Spectral and homogenization problems

Dissertation for the Degree of Doctor of Philosophy in Mathematics

Moment Operators of Observables in Quantum Mechanics, with Applications to Quantization and Homodyne Detection

The questions studied in this thesis are centered around the moment operators of a quantum observable, the latter being represented by a normalized positive operator measure. The moment operators of an observable are physically relevant, in the sense that these operators give, as averages, the moments of the outcome statistics for the measurement of the observable. The main questions under consideration in this work arise from the fact that, unlike a projection valued observable of the von Neumann formulation, a general positive operator measure cannot be characterized by its first moment operator. The possibility of characterizing certain observables by also involving higher moment operators is investigated and utilized in three different cases: a characterization of projection valued measures among all the observables is given, a quantization scheme for unbounded classical variables using translation covariant phase space operator measures is presented, and, finally, a mathematically rigorous description is obtained for the measurements of rotated quadratures and phase space observables via the high amplitude limit in the balanced homodyne and eight-port homodyne detectors, respectively. In addition, the structure of the covariant phase space operator measures, which is essential for the above quantization, is analyzed in detail in the context of a (not necessarily unimodular) locally compact group as the phase space.

Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

Many valued algebraic structures as measures of comparison

This thesis studies the properties and usability of operators called t-norms, t-conorms, uninorms, as well as many valued implications and equivalences. Into these operators, weights and a generalized mean are embedded for aggregation, and they are used for comparison tasks and for this reason they are referred to as comparison measures. The thesis illustrates how these operators can be weighted with a differential evolution and aggregated with a generalized mean, and the kinds of measures of comparison that can be achieved from this procedure. New operators suitable for comparison measures are suggested. These operators are combination measures based on the use of t-norms and t-conorms, the generalized 3_-uninorm and pseudo equivalence measures based on S-type implications. The empirical part of this thesis demonstrates how these new comparison measures work in the field of classification, for example, in the classification of medical data. The second application area is from the field of sports medicine and it represents an expert system for defining an athlete's aerobic and anaerobic thresholds. The core of this thesis offers definitions for comparison measures and illustrates that there is no actual difference in the results achieved in comparison tasks, by the use of comparison measures based on distance, versus comparison measures based on many valued logical structures. The approach has been highly practical in this thesis and all usage of the measures has been validated mainly by practical testing. In general, many different types of operators suitable for comparison tasks have been presented in fuzzy logic literature and there has been little or no experimental work with these operators.

Genetic and environmental factors affecting ultrasound measures of longissimus muscle area and backfat thickness in Nelore cattle

The aim of the present study was to evaluate the genetic and environmental factors affecting records of longissimus muscle area (LMA) and back fat thickness (BF) obtained between the 12th and 13th ribs, and rump fat thickness (RF) between the hook and pin bones, measured by real-time ultrasound in Nelore cattle. Also, weight records of 22,778 animals born from 1998 to 2003, in ten farms across six Brazilian states were used. Carcass traits as measured by ultrasound of the live animal were recorded from 2002 to 2004 in 2590 males and females with ages varying from 450 to 599 days. Fixed models including farm, year and season of birth, sex and type of feed effects, and the covariates age of dam (AOD) and age of animal at measurement were used to study the effect of environmental factors on these traits. The genetic parameters for LMA, BF and RF were estimated with two and three-trait animal models with 120-day weights using a restricted maximum likelihood method. All environmental effects significantly affected carcass traits, with the exception of year of birth for BF and RF and AOD for LMA. The heritability estimates for LMA, BF and RF were 0.35, 0.51 and 0.39, respectively. Standard errors obtained in one-trait analyses were from 0.07 to 0.09. Genetic correlation estimates between LMA and the two traits of subcutaneous fat were low (close to zero) and 0.74 between BF and RF, indicating that the selection for LMA should not cause antagonism in the genetic improvement of subcutaneous fat measured by real-time ultrasound. (C) 2007 Elsevier B.V. All fights reserved.

Measuring and evaluating the impacts of TOD measures: searching for evidence of TOD characteristics in Azambuja train line

TOD (Transit Oriented Development) is typically defined as a high density mixed area (residential and commercial) within easy walking distance of a high capacity public transport station (typically within an 800m buffer area). TOO is viewed as a set of strategies to increase the use of public transport, increasing walking activity, containing urban sprawl, and creating more liveable places. It is believed that this type of combined strategies will improve sustainable growth. This work is an exploratory work for evidence of TOD characteristics in train station areas in Azambuja train line, setting further methodologies to evaluate the success of TOD areas.

Well-posedness and invariant measures for HJM models with deterministic volatility and Lévy noise

We give sufficient conditions for existence, uniqueness and ergodicity of invariant measures for Musiela's stochastic partial differential equation with deterministic volatility and a Hilbert space valued driving Lévy noise. Conditions for the absence of arbitrage and for the existence of mild solutions are also discussed.

Are superhumps good measures of the mass ratio for AM CVn systems?

We extend recent work that included the effect of pressure forces to derive the precession rate of eccentric accretion discs in cataclysmic variables to the case of double degenerate systems. We find that the logical scaling of the pressure force in such systems results in predictions of unrealistically high primary masses. Using the prototype AM CVn as a calibrator for the magnitude of the effect, we find that there is no scaling that applies consistently to all the systems in the class. We discuss the reasons for the lack of a superhump period to mass ratio relationship analogous to that known for SU UMa systems and suggest that this is because these secondaries do not have a single valued mass-radius relationship. We highlight the unreliability of mass-ratios derived by applying the SU UMa expression to the AM CVn binaries.

Time valued life cycle greenhouse gas emissions from buildings

The UK has adopted legally binding carbon reduction targets of 34% by 2020 and 80% by 2050 (measured against the 1990 baseline). Buildings are estimated to be responsible for more than 50% of greenhouse gas (GHG) emissions in the UK. These consist of both operational, produced during use, and embodied, produced during manufacture of materials and components, and during construction, refurbishments and demolition. A brief assessment suggests that it is unlikely that UK emission reduction targets can be met without substantial reductions in both Oc and Ec. Oc occurs over the lifetime of a building whereas the bulk of Ec occurs at the start of a building’s life. A time value for emissions could influence the decision making process when it comes to comparing mitigation measures which have benefits that occur at different times. An example might be the choice between building construction using low Ec construction materials versus building construction using high Ec construction materials but with lower Oc, although the use of high Ec materials does not necessarily imply a lower Oc. Particular time related issues examined here are: the urgency of the need to achieve large emissions reductions during the next 10 to 20 years; the earlier effective action is taken, the less costly it will be; future reduction in carbon intensity of energy supply; the carbon cycle and relationship between the release of GHG’s and their subsequent concentrations in the atmosphere. An equation is proposed, which weights emissions according to when they occur during the building life cycle, and which effectively increases Ec as a proportion of the total, suggesting that reducing Ec is likely to be more beneficial, in terms of climate change, for most new buildings. Thus, giving higher priority to Ec reductions is likely to result in a bigger positive impact on climate change and mitigation costs.

Building binary-tree-based multiclass classifiers using separability measures

Various popular machine learning techniques, like support vector machines, are originally conceived for the solution of two-class (binary) classification problems. However, a large number of real problems present more than two classes. A common approach to generalize binary learning techniques to solve problems with more than two classes, also known as multiclass classification problems, consists of hierarchically decomposing the multiclass problem into multiple binary sub-problems, whose outputs are combined to define the predicted class. This strategy results in a tree of binary classifiers, where each internal node corresponds to a binary classifier distinguishing two groups of classes and the leaf nodes correspond to the problem classes. This paper investigates how measures of the separability between classes can be employed in the construction of binary-tree-based multiclass classifiers, adapting the decompositions performed to each particular multiclass problem. (C) 2010 Elsevier B.V. All rights reserved.

Improved testing inference in mixed linear models

Mixed linear models are commonly used in repeated measures studies. They account for the dependence amongst observations obtained from the same experimental unit. Often, the number of observations is small, and it is thus important to use inference strategies that incorporate small sample corrections. In this paper, we develop modified versions of the likelihood ratio test for fixed effects inference in mixed linear models. In particular, we derive a Bartlett correction to such a test, and also to a test obtained from a modified profile likelihood function. Our results generalize those in [Zucker, D.M., Lieberman, O., Manor, O., 2000. Improved small sample inference in the mixed linear model: Bartlett correction and adjusted likelihood. Journal of the Royal Statistical Society B, 62,827-838] by allowing the parameter of interest to be vector-valued. Additionally, our Bartlett corrections allow for random effects nonlinear covariance matrix structure. We report simulation results which show that the proposed tests display superior finite sample behavior relative to the standard likelihood ratio test. An application is also presented and discussed. (C) 2008 Elsevier B.V. All rights reserved.

Efficacy of sulfadoxine plus trimethoprim compared to management measures for the control of Eimeria parasitism in naturally infected and clinically asymptomatic sheep that were maintained in a feedlot

The efficacy of sulfadoxine + trimethoprim in comparison to management measures for the control of Eimeria parasitism was studied in naturally infected sheep that were raised in a feedlot and were clinically asymptomatic for eimeriosis. Weight gain was also evaluated in these animals. The following groups were formed with 15 animals/group: TO!, control animals that received saline solution and maintenance of the same management measures that were performed before the study; T02, animals that received two intramuscular doses of sulfadoxine (20 mg/kg) + trimethoprim (4 mg/kg) with a 14-day interval; T03, sheep that received two intramuscular doses of sulfadoxine (20 mg/kg) + trimethoprim (4 mg/kg) with a 14-day interval plus management measures (wood shaving bedding was changed every Monday, and 30g of ammonium sulfate were applied to the bedding and other facilities were performed every Thursday, 10 mL/20 L of water); and T04, animals that received only the management measures described for the previous group. The highest efficacy rates (arithmetic mean) for the T02 group (sulfadoxine + trimethoprim at days 0 and 14) were 21.04% and 21.98% on the 14th and 28th days after the first treatment (DAFT), respectively. However, the treatment showed efficacy rates below 17% and was totally ineffective from the 70th DAFT to the end of the study. In both the T03 (chemical treatment+ management) and T04 (management only) groups, a significant (P <= 0.05) reduction of oocyst shedding per gram of feces was observed in the animals from the 14th DAFT in comparison to the control group; however, an efficacy rate above 90% was observed from the 28th DAFT. Animals belonging to the T02, T03 and T04 groups presented with alterations in weight gain of 0.57 kg, 4.30 kg and 4.53 kg, respectively, in comparison with the control animals (T01) throughout the 91-day study period. Thus, it is possible to conclude that the two-dose sulfadoxine + trimethoprim treatment, given with a 14-day interval, had little no effect on the oocyst shedding. Moreover, the adopted management measures were enough to cause a significant decrease in the animal parasite loads. (C) 2013 Published by Elsevier B.V.

Labor pain: Non-pharmacological measures preferred by parturient

Background: Labor pain is a legacy given by bipedalism, sendentarism and greater fetos robustness. It is expected that nurses mostly apply non-pharmacological methods of pain relief, putting the account of the mother to your preferences. Aim: To describe the women preferences about pain relief no-pharmacological measures. Method: Convenience sample of 180 parturients, with mean age of 30.81 years (SD = 5.31), ranging from 17 to 43 years. Results: all positions are valued as a pain relief way. The most valued, classified as "strongly relief" is the lateral decubitus in bed (45.7%), followed by walking (40.4%) and sitting swing (38.9%). Conclusion: Mothers show preference for traditional measure as lateral position on the bed. A greater familiarity with other relief measures could facilitate labor experience.

Self-reported Diabetes In Older People: Comparison Of Prevalences And Control Measures.

The objective of this study was to analyze the prevalence of diabetes in older people and the adopted control measures. Data regarding older diabetic individuals who participated in the Health Surveys conducted in the Municipality of Sao Paulo, SP, ISA-Capital, in 2003 and 2008, which were cross-sectional studies, were analyzed. Prevalences and confidence intervals were compared between 2003 and 2008, according to sociodemographic variables. The combination of the databases was performed when the confidence intervals overlapped. The Chi-square (level of significance of 5%) and the Pearson's Chi-square (Rao-Scott) tests were performed. The variables without overlap between the confidence intervals were not tested. The age of the older adults was 60-69 years. The majority were women, Caucasian, with an income of between > 0.5 and 2.5 times the minimum salary and low levels of schooling. The prevalence of diabetes was 17.6% (95%CI 14.9;20.6) in 2003 and 20.1% (95%CI 17.3;23.1) in 2008, which indicates a growth over this period (p at the limit of significance). The most prevalent measure adopted by the older adults to control diabetes was hypoglycemic agents, followed by diet. Physical activity was not frequent, despite the significant differences observed between 2003 and 2008 results. The use of public health services to control diabetes was significantly higher in older individuals with lower income and lower levels of education. Diabetes is a complex and challenging disease for patients and the health systems. Measures that encourage health promotion practices are necessary because they presented a smaller proportion than the use of hypoglycemic agents. Public health policies should be implemented, and aimed mainly at older individuals with low income and schooling levels. These changes are essential to improve the health condition of older diabetic patients.