Approximation of Univariate Set-Valued Functions - an Overview

2000 Mathematics Subject Classification: 26E25, 41A35, 41A36, 47H04, 54C65.

On the Mixed Modulus of Smoothness and a Class of Double Fourier Series

MSC 2010: 42A32; 42A20

Strict LpSolutions for Nonautonomous Fractional Evolution Equations

MSC 2010: 26A33, 34A08, 34K37

Cooperative greedy pursuit strategies for sparse signal representation by partitioning

Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition subjected to a global constraint on sparsity. The approach aims at producing a high quality sparse approximation of the whole signal, using highly coherent redundant dictionaries. The cooperation takes place by ranking the partition units for their sequential stepwise approximation, and is realized by means of i)forward steps for the upgrading of an approximation and/or ii) backward steps for the corresponding downgrading. The advantage of the strategy is illustrated by approximation of music signals using redundant trigonometric dictionaries. In addition to rendering stunning improvements in sparsity with respect to the concomitant trigonometric basis, these dictionaries enable a fast implementation of the approach via the Fast Fourier Transform

Fault diagnosis scheme for open-circuit faults in switched reluctance motor drives using fast Fourier transform algorithm with bus current detection

Reliability of power converters is of crucial importance in switched reluctance motor drives used for safety-critical applications. Open-circuit faults in power converters will cause the motor to run in unbalanced states, and if left untreated, they will lead to damage to the motor and power modules, and even cause a catastrophic failure of the whole drive system. This study is focused on using a single current sensor to detect open-circuit faults accurately. An asymmetrical half-bridge converter is considered in this study and the faults of single-phase open and two-phase open are analysed. Three different bus positions are defined. On the basis of a fast Fourier transform algorithm with Blackman window interpolation, the bus current spectrums before and after open-circuit faults are analysed in details. Their fault characteristics are extracted accurately by the normalisations of the phase fundamental frequency component and double phase fundamental frequency component, and the fault characteristics of the three bus detection schemes are also compared. The open-circuit faults can be located by finding the relationship between the bus current and rotor position. The effectiveness of the proposed diagnosis method is validated by the simulation results and experimental tests.

Improving the predictability of time series by chaotic parameter estimation

Limited literature regarding parameter estimation of dynamic systems has been identified as the central-most reason for not having parametric bounds in chaotic time series. However, literature suggests that a chaotic system displays a sensitive dependence on initial conditions, and our study reveals that the behavior of chaotic system: is also sensitive to changes in parameter values. Therefore, parameter estimation technique could make it possible to establish parametric bounds on a nonlinear dynamic system underlying a given time series, which in turn can improve predictability. By extracting the relationship between parametric bounds and predictability, we implemented chaos-based models for improving prediction in time series. ^ This study describes work done to establish bounds on a set of unknown parameters. Our research results reveal that by establishing parametric bounds, it is possible to improve the predictability of any time series, although the dynamics or the mathematical model of that series is not known apriori. In our attempt to improve the predictability of various time series, we have established the bounds for a set of unknown parameters. These are: (i) the embedding dimension to unfold a set of observation in the phase space, (ii) the time delay to use for a series, (iii) the number of neighborhood points to use for avoiding detection of false neighborhood and, (iv) the local polynomial to build numerical interpolation functions from one region to another. Using these bounds, we are able to get better predictability in chaotic time series than previously reported. In addition, the developments of this dissertation can establish a theoretical framework to investigate predictability in time series from the system-dynamics point of view. ^ In closing, our procedure significantly reduces the computer resource usage, as the search method is refined and efficient. Finally, the uniqueness of our method lies in its ability to extract chaotic dynamics inherent in non-linear time series by observing its values. ^

Three-dimensional brain fiber tracking modeling in diffusion tensor imaging

This dissertation establishes the foundation for a new 3-D visual interface integrating Magnetic Resonance Imaging (MRI) to Diffusion Tensor Imaging (DTI). The need for such an interface is critical for understanding brain dynamics, and for providing more accurate diagnosis of key brain dysfunctions in terms of neuronal connectivity. ^ This work involved two research fronts: (1) the development of new image processing and visualization techniques in order to accurately establish relational positioning of neuronal fiber tracts and key landmarks in 3-D brain atlases, and (2) the obligation to address the computational requirements such that the processing time is within the practical bounds of clinical settings. The system was evaluated using data from thirty patients and volunteers with the Brain Institute at Miami Children's Hospital. ^ Innovative visualization mechanisms allow for the first time white matter fiber tracts to be displayed alongside key anatomical structures within accurately registered 3-D semi-transparent images of the brain. ^ The segmentation algorithm is based on the calculation of mathematically-tuned thresholds and region-detection modules. The uniqueness of the algorithm is in its ability to perform fast and accurate segmentation of the ventricles. In contrast to the manual selection of the ventricles, which averaged over 12 minutes, the segmentation algorithm averaged less than 10 seconds in its execution. ^ The registration algorithm established searches and compares MR with DT images of the same subject, where derived correlation measures quantify the resulting accuracy. Overall, the images were 27% more correlated after registration, while an average of 1.5 seconds is all it took to execute the processes of registration, interpolation, and re-slicing of the images all at the same time and in all the given dimensions. ^ This interface was fully embedded into a fiber-tracking software system in order to establish an optimal research environment. This highly integrated 3-D visualization system reached a practical level that makes it ready for clinical deployment. ^

Spatial and Temporal Changes in Groundwater Salinity in South Florida

A combination of statistical and interpolation methods and Geographic Information System (GIS) spatial analysis was used to evaluate the spatial and temporal changes in groundwater Cl− concentrations in Collier and Lee Counties (southwestern Florida), and Miami-Dade and Broward Counties (southeastern Florida), since 1985. In southwestern Florida, the average Cl− concentrations in the shallow wells (0–43 m) in Collier and Lee Counties increased from 132 mg L−1 in 1985 to 230 mg L−1 in 2000. The average Cl− concentrations in the deep wells (>43 m) of southwestern Florida increased from 392 mg L−1 in 1985 to 447 mg L−1 in 2000. Results also indicated a positive correlation between the mean sea level and Cl− concentrations and between the mean sea level and groundwater levels for the shallow wells. Concentrations in the Biscayne Aquifer (southeastern Florida) were significantly higher than those of southwestern Florida. The average Cl− concentrations increased from 159 mg L−1 in 1985 to 470 mg L−1 in 2010 for the shallow wells (<33 m) and from 1360 mg L−1 in 1985 to 2050 mg L−1 in 2010 for the deep wells (>33 m). In the Biscayne Aquifer, wells showed a positive or negative correlation between mean sea level and Cl− concentrations according to their location with respect to the saltwater intrusion line. Wells located inland behind canal control structures and west of the saltwater intrusion line showed negative correlation values, whereas wells located east of the saltwater intrusion line showed positive values. Overall, the results indicated that since 1985, there was a potential decline in the available freshwater resources estimated at about 12–17% of the available drinking-quality groundwater of the southeastern study area located in the Biscayne Aquifer.

Rainfall variability in the upper Napo River Basin, Ecuadorian Amazon

The purpose of this research was to investigate the influence of elevation and other terrain characteristics over the spatial and temporal distribution of rainfall. A comparative analysis was conducted between several methods of spatial interpolations using mean monthly precipitation values in order to select the best. Following those previous results it was possible to fit an Artificial Neural Network model for interpolation of monthly precipitation values for a period of 20 years, with input values such as longitude, latitude, elevation, four geomorphologic characteristics and anchored by seven weather stations, it reached a high correlation coefficient (r=0.85). This research demonstrated a strong influence of elevation and other geomorphologic variables over the spatial distribution of precipitation and the agreement that there are nonlinear relationships. This model will be used to fill gaps in time-series of monthly precipitation, and to generate maps of spatial distribution of monthly precipitation at a resolution of 1km2.

Implementação de uma arquitetura fuzzy neural em hardware com treinamento online

Computational Intelligence Methods have been expanding to industrial applications motivated by their ability to solve problems in engineering. Therefore, the embedded systems follow the same idea of using computational intelligence tools embedded on machines. There are several works in the area of embedded systems and intelligent systems. However, there are a few papers that have joined both areas. The aim of this study was to implement an adaptive fuzzy neural hardware with online training embedded on Field Programmable Gate Array – FPGA. The system adaptation can occur during the execution of a given application, aiming online performance improvement. The proposed system architecture is modular, allowing different configurations of fuzzy neural network topologies with online training. The proposed system was applied to: mathematical function interpolation, pattern classification and selfcompensation of industrial sensors. The proposed system achieves satisfactory performance in both tasks. The experiments results shows the advantages and disadvantages of online training in hardware when performed in parallel and sequentially ways. The sequentially training method provides economy in FPGA area, however, increases the complexity of architecture actions. The parallel training method achieves high performance and reduced processing time, the pipeline technique is used to increase the proposed architecture performance. The study development was based on available tools for FPGA circuits.

Dinâmica das configurações de formação e inibição das chuvas no Rio Grande do Norte: caracterização hidroclimática do estado

This study aimed to evaluate the influence of the main meteorological mechanisms trainers and inhibitors of precipitation, and the interactions between different scales of operation, the spatial and temporal variability of the annual cycle of precipitation in the Rio Grande do Norte. Além disso, considerando as circunstâncias locais e regionais, criando assim uma base científica para apoiar ações futuras na gestão da demanda de água no Estado. Database from monthly precipitation of 45 years, ranging between 1963 and 2007, data provided by EMPARN. The methodology used to achieve the results was initially composed of descriptive statistical analysis of historical data to prove the stability of the series, were applied after, geostatistics tool for plotting maps of the variables, within the geostatistical we opted for by Kriging interpolation method because it was the method that showed the best results and minor errors. Among the results, we highlight the annual cycle of rainfall the State which is influenced by meteorological mechanisms of different spatial and temporal scales, where the main mechanisms cycle modulators are the Conference Intertropical Zone (ITCZ) acting since midFebruary to mid May throughout the state, waves Leste (OL), Lines of instability (LI), breeze systems and orographic rainfall acting mainly in the Coastal strip between February and July. Along with vortice of high levels (VCANs), Complex Mesoscale Convective (CCMs) and orographic rain in any region of the state mainly in spring and summer. In terms of larger scale phenomena stood out El Niño and La Niña, ENSO in the tropical Pacific basin. In La Niña episodes usually occur normal or rainy years, as upon the occurrence of prolonged periods of drought are influenced by EL NIÑO. In the Atlantic Ocean the standard Dipole also affects the intensity of the rainfall cycle in State. The cycle of rains in Rio Grande do Norte is divided into two periods, one comprising the regions West, Central and the Western Portion of the Wasteland Potiguar mesoregions of west Chapada Borborema, causing rains from midFebruary to mid-May and a second period of cycle, between February-July, where rains occur in mesoregions East and of the Wasteland, located upwind of the Chapada Borborema, both interspersed with dry periods without occurrence of significant rainfall and transition periods of rainy - dry and dry-rainy where isolated rainfall occur. Approximately 82% of the rainfall stations of the state which corresponds to 83.4% of the total area of Rio Grande do Norte, do not record annual volumes above 900 mm. Because the water supply of the State be maintained by small reservoirs already are in an advanced state of eutrophication, when the rains occur, act to wash and replace the water in the reservoirs, improving the quality of these, reducing the eutrophication process. When rain they do not significantly occur or after long periods of shortages, the process of eutrophication and deterioration of water in dams increased significantly. Through knowledge of the behavior of the annual cycle of rainfall can have an intimate knowledge of how it may be the tendency of rainy or prone to shortages following period, mainly observing the trends of larger scale phenomena

Estudo e aplicação da transformada de Fourier na regularização de dados sísmicos na exploração de petróleo

In the oil prospection research seismic data are usually irregular and sparsely sampled along the spatial coordinates due to obstacles in placement of geophones. Fourier methods provide a way to make the regularization of seismic data which are efficient if the input data is sampled on a regular grid. However, when these methods are applied to a set of irregularly sampled data, the orthogonality among the Fourier components is broken and the energy of a Fourier component may "leak" to other components, a phenomenon called "spectral leakage". The objective of this research is to study the spectral representation of irregularly sampled data method. In particular, it will be presented the basic structure of representation of the NDFT (nonuniform discrete Fourier transform), study their properties and demonstrate its potential in the processing of the seismic signal. In this way we study the FFT (fast Fourier transform) and the NFFT (nonuniform fast Fourier transform) which rapidly calculate the DFT (discrete Fourier transform) and NDFT. We compare the recovery of the signal using the FFT, DFT and NFFT. We approach the interpolation of seismic trace using the ALFT (antileakage Fourier transform) to overcome the problem of spectral leakage caused by uneven sampling. Applications to synthetic and real data showed that ALFT method works well on complex geology seismic data and suffers little with irregular spatial sampling of the data and edge effects, in addition it is robust and stable with noisy data. However, it is not as efficient as the FFT and its reconstruction is not as good in the case of irregular filling with large holes in the acquisition.

Estudo e aplicação da transformada de Fourier na regularização de dados sísmicos na exploração de petróleo

In the oil prospection research seismic data are usually irregular and sparsely sampled along the spatial coordinates due to obstacles in placement of geophones. Fourier methods provide a way to make the regularization of seismic data which are efficient if the input data is sampled on a regular grid. However, when these methods are applied to a set of irregularly sampled data, the orthogonality among the Fourier components is broken and the energy of a Fourier component may "leak" to other components, a phenomenon called "spectral leakage". The objective of this research is to study the spectral representation of irregularly sampled data method. In particular, it will be presented the basic structure of representation of the NDFT (nonuniform discrete Fourier transform), study their properties and demonstrate its potential in the processing of the seismic signal. In this way we study the FFT (fast Fourier transform) and the NFFT (nonuniform fast Fourier transform) which rapidly calculate the DFT (discrete Fourier transform) and NDFT. We compare the recovery of the signal using the FFT, DFT and NFFT. We approach the interpolation of seismic trace using the ALFT (antileakage Fourier transform) to overcome the problem of spectral leakage caused by uneven sampling. Applications to synthetic and real data showed that ALFT method works well on complex geology seismic data and suffers little with irregular spatial sampling of the data and edge effects, in addition it is robust and stable with noisy data. However, it is not as efficient as the FFT and its reconstruction is not as good in the case of irregular filling with large holes in the acquisition.

Global data compilation of benthic data sets II

In this study we present a global distribution pattern and budget of the minimum flux of particulate organic carbon to the sea floor (J POC alpha). The estimations are based on regionally specific correlations between the diffusive oxygen flux across the sediment-water interface, the total organic carbon content in surface sediments, and the oxygen concentration in bottom waters. For this, we modified the principal equation of Cai and Reimers [1995] as a basic monod reaction rate, applied within 11 regions where in situ measurements of diffusive oxygen uptake exist. By application of the resulting transfer functions to other regions with similar sedimentary conditions and areal interpolation, we calculated a minimum global budget of particulate organic carbon that actually reaches the sea floor of ~0.5 GtC yr**-1 (>1000 m water depth (wd)), whereas approximately 0.002-0.12 GtC yr**-1 is buried in the sediments (0.01-0.4% of surface primary production). Despite the fact that our global budget is in good agreement with previous studies, we found conspicuous differences among the distribution patterns of primary production, calculations based on particle trap collections of the POC flux, and J POC alpha of this study. These deviations, especially located at the southeastern and southwestern Atlantic Ocean, the Greenland and Norwegian Sea and the entire equatorial Pacific Ocean, strongly indicate a considerable influence of lateral particle transport on the vertical link between surface waters and underlying sediments. This observation is supported by sediment trap data. Furthermore, local differences in the availability and quality of the organic matter as well as different transport mechanisms through the water column are discussed.

Sea surface and the sea floor regionalization of the Southern Ocean by multivariate cluster analysis, links to ArcGIS project files

This study subdivides the Weddell Sea, Antarctica, into seafloor regions using multivariate statistical methods. These regions are categories used for comparing, contrasting and quantifying biogeochemical processes and biodiversity between ocean regions geographically but also regions under development within the scope of global change. The division obtained is characterized by the dominating components and interpreted in terms of ruling environmental conditions. The analysis uses 28 environmental variables for the sea surface, 25 variables for the seabed and 9 variables for the analysis between surface and bottom variables. The data were taken during the years 1983-2013. Some data were interpolated. The statistical errors of several interpolation methods (e.g. IDW, Indicator, Ordinary and Co-Kriging) with changing settings have been compared for the identification of the most reasonable method. The multivariate mathematical procedures used are regionalized classification via k means cluster analysis, canonical-correlation analysis and multidimensional scaling. Canonical-correlation analysis identifies the influencing factors in the different parts of the cove. Several methods for the identification of the optimum number of clusters have been tested. For the seabed 8 and 12 clusters were identified as reasonable numbers for clustering the Weddell Sea. For the sea surface the numbers 8 and 13 and for the top/bottom analysis 8 and 3 were identified, respectively. Additionally, the results of 20 clusters are presented for the three alternatives offering the first small scale environmental regionalization of the Weddell Sea. Especially the results of 12 clusters identify marine-influenced regions which can be clearly separated from those determined by the geological catchment area and the ones dominated by river discharge.