Qualitative Characteristics and Quantitative Measures of Solution's Reliability in Discrete Optimization: Traditional Analytical Approaches, Innovative Computational Methods and Applicability

The purpose of this thesis is twofold. The first and major part is devoted to sensitivity analysis of various discrete optimization problems while the second part addresses methods applied for calculating measures of solution stability and solving multicriteria discrete optimization problems. Despite numerous approaches to stability analysis of discrete optimization problems two major directions can be single out: quantitative and qualitative. Qualitative sensitivity analysis is conducted for multicriteria discrete optimization problems with minisum, minimax and minimin partial criteria. The main results obtained here are necessary and sufficient conditions for different stability types of optimal solutions (or a set of optimal solutions) of the considered problems. Within the framework of quantitative direction various measures of solution stability are investigated. A formula for a quantitative characteristic called stability radius is obtained for the generalized equilibrium situation invariant to changes of game parameters in the case of the H¨older metric. Quality of the problem solution can also be described in terms of robustness analysis. In this work the concepts of accuracy and robustness tolerances are presented for a strategic game with a finite number of players where initial coefficients (costs) of linear payoff functions are subject to perturbations. Investigation of stability radius also aims to devise methods for its calculation. A new metaheuristic approach is derived for calculation of stability radius of an optimal solution to the shortest path problem. The main advantage of the developed method is that it can be potentially applicable for calculating stability radii of NP-hard problems. The last chapter of the thesis focuses on deriving innovative methods based on interactive optimization approach for solving multicriteria combinatorial optimization problems. The key idea of the proposed approach is to utilize a parameterized achievement scalarizing function for solution calculation and to direct interactive procedure by changing weighting coefficients of this function. In order to illustrate the introduced ideas a decision making process is simulated for three objective median location problem. The concepts, models, and ideas collected and analyzed in this thesis create a good and relevant grounds for developing more complicated and integrated models of postoptimal analysis and solving the most computationally challenging problems related to it.

Spectral invariant behavior of zenith radiance around cloud edges observed by ARM SWS

The ARM Shortwave Spectrometer (SWS) measures zenith radiance at 418 wavelengths between 350 and 2170 nm. Because of its 1-sec sampling resolution, the SWS provides a unique capability to study the transition zone between cloudy and clear sky areas. A spectral invariant behavior is found between ratios of zenith radiance spectra during the transition from cloudy to cloud-free. This behavior suggests that the spectral signature of the transition zone is a linear mixture between the two extremes (definitely cloudy and definitely clear). The weighting function of the linear mixture is a wavelength-independent characteristic of the transition zone. It is shown that the transition zone spectrum is fully determined by this function and zenith radiance spectra of clear and cloudy regions. An important result of these discoveries is that high temporal resolution radiance measurements in the clear-to-cloud transition zone can be well approximated by lower temporal resolution measurements plus linear interpolation.

Extreme value distribution for singular measures

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that, numerically, the Extreme Value distribution for these maps can be associated to the Generalised Extreme Value family where the parameters scale with the information dimension. The numerical analysis are performed on a few low dimensional maps. For the middle third Cantor set and the Sierpinskij triangle obtained using Iterated Function Systems, experimental parameters show a very good agreement with the theoretical values. For strange attractors like Lozi and H\`enon maps a slower convergence to the Generalised Extreme Value distribution is observed. Even in presence of large statistics the observed convergence is slower if compared with the maps which have an absolute continuous invariant measure. Nevertheless and within the uncertainty computed range, the results are in good agreement with the theoretical estimates.

SUPPORT OF MAXIMIZING MEASURES FOR TYPICAL C(0) DYNAMICS ON COMPACT MANIFOLDS

Given a compact manifold X, a continuous function g : X -> IR, and a map T : X -> X, we study properties of the T-invariant Borel probability measures that maximize the integral of g. We show that if X is a n-dimensional connected Riemaniann manifold, with n >= 2, then the set of homeomorphisms for which there is a maximizing measure supported on a periodic orbit is meager. We also show that, if X is the circle, then the ""topological size"" of the set of endomorphisms for which there are g maximizing measures with support on a periodic orbit depends on properties of the function g. In particular, if g is C(1), it has interior points.

Maximizing measures for endomorphisms of the circle

We study a given fixed continuous function phi : S(1) -> R and an endomorphism f : S(1)-> S(1), whose f-invariant probability measures maximize integral phi d mu. We prove that the set of endomorphisms having a f maximizing invariant measure supported on a periodic orbit is C(0) dense.

On maximizing measures of homeomorphisms on compact manifolds

We prove that given a compact n-dimensional connected Riemannian manifold X and a continuous function g : X -> R, there exists a dense subset of the space of homeomorphisms of X such that for all T in this subset, the integral integral(X) g d mu, considered as a function on the space of all T-invariant Borel probability measures mu, attains its maximum on a measure supported on a periodic orbit.

CID: an efficient complexity-invariant distance for time series

The ubiquity of time series data across almost all human endeavors has produced a great interest in time series data mining in the last decade. While dozens of classification algorithms have been applied to time series, recent empirical evidence strongly suggests that simple nearest neighbor classification is exceptionally difficult to beat. The choice of distance measure used by the nearest neighbor algorithm is important, and depends on the invariances required by the domain. For example, motion capture data typically requires invariance to warping, and cardiology data requires invariance to the baseline (the mean value). Similarly, recent work suggests that for time series clustering, the choice of clustering algorithm is much less important than the choice of distance measure used.In this work we make a somewhat surprising claim. There is an invariance that the community seems to have missed, complexity invariance. Intuitively, the problem is that in many domains the different classes may have different complexities, and pairs of complex objects, even those which subjectively may seem very similar to the human eye, tend to be further apart under current distance measures than pairs of simple objects. This fact introduces errors in nearest neighbor classification, where some complex objects may be incorrectly assigned to a simpler class. Similarly, for clustering this effect can introduce errors by “suggesting” to the clustering algorithm that subjectively similar, but complex objects belong in a sparser and larger diameter cluster than is truly warranted.We introduce the first complexity-invariant distance measure for time series, and show that it generally produces significant improvements in classification and clustering accuracy. We further show that this improvement does not compromise efficiency, since we can lower bound the measure and use a modification of triangular inequality, thus making use of most existing indexing and data mining algorithms. We evaluate our ideas with the largest and most comprehensive set of time series mining experiments ever attempted in a single work, and show that complexity-invariant distance measures can produce improvements in classification and clustering in the vast majority of cases.

Affect and cognition measures in preference-based decisions: Validity testing of the Ottawa Decisional Conflict Scale and a decision-specific anxiety measure with men eligible for prostate cancer screening

Background. At present, prostate cancer screening (PCS) guidelines require a discussion of risks, benefits, alternatives, and personal values, making decision aids an important tool to help convey information and to help clarify values. Objective: The overall goal of this study is to provide evidence of the reliability and validity of a PCS anxiety measure and the Decisional Conflict Scale (DCS). Methods. Using data from a randomized, controlled PCS decision aid trial that measured PCS anxiety at baseline and DCS at baseline (T0) and at two-weeks (T2), four psychometric properties were assessed: (1) internal consistency reliability, indicated by factor analysis intraclass correlations and Cronbach's α; (2) construct validity, indicated by patterns of Pearson correlations among subscales; (3) discriminant validity, indicated by the measure's ability to discriminate between undecided men and those with a definite screening intention; and (4) factor validity and invariance using confirmatory factor analyses (CFA). Results. The PCS anxiety measure had adequate internal consistency reliability and good construct and discriminant validity. CFAs indicated that the 3-factor model did not have adequate fit. CFAs for a general PCS anxiety measure and a PSA anxiety measure indicated adequate fit. The general PCS anxiety measure was invariant across clinics. The DCS had adequate internal consistency reliability except for the support subscale and had adequate discriminate validity. Good construct validity was found at the private clinic, but was only found for the feeling informed subscale at the public clinic. The traditional DCS did not have adequate fit at T0 or at T2. The alternative DCS had adequate fit at T0 but was not identified at T2. Factor loadings indicated that two subscales, feeling informed and feeling clear about values, were not distinct factors. Conclusions. Our general PCS anxiety measure can be used in PCS decision aid studies. The alternative DCS may be appropriate for men eligible for PCS. Implications: More emphasis needs to be placed on the development of PCS anxiety items relating to testing procedures. We recommend that the two DCS versions be validated in other samples of men eligible for PCS and in other health care decisions that involve uncertainty. ^

Invariant scaling relationships for interspecific plant biomass production rates and body size

The allometric relationships for plant annualized biomass production (“growth”) rates, different measures of body size (dry weight and length), and photosynthetic biomass (or pigment concentration) per plant (or cell) are reported for multicellular and unicellular plants representing three algal phyla; aquatic ferns; aquatic and terrestrial herbaceous dicots; and arborescent monocots, dicots, and conifers. Annualized rates of growth G scale as the 3/4-power of body mass M over 20 orders of magnitude of M (i.e., G ∝ M3/4); plant body length L (i.e., cell length or plant height) scales, on average, as the 1/4-power of M over 22 orders of magnitude of M (i.e., L ∝ M1/4); and photosynthetic biomass Mp scales as the 3/4-power of nonphotosynthetic biomass Mn (i.e., Mp ∝ Mn3/4). Because these scaling relationships are indifferent to phylogenetic affiliation and habitat, they have far-reaching ecological and evolutionary implications (e.g., net primary productivity is predicted to be largely insensitive to community species composition or geological age).

Quantum groups with invariant integrals

Quantum groups have been studied intensively for the last two decades from various points of view. The underlying mathematical structure is that of an algebra with a coproduct. Compact quantum groups admit Haar measures. However, if we want to have a Haar measure also in the noncompact case, we are forced to work with algebras without identity, and the notion of a coproduct has to be adapted. These considerations lead to the theory of multiplier Hopf algebras, which provides the mathematical tool for studying noncompact quantum groups with Haar measures. I will concentrate on the *-algebra case and assume positivity of the invariant integral. Doing so, I create an algebraic framework that serves as a model for the operator algebra approach to quantum groups. Indeed, the theory of locally compact quantum groups can be seen as the topological version of the theory of quantum groups as they are developed here in a purely algebraic context.

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.

Convergence Of Soil Nitrogen Isotopes Across Global Climate Gradients.

Quantifying global patterns of terrestrial nitrogen (N) cycling is central to predicting future patterns of primary productivity, carbon sequestration, nutrient fluxes to aquatic systems, and climate forcing. With limited direct measures of soil N cycling at the global scale, syntheses of the (15)N:(14)N ratio of soil organic matter across climate gradients provide key insights into understanding global patterns of N cycling. In synthesizing data from over 6000 soil samples, we show strong global relationships among soil N isotopes, mean annual temperature (MAT), mean annual precipitation (MAP), and the concentrations of organic carbon and clay in soil. In both hot ecosystems and dry ecosystems, soil organic matter was more enriched in (15)N than in corresponding cold ecosystems or wet ecosystems. Below a MAT of 9.8°C, soil δ(15)N was invariant with MAT. At the global scale, soil organic C concentrations also declined with increasing MAT and decreasing MAP. After standardizing for variation among mineral soils in soil C and clay concentrations, soil δ(15)N showed no consistent trends across global climate and latitudinal gradients. Our analyses could place new constraints on interpretations of patterns of ecosystem N cycling and global budgets of gaseous N loss.

Corpos na escola : (des)compassos entre a educação física e a religião = Bodies in school: (un)measures between physical education and religion

Universidade Estadual de Campinas . Faculdade de Educação Física

Insights into preventive measures for dental erosion

Dental erosion is defined as the loss of tooth substance by acid exposure not involving bacteria. The etiology of erosion is related to different behavioral, biological and chemical factors. Based on an overview of the current literature, this paper presents a summary of the preventive strategies relevant for patients suffering from dental erosion. Behavioral factors, such as special drinking habits, unhealthy lifestyle factors or occupational acid exposure, might modify the extent of dental erosion. Thus, preventive strategies have to include measures to reduce the frequency and duration of acid exposure as well as adequate oral hygiene measures, as it is known that eroded surfaces are more susceptible to abrasion. Biological factors, such as saliva or acquired pellicle, act protectively against erosive demineralization. Therefore, the production of saliva should be enhanced, especially in patients with hyposalivation or xerostomia. With regard to chemical factors, the modification of acidic solutions with ions, especially calcium, was shown to reduce the demineralization, but the efficacy depends on the other chemical factors, such as the type of acid. To enhance the remineralization of eroded surfaces and to prevent further progression of dental wear, high-concentrated fluoride applications are recommended. Currently, little information is available about the efficacy of other preventive strategies, such as calcium and laser application, as well as the use of matrix metalloproteinase inhibitors. Further studies considering these factors are required. In conclusion, preventive strategies for patients suffering from erosion are mainly obtained from in vitro and in situ studies and include dietary counseling, stimulation of salivary flow, optimization of fluoride regimens, modification of erosive beverages and adequate oral hygiene measures.

Validity and reliability of self-reported weight and height measures for the diagnoses of adolescent's nutritional status

OBJETIVO: Avaliar a validade do peso, estatura e Índice de Massa Corporal (IMC) referidos e sua confiabilidade para o diagnóstico do estado nutricional de adolescentes de Piracicaba. MÉTODOS: Participaram do estudo 360 adolescentes de ambos os sexos, de escolas públicas de Piracicaba, com idade entre 10 e 15 anos. Os adolescentes auto-relataram seu peso e estatura, sendo esses valores obtidos por medidas diretas, logo em seguida, pelos entrevistadores. A validade do IMC referido foi calculada segundo índices de sensibilidade, especificidade e valor preditivo positivo (VPP). Avaliou-se a concordância entre as categorias de IMC obtido por meio das medidas referidas e aferidas a partir do coeficiente kappa ponderado, coeficiente de correlação de Lin. e gráficos de Bland e Altman e Lin. RESULTADOS: Verificou-se que tanto os meninos quanto as meninas subestimaram o peso (-1,0 meninas e meninos) e a estatura (meninas -1,2 e meninos -0,8) (p < 0,001). Os valores de IMC aferidos e referidos apresentaram uma concordância moderada. A sensibilidade do IMC referido para classificar os indivíduos obesos foi maior para os meninos (87,5%), enquanto a especificidade foi maior para as meninas (92,7%). O VPP foi elevado somente para a classificação da eutrofia. CONCLUSÕES: As medidas referidas de peso e estatura de adolescentes não representam medidas válidas e, portanto, não devem ser usadas em substituição aos valores mensurados. Além disso, verificou-se que 10% dos meninos obesos e 40% das meninas obesas poderiam permanecer não identificados utilizando-se as medidas auto-referidas, confirmando a baixa validade das medidas auto-referidas.