic or applied. From the latter, the following information was extracted: author, study location, year, type of population (general or patients), dependent variable(s), independent variable(s), type of CCO design, and whether effect modification was analyzed for variables at the individual level. Data synthesis: The review covered 105 reports that fulfilled the inclusion criteria. Of these, 24 addressed methodological aspects, and the remainder involved the design’s application. In the methodological reports, the designs that yielded the best results in simulation were symmetric bidirectional CCO and time-stratified CCO. Furthermore, we observed an increase across time in the use of certain CCO designs, mainly symmetric bidirectional and time-stratified CCO. The dependent variables most frequently analyzed were those relating to hospital morbidity; the pollutants most often studied were those linked to particulate matter. Among the CCO-application reports, 13.6% studied effect modification for variables at the individual level.Conclusions: The use of CCO designs has undergone considerable growth; the most widely used designs were those that yielded better results in simulation studies: symmetric bidirectional and time-stratified CCO. However, the advantages of CCO as a method of analysis of variables at the individual level are put to little use

New Ruthenium complexes containing N, P and S-donor type of ligands: coordination chemistry, characterization and application to asymetric and non-asymetric catalysis

Síntesi de nous complexos de Ruteni amb lligands no quirals que tenen per fórmula [Ru(phen)([9]aneS3)X] (on X = H2O, py i MeCN). Caracterització espectroscòpica electroquímica i estructural d'aquesta família de complexos. Estudi de les seves propietats catalítiques en front a l'oxidació de substrats orgànics com l'alcohol benzílic en reaccions d'electrocatàlisi. Avaluació cinètica dels mecanismes de substitució entre els complexos Ru-py i Ru-MeCN. Generació d'un interruptor molecular foto-induït. Síntesi de nous complexos quirals de Ru atropoisomèricament purs amb lligands oxazolínics que tenen per fórmula [Ru(trpy)(Ph-box-R)X] on (X = Cl, H2O, py, MeCN, 2-OH-py). Caracterització estructural exhaustiva en estat sòlid (Raig-X) en solució (RMN) i en fase gas (càlculs DFT). Avaluació de la seva activitat catalítica en reaccions asimmetriques d'epoxidació de substrats proquirals. Síntesi de nous lligands polipiridílics quirals amb simetria C3. Estudi de la seva química de coordinació i avaluació de la seva activitat catalítica en reaccions asimmetriques d'oxidació i reducció.

The mapping of the local contributions of Fermi and Coulomb correlation into intracule and extracule density distributions

The contributions of the correlated and uncorrelated components of the electron-pair density to atomic and molecular intracule I(r) and extracule E(R) densities and its Laplacian functions ∇2I(r) and ∇2E(R) are analyzed at the Hartree-Fock (HF) and configuration interaction (CI) levels of theory. The topologies of the uncorrelated components of these functions can be rationalized in terms of the corresponding one-electron densities. In contrast, by analyzing the correlated components of I(r) and E(R), namely, IC(r) and EC(R), the effect of electron Fermi and Coulomb correlation can be assessed at the HF and CI levels of theory. Moreover, the contribution of Coulomb correlation can be isolated by means of difference maps between IC(r) and EC(R) distributions calculated at the two levels of theory. As application examples, the He, Ne, and Ar atomic series, the C2-2, N2, O2+2 molecular series, and the C2H4 molecule have been investigated. For these atoms and molecules, it is found that Fermi correlation accounts for the main characteristics of IC(r) and EC(R), with Coulomb correlation increasing slightly the locality of these functions at the CI level of theory. Furthermore, IC(r), EC(R), and the associated Laplacian functions, reveal the short-ranged nature and high isotropy of Fermi and Coulomb correlation in atoms and molecules