Simulation of interacting populations in inhomogeneous flows using reduced models

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2010

Thermal comfort in reduced models of broilers' houses, under different types of roofing materials

The research was developed to evaluate the use of different types of roofing materials regularly used in poultry houses. Measurements of thermal comfort were made through the use of techniques such as the Black Globe and Humidity Index (BGHI), the Thermal Heat Load (THL) and Enthalpy (H). Conducted in the State University of Goiás, during the months of April and May, 2011, the experiment was composed of five different treatments: AC - Asbestos cement tiles, BA -Bamboo tiles, BAP - Bamboo tiles painted in white, FB -Vegetable fiber tiles and bitumen, FBP -Vegetable fiber tiles and bitumen painted in white. The experiment consisted in 15 repetitions, which were considered the different days of measurements taken. Throughout the studied period, the time of the day considered the least comfortable was the one observed at 2:00pm, and the coverage of vegetable fiber and bitumen showed the highest value of BGHI (84.1) when compared to other types of coverage, characterizing a situation of lower thermal comfort, and no difference was found for THL and H on treatments in the studied region.

Evaluation of roof slope and exposure with different roofing materials in reduced models of animal production facilities in spring and summer

The present study was conducted at the Department of Rural Engineering and the Department of Animal Morphology and Physiology of FCAV/Unesp, Jaboticabal, SP, Brazil. The objective was to verify the influence of roof slope, exposure and roofing material on the internal temperature of reduced models of animal production facilities. For the development of the research, 48 reduced and dissemble models with dimensions 1.00 × 1.00 × 0.50 m were used. The roof was shed-type, and the models faced to the North or South directions, with 24 models for each side of exposure. Ceramic, galvanized-steel and fibro tiles were used to build the roofs. Slopes varied between 20, 30, 40 and 50% for the ceramic tile and 10, 30, 40 and 50% for the other two. Inside the models, temperature readings were performed at every hour, for 12 months. The results were evaluated in a general linear model in a nested 3 × 4 × 2 factorial arrangement, in which the effects of roofing material and exposure were nested on the factor Slope. Means were compared by the Tukey test at 5% of probability. After analyzing the data, we observed that with the increase in the slope and exposure to the South, there was a drop in the internal temperature within the model at the geographic coordinates of Jaboticabal city (SP/Brazil).

Thermal comfort in reduced models of broilers' houses, under different types of roofing materials

Esta pesquisa foi conduzida com o objetivo de avaliar diferentes tipos de coberturas em instalações para aves, por meio do Índice de Temperatura de Globo Negro e Umidade (ITGU), Carga Térmica de Radiação (CTR) e Entalpia (H). O experimento foi conduzido na Universidade Estadual de Goiás, entre os meses de abril e maio de 2011, sendo composto por cinco tratamentos (coberturas): CA -Telha de cimento-amianto; BA -Telha de bambu; BAP -Telha de bambu pintada de branco; FB -Telha de fibra vegetal e betume; FBP -Telha de fibra vegetal e betume pintada de branco, com 15 repetições, sendo as repetições os dias de medição. Dentre os horários estudados, o considerado menos confortável foi às 14h, sendo que a cobertura de fibra vegetal e betume foi a que apresentou maior valor de ITGU (84,1) quando comparada às demais coberturas, caracterizando uma situação de menor conforto térmico, não sendo observada diferença para CTR e H entre os tratamentos na região estudada.

Evaluation of roof slope and exposure with different roofing materials in reduced models of animal production facilities in spring and summer

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Reduced models of chemical reaction in chaotic flows

We describe and evaluate two reduced models for nonlinear chemical reactions in a chaotic laminar flow. Each model involves two separate steps to compute the chemical composition at a given location and time. The “manifold tracking model” first tracks backwards in time a segment of the stable manifold of the requisite point. This then provides a sample of the initial conditions appropriate for the second step, which requires solving one-dimensional problems for the reaction in Lagrangian coordinates. By contrast, the first step of the “branching trajectories model” simulates both the advection and diffusion of fluid particles that terminate at the appropriate point; the chemical reaction equations are then solved along each of the branched trajectories in a second step. Results from each model are compared with full numerical simulations of the reaction processes in a chaotic laminar flow.

A reduced model clarifies the role of feedback loops and time delays in the Drosophila circadian oscillator.

Although several detailed models of molecular processes essential for circadian oscillations have been developed, their complexity makes intuitive understanding of the oscillation mechanism difficult. The goal of the present study was to reduce a previously developed, detailed model to a minimal representation of the transcriptional regulation essential for circadian rhythmicity in Drosophila. The reduced model contains only two differential equations, each with time delays. A negative feedback loop is included, in which PER protein represses per transcription by binding the dCLOCK transcription factor. A positive feedback loop is also included, in which dCLOCK indirectly enhances its own formation. The model simulated circadian oscillations, light entrainment, and a phase-response curve with qualitative similarities to experiment. Time delays were found to be essential for simulation of circadian oscillations with this model. To examine the robustness of the simplified model to fluctuations in molecule numbers, a stochastic variant was constructed. Robust circadian oscillations and entrainment to light pulses were simulated with fewer than 80 molecules of each gene product present on average. Circadian oscillations persisted when the positive feedback loop was removed. Moreover, elimination of positive feedback did not decrease the robustness of oscillations to stochastic fluctuations or to variations in parameter values. Such reduced models can aid understanding of the oscillation mechanisms in Drosophila and in other organisms in which feedback regulation of transcription may play an important role.

THE NATURAL AND ORTHOGONAL INTERACTION (NOIA) MODELS FOR QUANTITATIVE TRAITS (QTs) AND COMPLEX DISEASES

My dissertation focuses on developing methods for gene-gene/environment interactions and imprinting effect detections for human complex diseases and quantitative traits. It includes three sections: (1) generalizing the Natural and Orthogonal interaction (NOIA) model for the coding technique originally developed for gene-gene (GxG) interaction and also to reduced models; (2) developing a novel statistical approach that allows for modeling gene-environment (GxE) interactions influencing disease risk, and (3) developing a statistical approach for modeling genetic variants displaying parent-of-origin effects (POEs), such as imprinting. In the past decade, genetic researchers have identified a large number of causal variants for human genetic diseases and traits by single-locus analysis, and interaction has now become a hot topic in the effort to search for the complex network between multiple genes or environmental exposures contributing to the outcome. Epistasis, also known as gene-gene interaction is the departure from additive genetic effects from several genes to a trait, which means that the same alleles of one gene could display different genetic effects under different genetic backgrounds. In this study, we propose to implement the NOIA model for association studies along with interaction for human complex traits and diseases. We compare the performance of the new statistical models we developed and the usual functional model by both simulation study and real data analysis. Both simulation and real data analysis revealed higher power of the NOIA GxG interaction model for detecting both main genetic effects and interaction effects. Through application on a melanoma dataset, we confirmed the previously identified significant regions for melanoma risk at 15q13.1, 16q24.3 and 9p21.3. We also identified potential interactions with these significant regions that contribute to melanoma risk. Based on the NOIA model, we developed a novel statistical approach that allows us to model effects from a genetic factor and binary environmental exposure that are jointly influencing disease risk. Both simulation and real data analyses revealed higher power of the NOIA model for detecting both main genetic effects and interaction effects for both quantitative and binary traits. We also found that estimates of the parameters from logistic regression for binary traits are no longer statistically uncorrelated under the alternative model when there is an association. Applying our novel approach to a lung cancer dataset, we confirmed four SNPs in 5p15 and 15q25 region to be significantly associated with lung cancer risk in Caucasians population: rs2736100, rs402710, rs16969968 and rs8034191. We also validated that rs16969968 and rs8034191 in 15q25 region are significantly interacting with smoking in Caucasian population. Our approach identified the potential interactions of SNP rs2256543 in 6p21 with smoking on contributing to lung cancer risk. Genetic imprinting is the most well-known cause for parent-of-origin effect (POE) whereby a gene is differentially expressed depending on the parental origin of the same alleles. Genetic imprinting affects several human disorders, including diabetes, breast cancer, alcoholism, and obesity. This phenomenon has been shown to be important for normal embryonic development in mammals. Traditional association approaches ignore this important genetic phenomenon. In this study, we propose a NOIA framework for a single locus association study that estimates both main allelic effects and POEs. We develop statistical (Stat-POE) and functional (Func-POE) models, and demonstrate conditions for orthogonality of the Stat-POE model. We conducted simulations for both quantitative and qualitative traits to evaluate the performance of the statistical and functional models with different levels of POEs. Our results showed that the newly proposed Stat-POE model, which ensures orthogonality of variance components if Hardy-Weinberg Equilibrium (HWE) or equal minor and major allele frequencies is satisfied, had greater power for detecting the main allelic additive effect than a Func-POE model, which codes according to allelic substitutions, for both quantitative and qualitative traits. The power for detecting the POE was the same for the Stat-POE and Func-POE models under HWE for quantitative traits.

Towards the systematic simplification of mechanistic models

Mechanistic models used for prediction should be parsimonious, as models which are over-parameterised may have poor predictive performance. Determining whether a model is parsimonious requires comparisons with alternative model formulations with differing levels of complexity. However, creating alternative formulations for large mechanistic models is often problematic, and usually time-consuming. Consequently, few are ever investigated. In this paper, we present an approach which rapidly generates reduced model formulations by replacing a model’s variables with constants. These reduced alternatives can be compared to the original model, using data based model selection criteria, to assist in the identification of potentially unnecessary model complexity, and thereby inform reformulation of the model. To illustrate the approach, we present its application to a published radiocaesium plant-uptake model, which predicts uptake on the basis of soil characteristics (e.g. pH, organic matter content, clay content). A total of 1024 reduced model formulations were generated, and ranked according to five model selection criteria: Residual Sum of Squares (RSS), AICc, BIC, MDL and ICOMP. The lowest scores for RSS and AICc occurred for the same reduced model in which pH dependent model components were replaced. The lowest scores for BIC, MDL and ICOMP occurred for a further reduced model in which model components related to the distinction between adsorption on clay and organic surfaces were replaced. Both these reduced models had a lower RSS for the parameterisation dataset than the original model. As a test of their predictive performance, the original model and the two reduced models outlined above were used to predict an independent dataset. The reduced models have lower prediction sums of squares than the original model, suggesting that the latter may be overfitted. The approach presented has the potential to inform model development by rapidly creating a class of alternative model formulations, which can be compared.

Hidden Schrödinger symmetry in FLRW and Bianchi I minisuperspace models of cosmology and black holes Schwarzschild dynamics

A broad sector of literature focuses on the relationship between fluid dynamics and gravitational systems. This thesis presents results that suggest the existence of a new kind of fluid/gravity duality not based on the holographic principle. The goal is to provide tools that allow us to systematically unearth hidden symmetries for reduced models of cosmology. The focus is on the field space of these models, i.e. the superspace. In fact, conformal isometries of the supermetric leave geodesics in the field space unaltered; this leads to symmetries of the models. An innovative aspect is the use of the Eisenhart-Duval’s lift. Using this method, systems constrained by a potential can be treated as free ones. Moreover, charges explicitly dependent on time, i.e. dynamical, can be found. A detailed analysis is carried out on three basic models of homogenous cosmology: i) flat Friedmann-Lemaître-Robertson-Walker’s isotropic universe filled with a massless scalar field; ii) Schwarzschild’s black hole mechanics and its extension to vacuum (A)dS gravity; iii) Bianchi’s anisotropic type I universe with a massless scalar field. The results show the presence of a hidden Schrödinger’s symmetry which, being intrinsic to both Navier-Stokes’ and Schrödinger’s equations, indicates a correspondence between cosmology and hydrodynamics. Furthermore, the central extension of this algebra explicitly relates two concepts. The first is the number of particles coming from the fluid picture; while the second is the ratio between the IR and UV cutoffs that weighs how much a theory has of “classical” over “quantum”. This suggests a spacetime that emerges from an underlying world which is described by quantum building blocks. These quanta statistically conspire to appear as gravitational phenomena from a macroscopic point of view.

Numerical schemes of diffusion asymptotics and moment closures for kinetic equations

We investigate different models that are intended to describe the small mean free path regime of a kinetic equation, a particular attention being paid to the moment closure by entropy minimization. We introduce a specific asymptotic-induced numerical strategy which is able to treat the stiff terms of the asymptotic diffusive regime. We evaluate on numerics the performances of the method and the abilities of the reduced models to capture the main features of the full kinetic equation.

Predicting Non Return to Work after Orthopaedic Trauma: The Wallis Occupational Rehabilitation RisK (WORRK) Model.

BACKGROUND: Workers with persistent disabilities after orthopaedic trauma may need occupational rehabilitation. Despite various risk profiles for non-return-to-work (non-RTW), there is no available predictive model. Moreover, injured workers may have various origins (immigrant workers), which may either affect their return to work or their eligibility for research purposes. The aim of this study was to develop and validate a predictive model that estimates the likelihood of non-RTW after occupational rehabilitation using predictors which do not rely on the worker's background. METHODS: Prospective cohort study (3177 participants, native (51%) and immigrant workers (49%)) with two samples: a) Development sample with patients from 2004 to 2007 with Full and Reduced Models, b) External validation of the Reduced Model with patients from 2008 to March 2010. We collected patients' data and biopsychosocial complexity with an observer rated interview (INTERMED). Non-RTW was assessed two years after discharge from the rehabilitation. Discrimination was assessed by the area under the receiver operating curve (AUC) and calibration was evaluated with a calibration plot. The model was reduced with random forests. RESULTS: At 2 years, the non-RTW status was known for 2462 patients (77.5% of the total sample). The prevalence of non-RTW was 50%. The full model (36 items) and the reduced model (19 items) had acceptable discrimination performance (AUC 0.75, 95% CI 0.72 to 0.78 and 0.74, 95% CI 0.71 to 0.76, respectively) and good calibration. For the validation model, the discrimination performance was acceptable (AUC 0.73; 95% CI 0.70 to 0.77) and calibration was also adequate. CONCLUSIONS: Non-RTW may be predicted with a simple model constructed with variables independent of the patient's education and language fluency. This model is useful for all kinds of trauma in order to adjust for case mix and it is applicable to vulnerable populations like immigrant workers.

Powder flow criteria for design of vertical silo walls

For design of vertical silos walls involving the storage of bulk solids to be safe and reliable, it is important knowing the largest possible number of variables such as: flow properties, silo geometry and pattern of flow desired. In order to validate the theories of flow prediction and design of conical hoppers, the flow properties of two bulk solids were determined, the theories of Jenike's flowability and Enstad and Walker for hopper design were analyzed and the results were compared with those experimentally obtained in a reduced model of a semicircular-section silo. Results show that Enstad theory for the hopper design is adequate to occur mass flow inside the silo, and for the sizing of the discharge outlet, the Walker's theory was closer to the appropriate than Jenike's theory, which was higher around 100% than the experimental hopper outlet.

Aplicação da resistividade e cargabilidade em estudos de contaminação de sedimentos por derivados de hidrocarbonetos

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Solitons, τ-functions and hamiltonian reduction for non-Abelian conformal affine Toda theories

We consider the Hamiltonian reduction of the two-loop Wess-Zumino-Novikov-Witten model (WZNW) based on an untwisted affine Kac-Moody algebra script Ĝ. The resulting reduced models, called Generalized Non-Abelian Conformal Affine Toda (G-CAT), are conformally invariant and a wide class of them possesses soliton solutions; these models constitute non-Abelian generalizations of the conformal affine Toda models. Their general solution is constructed by the Leznov-Saveliev method. Moreover, the dressing transformations leading to the solutions in the orbit of the vacuum are considered in detail, as well as the τ-functions, which are defined for any integrable highest weight representation of script Ĝ, irrespectively of its particular realization. When the conformal symmetry is spontaneously broken, the G-CAT model becomes a generalized affine Toda model, whose soliton solutions are constructed. Their masses are obtained exploring the spontaneous breakdown of the conformal symmetry, and their relation to the fundamental particle masses is discussed. We also introduce what we call the two-loop Virasoro algebra, describing extended symmetries of the two-loop WZNW models.