The finite bandwidth model for spin fluctuations in Pd

The frequency dependence of the electron-spin fluctuation spectrum, P(Q), is calculated in the finite bandwidth model. We find that for Pd, which has a nearly full d-band, the magnitude, the range, and the peak frequency of P(Q) are greatly reduced from those in the standard spin fluctuation theory. The electron self-energy due to spin fluctuations is calculated within the finite bandwidth model. Vertex corrections are examined, and we find that Migdal's theorem is valid for spin fluctuations in the nearly full band. The conductance of a normal metal-insulator-normal metal tunnel junction is examined when spin fluctuations are present in one electrode. We find that for the nearly full band, the momentum independent self-energy due to spin fluctuations enters the expression for the tunneling conductance with approximately the same weight as the self-energy due to phonons. The effect of spin fluctuations on the tunneling conductance is slight within the finite bandwidth model for Pd. The effect of spin fluctuations on the tunneling conductance of a metal with a less full d-band than Pd may be more pronounced. However, in this case the tunneling conductance is not simply proportional to the self-energy.

Zero-sum problems in finite cyclic groups

The purpose of this thesis is to investigate some open problems in the area of combinatorial number theory referred to as zero-sum theory. A zero-sequence in a finite cyclic group G is said to have the basic property if it is equivalent under group automorphism to one which has sum precisely IGI when this sum is viewed as an integer. This thesis investigates two major problems, the first of which is referred to as the basic pair problem. This problem seeks to determine conditions for which every zero-sequence of a given length in a finite abelian group has the basic property. We resolve an open problem regarding basic pairs in cyclic groups by demonstrating that every sequence of length four in Zp has the basic property, and we conjecture on the complete solution of this problem. The second problem is a 1988 conjecture of Kleitman and Lemke, part of which claims that every sequence of length n in Zn has a subsequence with the basic property. If one considers the special case where n is an odd integer we believe this conjecture to hold true. We verify this is the case for all prime integers less than 40, and all odd integers less than 26. In addition, we resolve the Kleitman-Lemke conjecture for general n in the negative. That is, we demonstrate a sequence in any finite abelian group isomorphic to Z2p (for p ~ 11 a prime) containing no subsequence with the basic property. These results, as well as the results found along the way, contribute to many other problems in zero-sum theory.

Generating finite integral relation algebras

Relation algebras and categories of relations in particular have proven to be extremely useful as a fundamental tool in mathematics and computer science. Since relation algebras are Boolean algebras with some well-behaved operations, every such algebra provides an atom structure, i.e., a relational structure on its set of atoms. In the case of complete and atomic structure (e.g. finite algebras), the original algebra can be recovered from its atom structure by using the complex algebra construction. This gives a representation of relation algebras as the complex algebra of a certain relational structure. This property is of particular interest because storing the atom structure requires less space than the entire algebra. In this thesis I want to introduce and implement three structures representing atom structures of integral heterogeneous relation algebras, i.e., categorical versions of relation algebras. The first structure will simply embed a homogeneous atom structure of a relation algebra into the heterogeneous context. The second structure is obtained by splitting all symmetric idempotent relations. This new algebra is in almost all cases an heterogeneous structure having more objects than the original one. Finally, I will define two different union operations to combine two algebras into a single one.

Aspects of spatial and habitat ecology of multiple Anopheles species (Diptera: Culicidae): malaria vectors in the highlands and foothills of Ecuador

The resurgence of malaria in highland regions of Africa, Oceania and recently in South America underlines the importance of the study of the ecology of highland mosquito vectors of malaria. Since the incidence of malaria is limited by the distribution of its vectors, the purpose of this PhD thesis was to examine aspects of the ecology of Anopheles mosquitoes in the Andes of Ecuador, South America. A historical literature and archival data review (Chapter 2) indicated that Anopheles pseudopunctipennis transmitted malaria in highland valleys of Ecuador prior to 1950, although it was eliminated through habitat removal and the use of chemical insecticides. Other anopheline species were previously limited to low-altitude regions, except in a few unconfirmed cases. A thorough larval collection effort (n=438 attempted collection sites) in all road-accessible parts of Ecuador except for the lowland Amazon basin was undertaken between 2008 - 2010 (Chapter 3). Larvae were identified morphologically and using molecular techniques (mitochondrial COl gene), and distribution maps indicated that all five species collected (Anopheles albimanus, An. pseudopunctipennis, Anopheles punctimacula, Anopheles oswaldoi s.l. and Anopheles eiseni) were more widespread throughout highland regions than previously recorded during the 1940s, with higher maximum altitudes for all except An. pseudopunctipennis (1541 m, 1930 m, 1906 m, 1233 m and 1873 m, respectively). During larval collections, to characterize species-specific larval habitat, a variety of abiotic and biotic habitat parameters were measured and compared between species-present and species-absent sites using chi-square tests and stepwise binary logistic regression analyses (Chapter 4). An. albimanus was significantly associated with permanent pools with sand substrates and An. pseudopunctipennis with gravel and boulder substrates. Both species were significantly associated with floating cyanobacterial mats and warmer temperatures, which may limit their presence in cooler highland regions. Anopheles punctimacula was collected more often than expected from algae-free, shaded pools with higher-than-average calculated dissolved oxygen. Anopheles oswaldoi s.l., the species occurring on the Amazonian side of the Andes, was associated with permanent, anthropogenic habitats such as roadside ditches and ponds. To address the hypothesis that human land use change is responsible for the emergence of multiple highland Anopheles species by creating larval habitat, common land uses in the western Andes were surveyed for standing water and potential larval habitat suitability (Chapter 5). Rivers and road edges provided large amounts of potentially suitable anopheline habitat in the western Andes, while cattle pasture also created potentially suitable habitat in irrigation canals and watering ponds. Other common land uses surveyed (banana farms, sugarcane plantations, mixed tree plantations, and empty lots) were usually established on steep slopes and had very little standing water present. Using distribution and larval habitat data, a GIS-based larval habitat distribution model for the common western species was constructed in ArcGIS v.l 0 (ESRI 2010) using derived data layers from field measurements and other sources (Chapter 6). The additive model predicted 76.4 - 97.9% of the field-observed collection localities of An. albimanus, An. pseudopunctipennis and An. punctimacula, although it could not accurately distinguish between species-absent and speciespresent sites due to its coarse scale. The model predicted distributional expansion and/or shift of one or more anopheline species into the following highland valleys with climate warming: Mira/Chota, Imbabura province, Tumbaco, Pichincha province, Pallatanga and Sibambe, Chimborazo province, and Yungilla, Azuay province. These valleys may serve as targeted sites of future monitoring to prevent highland epidemics of malaria. The human perceptions of malaria and mosquitoes in relation to land management practices were assessed through an interview-based survey (n=262) in both highlands and lowlands, of male and female land owners and managers of five property types (Chapter 7). Although respondents had a strong understanding of where the disease occurs in their own country and of the basic relationship among standing water, mosquitoes and malaria, about half of respondents in potential risk areas denied the current possibility of malaria infection on their own property. As well, about half of respondents with potential anopheline larval habitat did not report its presence, likely due to a highly specific definition of suitable mosquito habitat. Most respondents who are considered at risk of malaria currently use at least one type of mosquito bite prevention, most commonly bed nets. In conclusion, this interdisciplinary thesis examines the occurrence of Anopheles species in the lowland transition area and highlands in Ecuador, from a historic, geographic, ecological and sociological perspective.

Generalization of the BTK Theory to the Case of Finite Quasiparticle Lifetimes

A generalization to the BTK theory is developed based on the fact that the quasiparticle lifetime is finite as a result of the damping caused by the interactions. For this purpose, appropriate self-energy expressions and wave functions are inserted into the strong coupling version of the Bogoliubov equations and subsequently, the coherence factors are computed. By applying the suitable boundary conditions to the case of a normal-superconducting interface, the probability current densities for the Andreev reflection, the normal reflection, the transmission without branch crossing and the transmission with branch crossing are determined. Accordingly the electric current and the differential conductance curves are calculated numerically for Nb, Pb, and Pb0.9Bi0.1 alloy. The generalization of the BTK theory by including the phenomenological damping parameter is critically examined. The observed differences between our approach and the phenomenological approach are investigated by the numerical analysis.

Larval habitat associations with human land uses, roads, rivers, and land cover for Anopheles albimanus, A. pseudopunctipennis, and A. punctimacula (Diptera: Culicidae) in coastal and highland Ecuador

Larval habitat for three highland Anopheles species: Anopheles albimanus Wiedemann, Anopheles pseudopunctipennis Theobald, and Anopheles punctimacula Dyar and Knab was related to human land uses, rivers, roads, and remotely sensed land cover classifications in the western Ecuadorian Andes. Of the five commonly observed human land uses, cattle pasture (n = 30) provided potentially suitable habitat for A. punctimacula and A. albimanus in less than 14% of sites, and was related in a principal components analysis (PCA) to the presence of macrophyte vegetation, greater surface area, clarity, and algae cover. Empty lots (n = 30) were related in the PCA to incident sunlight and provided potential habitat for A. pseudopunctipennis and A. albimanus in less than 14% of sites. The other land uses surveyed (banana, sugarcane, and mixed tree plantations; n = 28, 21, 25, respectively) provided very little standing water that could potentially be used for larval habitat. River edges and eddies (n = 41) were associated with greater clarity, depth, temperature, and algae cover, which provide potentially suitable habitat for A. albimanus in 58% of sites and A. pseudopunctipennis in 29% of sites. Road-associated water bodies (n = 38) provided potential habitat for A. punctimacula in 44% of sites and A. albimanus in 26% of sites surveyed. Species collection localities were compared to land cover classifications using Geographic Information Systems software. All three mosquito species were associated more often with the category “closed/open broadleaved evergreen and/or semi-deciduous forests” than expected (P ≤ 0.01 in all cases), given such a habitat’s abundance. This study provides evidence that specific human land uses create habitat for potential malaria vectors in highland regions of the Andes.

Influencia de la estructura del habitat en la abundancia relativa de Peromyscus boylii ambiguus (RODENTIA).

Tesis (Maestría en Ciencias con Especialidad en Manejo de Vida Silvestre) UANL

Preferencia de habitat, dieta, amplitud y traslape de nicho de carnívoros simpátricos (Mammalia: carnivora) en la costa sur de Jalisco,México

Tesis (Maestría en Ciencias con Especialidad en Manejo de Vida Silvestre) UANL

Estructura y uso de habitat de las comunidades de aves en los bosques de encino de la Sierra Madre Oriental

Tesis (Maestro en Ciencias Forestales) U.A.N.L.

Simulation-Based Finite and Large Sample Tests in Multivariate Regressions.

In the context of multivariate linear regression (MLR) models, it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection. In this paper, we propose a general method for constructing exact tests of possibly nonlinear hypotheses on the coefficients of MLR systems. For the case of uniform linear hypotheses, we present exact distributional invariance results concerning several standard test criteria. These include Wilks' likelihood ratio (LR) criterion as well as trace and maximum root criteria. The normality assumption is not necessary for most of the results to hold. Implications for inference are two-fold. First, invariance to nuisance parameters entails that the technique of Monte Carlo tests can be applied on all these statistics to obtain exact tests of uniform linear hypotheses. Second, the invariance property of the latter statistic is exploited to derive general nuisance-parameter-free bounds on the distribution of the LR statistic for arbitrary hypotheses. Even though it may be difficult to compute these bounds analytically, they can easily be simulated, hence yielding exact bounds Monte Carlo tests. Illustrative simulation experiments show that the bounds are sufficiently tight to provide conclusive results with a high probability. Our findings illustrate the value of the bounds as a tool to be used in conjunction with more traditional simulation-based test methods (e.g., the parametric bootstrap) which may be applied when the bounds are not conclusive.

Markovian Processes, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes.

In this paper, we develop finite-sample inference procedures for stationary and nonstationary autoregressive (AR) models. The method is based on special properties of Markov processes and a split-sample technique. The results on Markovian processes (intercalary independence and truncation) only require the existence of conditional densities. They are proved for possibly nonstationary and/or non-Gaussian multivariate Markov processes. In the context of a linear regression model with AR(1) errors, we show how these results can be used to simplify the distributional properties of the model by conditioning a subset of the data on the remaining observations. This transformation leads to a new model which has the form of a two-sided autoregression to which standard classical linear regression inference techniques can be applied. We show how to derive tests and confidence sets for the mean and/or autoregressive parameters of the model. We also develop a test on the order of an autoregression. We show that a combination of subsample-based inferences can improve the performance of the procedure. An application to U.S. domestic investment data illustrates the method.

Simulation-Based Finite-Sample Tests for Heteroskedasticity and ARCH Effects.

A wide range of tests for heteroskedasticity have been proposed in the econometric and statistics literature. Although a few exact homoskedasticity tests are available, the commonly employed procedures are quite generally based on asymptotic approximations which may not provide good size control in finite samples. There has been a number of recent studies that seek to improve the reliability of common heteroskedasticity tests using Edgeworth, Bartlett, jackknife and bootstrap methods. Yet the latter remain approximate. In this paper, we describe a solution to the problem of controlling the size of homoskedasticity tests in linear regression contexts. We study procedures based on the standard test statistics [e.g., the Goldfeld-Quandt, Glejser, Bartlett, Cochran, Hartley, Breusch-Pagan-Godfrey, White and Szroeter criteria] as well as tests for autoregressive conditional heteroskedasticity (ARCH-type models). We also suggest several extensions of the existing procedures (sup-type of combined test statistics) to allow for unknown breakpoints in the error variance. We exploit the technique of Monte Carlo tests to obtain provably exact p-values, for both the standard and the new tests suggested. We show that the MC test procedure conveniently solves the intractable null distribution problem, in particular those raised by the sup-type and combined test statistics as well as (when relevant) unidentified nuisance parameter problems under the null hypothesis. The method proposed works in exactly the same way with both Gaussian and non-Gaussian disturbance distributions [such as heavy-tailed or stable distributions]. The performance of the procedures is examined by simulation. The Monte Carlo experiments conducted focus on : (1) ARCH, GARCH, and ARCH-in-mean alternatives; (2) the case where the variance increases monotonically with : (i) one exogenous variable, and (ii) the mean of the dependent variable; (3) grouped heteroskedasticity; (4) breaks in variance at unknown points. We find that the proposed tests achieve perfect size control and have good power.

Simulation-Based Finite-Sample Normality Tests in Linear Regressions

In the literature on tests of normality, much concern has been expressed over the problems associated with residual-based procedures. Indeed, the specialized tables of critical points which are needed to perform the tests have been derived for the location-scale model; hence reliance on available significance points in the context of regression models may cause size distortions. We propose a general solution to the problem of controlling the size normality tests for the disturbances of standard linear regression, which is based on using the technique of Monte Carlo tests.

Finite-Sample Inference Methods for Simultaneous Equations and Models with Unobserved and Generated Regressors

We propose finite sample tests and confidence sets for models with unobserved and generated regressors as well as various models estimated by instrumental variables methods. The validity of the procedures is unaffected by the presence of identification problems or \"weak instruments\", so no detection of such problems is required. We study two distinct approaches for various models considered by Pagan (1984). The first one is an instrument substitution method which generalizes an approach proposed by Anderson and Rubin (1949) and Fuller (1987) for different (although related) problems, while the second one is based on splitting the sample. The instrument substitution method uses the instruments directly, instead of generated regressors, in order to test hypotheses about the \"structural parameters\" of interest and build confidence sets. The second approach relies on \"generated regressors\", which allows a gain in degrees of freedom, and a sample split technique. For inference about general possibly nonlinear transformations of model parameters, projection techniques are proposed. A distributional theory is obtained under the assumptions of Gaussian errors and strictly exogenous regressors. We show that the various tests and confidence sets proposed are (locally) \"asymptotically valid\" under much weaker assumptions. The properties of the tests proposed are examined in simulation experiments. In general, they outperform the usual asymptotic inference methods in terms of both reliability and power. Finally, the techniques suggested are applied to a model of Tobin’s q and to a model of academic performance.

Simulation-Based Finite-and Large-sample Inference Methods in Multivariate Regressions and Seemingly Unrelated Regressions

In the context of multivariate regression (MLR) and seemingly unrelated regressions (SURE) models, it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection. in this paper, we propose finite-and large-sample likelihood-based test procedures for possibly non-linear hypotheses on the coefficients of MLR and SURE systems.