941 resultados para Orthogonal polynomials of a discrete variable


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In machine learning and pattern recognition tasks, the use of feature discretization techniques may have several advantages. The discretized features may hold enough information for the learning task at hand, while ignoring minor fluctuations that are irrelevant or harmful for that task. The discretized features have more compact representations that may yield both better accuracy and lower training time, as compared to the use of the original features. However, in many cases, mainly with medium and high-dimensional data, the large number of features usually implies that there is some redundancy among them. Thus, we may further apply feature selection (FS) techniques on the discrete data, keeping the most relevant features, while discarding the irrelevant and redundant ones. In this paper, we propose relevance and redundancy criteria for supervised feature selection techniques on discrete data. These criteria are applied to the bin-class histograms of the discrete features. The experimental results, on public benchmark data, show that the proposed criteria can achieve better accuracy than widely used relevance and redundancy criteria, such as mutual information and the Fisher ratio.

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A theory of free vibrations of discrete fractional order (FO) systems with a finite number of degrees of freedom (dof) is developed. A FO system with a finite number of dof is defined by means of three matrices: mass inertia, system rigidity and FO elements. By adopting a matrix formulation, a mathematical description of FO discrete system free vibrations is determined in the form of coupled fractional order differential equations (FODE). The corresponding solutions in analytical form, for the special case of the matrix of FO properties elements, are determined and expressed as a polynomial series along time. For the eigen characteristic numbers, the system eigen main coordinates and the independent eigen FO modes are determined. A generalized function of visoelastic creep FO dissipation of energy and generalized forces of system with no ideal visoelastic creep FO dissipation of energy for generalized coordinates are formulated. Extended Lagrange FODE of second kind, for FO system dynamics, are also introduced. Two examples of FO chain systems are analyzed and the corresponding eigen characteristic numbers determined. It is shown that the oscillatory phenomena of a FO mechanical chain have analogies to electrical FO circuits. A FO electrical resistor is introduced and its constitutive voltage–current is formulated. Also a function of thermal energy FO dissipation of a FO electrical relation is discussed.

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The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.

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A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

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Atypical P. vivax cases reported in Manaus municipality led us to detect a genetic isolate of P. vivax. Variable regions of SSUrRNA were examined from the initial time of infection and in the two recrudescences/relapses from a patient exhibiting chloroquine and primaquine resistance. A unique isolate, found at all stages of infection, suggests the presence of a clonal expansion.

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Dissertação para obtenção do Grau de Doutora em Estatística e Gestão de Risco, Especialidade em Estatística

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The nitrogen dioxide is a primary pollutant, regarded for the estimation of the air quality index, whose excessive presence may cause significant environmental and health problems. In the current work, we suggest characterizing the evolution of NO2 levels, by using geostatisti- cal approaches that deal with both the space and time coordinates. To develop our proposal, a first exploratory analysis was carried out on daily values of the target variable, daily measured in Portugal from 2004 to 2012, which led to identify three influential covariates (type of site, environment and month of measurement). In a second step, appropriate geostatistical tools were applied to model the trend and the space-time variability, thus enabling us to use the kriging techniques for prediction, without requiring data from a dense monitoring network. This method- ology has valuable applications, as it can provide accurate assessment of the nitrogen dioxide concentrations at sites where either data have been lost or there is no monitoring station nearby.

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The distribution and orientation of energy inside jets is predicted to be an experimental handle on colour connections between the hard--scatter quarks and gluons initiating the jets. This Letter presents a measurement of the distribution of one such variable, the jet pull angle. The pull angle is measured for jets produced in tt¯ events with one W boson decaying leptonically and the other decaying to jets using 20.3 fb−1 of data recorded with the ATLAS detector at a centre--of--mass energy of s√=8 TeV at the LHC. The jet pull angle distribution is corrected for detector resolution and acceptance effects and is compared to various models.

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The authors studied the rainfall in Pesqueira (Pernambuco, Brasil) in a period of 48 years (1910 through 1957) by the method of orthogonal polynomials, degrees up to the fourth having been tried. None of them was significant, so that it seems that no trend is present. The mean observed was 679.00 mm., with standard error of the mean 205.5 mm., and a 30.3% coefficient of variation. The 95% level of probability would include annual rainfall from 263.9 up to 1094.1mm.

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Our understanding of the population ecology of insect gallers is largely built on examples from temperate zones, but tropical and subtropical gallers may present distinct patterns of abundance and distribution across time. Eugeniamyia dispar Maia, Mendonça & Romanowski, 1996 is a multivoltine Neotropical cecidomyiid that induces spongy leaf galls on Eugenia uniflora (Myrtaceae). Galls were censused in the urban area of Porto Alegre, southern Brazil on six plants at two sites, for two years, at roughly weekly intervals. Overall 9,694 eggs, galling attempts and galls were counted. New galls continuously appear on developing leaves, but galls with live inducers are absent from June to at least early August. Galls on a same shoot develop synchronically, thus the shoot is probably the unit for oviposition. Given the also synchronic appearance of galls on different plants on a site, it seems midges can disperse and attack close-by plants. Gall cohorts varied in abundance by two orders of magnitude; there were more galls during summer than for spring and autumn, in a wave-like pattern. Host plant leaf production was seasonal, with low production during winter and cyclic production during the rest of the year. Perhaps because of this very variable pattern, gall abundance did not follow leaf production: this galler is not synchronised with its host at least during most of the year. This multivoltine gall inducer with "labile" galls, short development time, partially overlapping generations and low host synchronisation differs from the commonly studied species of the temperate regions providing a subject for ecological comparisons.

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The morphological characteristics of the mandible of adult Chaetophractus vellerosus (Gray, 1865) and Zaedyus pichiy (Desmarest, 1804) were studied to establish its generalized design and to identify inter- and intra- (sexual) specific differences. Morphological descriptions were complemented with the application of univariate and multivariate (analysis of correlation matrices, PCA, discriminant analysis) techniques. The mandible of both species is very similar, and is characterized by elevated condyle, well developed angular process, distinct coronoid process, tooth row which extends to the rear end of the angle between body and ramus, and unfused but firm symphysis. Although both armadillos are omnivorous, a more slender configuration of the jaw in Z. pichiy could be indicative of a better adaptation of its masticatory apparatus to insectivory. The PCA showed an almost total segregation of both species on PC1 (47.7% of the total variance), with C. vellerosus being associated to mandibles taller and with wider body and ramus. Zaedyus pichiy was characterized by heavy loadings of length parameters on PC2 (22.6% of the variance). A small degree of sexual dimorphism was found, with size-based differences in C. vellerosus (larger mandibles in females) and shape-based differences in Z. pichiy (taller mandibles in males, longer ones in females). Correlations between variables were higher in males of both species, indicating a more stable shape of the mandible than in females. The selected parameters to discriminate sexes were the body length of the mandible in C. vellerosus (correct classification: ca. 86% in males, 81% in females), and the height of the mandible at the level of the last tooth in Z. pichiy (near 85% of right assignment in both sexes). The inclusion of a new variable (body length) in the latter species improved the classification of the females to 100%. Teeth are typically 10 in C. vellerosus and 9 in Z. pichiy, but aberrancies in this basic number, such as unilateral or bilateral extra or fewer teeth, are common.

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Fractal geometry is a fundamental approach for describing the complex irregularities of the spatial structure of point patterns. The present research characterizes the spatial structure of the Swiss population distribution in the three Swiss geographical regions (Alps, Plateau and Jura) and at the entire country level. These analyses were carried out using fractal and multifractal measures for point patterns, which enabled the estimation of the spatial degree of clustering of a distribution at different scales. The Swiss population dataset is presented on a grid of points and thus it can be modelled as a "point process" where each point is characterized by its spatial location (geometrical support) and a number of inhabitants (measured variable). The fractal characterization was performed by means of the box-counting dimension and the multifractal analysis was conducted through the Renyi's generalized dimensions and the multifractal spectrum. Results showed that the four population patterns are all multifractals and present different clustering behaviours. Applying multifractal and fractal methods at different geographical regions and at different scales allowed us to quantify and describe the dissimilarities between the four structures and their underlying processes. This paper is the first Swiss geodemographic study applying multifractal methods using high resolution data.

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This paper reviews the evidence on the effects of recessions on potential output. In contrast to the assumption in mainstream macroeconomic models that economic fluctuations do not change potential output paths, the evidence is that they do in the case of recessions. A model is proposed to explain this phenomenon, based on an analogy with water flows in porous media. Because of the discrete adjustments made by heterogeneous economic agents in such a world, potential output displays hysteresis with regard to aggregate demand shocks, and thus retains a memory of the shocks associated with recessions.

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The hydrogen and oxygen isotopes of water and the carbon isotope composition of dissolved inorganic carbon (DIC) from different aquifers at an industrial site, highly contaminated by organic pollutants representing residues of the former gas production, have been used as natural tracers to characterize the hydrologic system. On the basis of their stable isotope compositions as well as the seasonal variations, different groups of waters (precipitation, surface waters, groundwaters and mineral waters) as well as seasonably variable processes of mixing between these waters can clearly be distinguished. In addition, reservoir effects and infiltration rates can be estimated. In the northern part of the site an influence of uprising mineral waters within the Quaternary aquifers, presumably along a fault zone, can be recognized. Marginal infiltration from the Neckar River in the cast and surface water infiltration adjacent to a steep hill on the western edge of the site with an infiltration rate of about one month can also be resolved through the seasonal variation. Quaternary aquifers closer to the centre of the site show no seasonal variations, except for one borehole close to a former mill channel and another borehole adjacent to a rain water channel. Distinct carbon isotope compositions and concentrations of DIC for these different groups of waters reflect variable influence of different components of the natural carbon cycle: dissolution of marine carbonates in the mineral waters, biogenic, soil-derived CO2 in ground- and surface waters, as well as additional influence of atmospheric CO2 for the surface waters. Many Quaternary aquifer waters have, however, distinctly lower delta(13)C(DIC) values and higher DIC concentrations compared to those expected for natural waters. Given the location of contaminated groundwaters at this site but also in the industrially well-developed valley outside of this site, the most likely source for the low C-13(DIC) values is a biodegradation of anthropogenic organic substances, in particular the tar oils at the site.

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This paper discusses how to identify individual-specific causal effects of an ordered discrete endogenous variable. The counterfactual heterogeneous causal information is recovered by identifying the partial differences of a structural relation. The proposed refutable nonparametric local restrictions exploit the fact that the pattern of endogeneity may vary across the level of the unobserved variable. The restrictions adopted in this paper impose a sense of order to an unordered binary endogeneous variable. This allows for a uni.ed structural approach to studying various treatment effects when self-selection on unobservables is present. The usefulness of the identi.cation results is illustrated using the data on the Vietnam-era veterans. The empirical findings reveal that when other observable characteristics are identical, military service had positive impacts for individuals with low (unobservable) earnings potential, while it had negative impacts for those with high earnings potential. This heterogeneity would not be detected by average effects which would underestimate the actual effects because different signs would be cancelled out. This partial identification result can be used to test homogeneity in response. When homogeneity is rejected, many parameters based on averages may deliver misleading information.