Mathematical tests about the existence and applications of PPS-wavelets in function approximation problems

Neural networks and wavelet transform have been recently seen as attractive tools for developing eficient solutions for many real world problems in function approximation. Function approximation is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. So, mathematical model is a very important tool to guarantee the development of the neural network area. In this article we will introduce one series of mathematical demonstrations that guarantee the wavelets properties for the PPS functions. As application, we will show the use of PPS-wavelets in pattern recognition problems of handwritten digit through function approximation techniques.

Comparative study between RBF and radial-PPS neural networks

The study of function approximation is motivated by the human limitation and inability to register and manipulate with exact precision the behavior variations of the physical nature of a phenomenon. These variations are referred to as signals or signal functions. Many real world problem can be formulated as function approximation problems and from the viewpoint of artificial neural networks these can be seen as the problem of searching for a mapping that establishes a relationship from an input space to an output space through a process of network learning. Several paradigms of artificial neural networks (ANN) exist. Here we will be investigated a comparative of the ANN study of RBF with radial Polynomial Power of Sigmoids (PPS) in function approximation problems. Radial PPS are functions generated by linear combination of powers of sigmoids functions. The main objective of this paper is to show the advantages of the use of the radial PPS functions in relationship traditional RBF, through adaptive training and ridge regression techniques.

Multidimensional polynomial powers of sigmoid (PPS) Wavelet neural networks

Wavelet functions have been used as the activation function in feedforward neural networks. An abundance of R&D has been produced on wavelet neural network area. Some successful algorithms and applications in wavelet neural network have been developed and reported in the literature. However, most of the aforementioned reports impose many restrictions in the classical backpropagation algorithm, such as low dimensionality, tensor product of wavelets, parameters initialization, and, in general, the output is one dimensional, etc. In order to remove some of these restrictions, a family of polynomial wavelets generated from powers of sigmoid functions is presented. We described how a multidimensional wavelet neural networks based on these functions can be constructed, trained and applied in pattern recognition tasks. As an example of application for the method proposed, it is studied the exclusive-or (XOR) problem.

Human face verification based on multidimensional Polynomial Powers of Sigmoid (PPS)

In this paper, we described how a multidimensional wavelet neural networks based on Polynomial Powers of Sigmoid (PPS) can be constructed, trained and applied in image processing tasks. In this sense, a novel and uniform framework for face verification is presented. The framework is based on a family of PPS wavelets,generated from linear combination of the sigmoid functions, and can be considered appearance based in that features are extracted from the face image. The feature vectors are then subjected to subspace projection of PPS-wavelet. The design of PPS-wavelet neural networks is also discussed, which is seldom reported in the literature. The Stirling Universitys face database were used to generate the results. Our method has achieved 92 % of correct detection and 5 % of false detection rate on the database.

Feedforward neural networks based on PPS-wavelet activation functions

Function approximation is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. Neural networks and wavenets have been recently seen as attractive tools for developing efficient solutions for many real world problems in function approximation. In this paper, it is shown how feedforward neural networks can be built using a different type of activation function referred to as the PPS-wavelet. An algorithm is presented to generate a family of PPS-wavelets that can be used to efficiently construct feedforward networks for function approximation.

Wavelets And Adaptive Grids For The Discontinuous Galerkin Method

In this paper, space adaptivity is introduced to control the error in the numerical solution of hyperbolic systems of conservation laws. The reference numerical scheme is a new version of the discontinuous Galerkin method, which uses an implicit diffusive term in the direction of the streamlines, for stability purposes. The decision whether to refine or to unrefine the grid in a certain location is taken according to the magnitude of wavelet coefficients, which are indicators of local smoothness of the numerical solution. Numerical solutions of the nonlinear Euler equations illustrate the efficiency of the method. © Springer 2005.

Analysis of stock market indices with multidimensional scaling and wavelets

Stock market indices SMIs are important measures of financial and economical performance. Considerable research efforts during the last years demonstrated that these signals have a chaotic nature and require sophisticated mathematical tools for analyzing their characteristics. Classical methods, such as the Fourier transform, reveal considerable limitations in discriminating different periods of time. This paper studies the dynamics of SMI by combining the wavelet transform and the multidimensional scaling MDS . Six continuous wavelets are tested for analyzing the information content of the stock signals. In a first phase, the real Shannon wavelet is adopted for performing the evaluation of the SMI dynamics, while their comparison is visualized by means of the MDS. In a second phase, the other wavelets are also tested, and the corresponding MDS plots are analyzed.

Classificação automática do sono: Contribuição utilizando distância de Itakura-Saito e Wavelets

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Engenharia Electrotécnica e de Computadores

ECG wave detector and delineation with wavelets

Proceedings of the International Conference on Computational Intelligence in Medicine Healthcare, CIMED 2005, Costa da Caparica, June 29 - July 1, 2005

Alterações da Actividade Autonómica Durante o Teste de Inclinação em Doentes com Fibrilhação Auricular Paroxística: Análise com Wavelets

The autonomic nervous system (ANS) is known to be an important modulator in the pathogenesis of paroxysmal atrial fibrillation (PAF). Changes in ANS control of heart rate variability (HRV) occur during orthostatism to maintain cardiovascular homeostasis. Wavelet transform has emerged as a useful tool that provides time-frequency decomposition of the signal under investigation, enabling intermittent components of transient phenomena to be analyzed. AIM: To study HRV during head-up tilt (HUT) with wavelet transform analysis in PAF patients and healthy individuals (normals). METHODS: Twenty-one patients with PAF (8 men; age 58 +/- 14 yrs) were examined and compared with 21 normals (7 men, age 48 +/- 12 yrs). After a supine resting period, all subjects underwent passive HUT (60 degrees) while in sinus rhythm. Continuous monitoring of ECG and blood pressure was carried out (Task Force Monitor, CNSystems). Acute changes in RR-intervals were assessed by wavelet analysis and low-frequency power (LF: 0.04-0.15 Hz), high-frequency power (HF: 0.15-0.60 Hz) and LF/HF (sympathovagal) were calculated for 1) the last 2 min of the supine period; 2) the 15 sec of tilting movement (TM); and 3) the 1st (TT1) and 2nd (TT2) min of HUT. Data are expressed as means +/- SEM. RESULTS: Baseline and HUT RR-intervals were similar for the two groups. Supine basal blood pressure was also similar for the two groups, with a sustained increase in PAF patients, and a decrease followed by an increase and then recovery in normals. Basal LF, HF and LF/ HF values in PAF patients were 632 +/- 162 ms2, 534 +/- 231 ms2 and 1.95 +/- 0.39 respectively, and 1058 +/- 223 ms2, 789 +/- 244 ms2 and 2.4 +/- 0.36 respectively in normals (p = NS). During TM, LF, HF and LF/HF values for PAF patients were 747 +/- 277 ms2, 387 +/- 94 ms2 and 2.9 +/- 0.6 respectively, and 1316 +/- 315 ms2, 698 +/- 148 ms2 and 2.8 +/- 0.6 respectively in normals (p < 0.05 for LF and HF). During TF1, LF, HF and LF/ HF values for PAF patients were 1243 +/- 432 ms2, 302 +/- 88 ms2 and 7.7 +/- 2.4 respectively, and 1992 +/- 398 ms2, 333 +/- 76 ms2 and 7.8 +/- 0.98 respectively for normals (p < 0.05 for LF). During TF2, LF, HF and LF/HF values for PAF patients were 871 +/- 256 ms2, 242 +/- 51 ms2 and 4.7 +/- 0.9 respectively, and 1263 +/- 335 ms2, 317 +/- 108 ms2 and 8.6 +/- 0.68 respectively for normals (p < 0.05 for LF/HF). The dynamic profile of HRV showed that LF and HF values in PAF patients did not change significantly during TM or TT2, and LF/HF did not change during TM but increased in TT1 and TT2. CONCLUSION: Patients with PAF present alterations in HRV during orthostatism, with decreased LF and HF power during TM, without significant variations during the first minutes of HUT. These findings suggest that wavelet transform analysis may provide new insights when assessing autonomic heart regulation and highlight the presence of ANS disturbances in PAF.

Análise espectral com wavelets do ECoG em crises epilépticas

Dissertação para obtenção do Grau de Mestre em Engenharia Biomédica

Previsão de consumo de energia de curto-prazo (dia seguinte) com recurso a wavelets

A actividade de produção de energia eléctrica, bem como o seu transporte e distri-buição até aos consumidores finais iniciou-se no final do século XIX e, desde essa altura, o sector tem conhecido muitas transformações aos mais variados níveis. Mais recentemente, nas últimas décadas, o sector eléctrico tem enfrentado muitos desafios que têm contribuí-do bastante para o seu desenvolvimento e inovação. A previsão de consumos de energia eléctrica é tradicionalmente importante para o equilíbrio entre a oferta e a procura, bem como para uma rigorosa gestão e planeamento das redes eléctricas de transporte e distribuição. A sua importância é ainda reforçada, ac-tualmente, com a liberalização dos mercados energéticos, na medida que os comercializa-dores pretendem dispor de ferramentas que lhes permita estimar com precisão a curva de procura agregada de consumidores com quem contratualizam. Os sistemas de previsão de carga podem ser classificados de acordo com o horizonte temporal, sendo regularmente divididos em três categorias: previsão a longo prazo; pre-visão a médio prazo; previsão a curto prazo. Neste trabalho de dissertação, pretende-se desenvolver um sistema de previsão de consumo de energia para o dia seguinte (hora a hora) com o recurso a Wavelets, capaz de apresentar o consumo associado a cada período horário ao longo do dia. Para tal, foram desenvolvidos dois métodos que diferem entre si na forma como o conceito de Wavelets é aplicado na decomposição dos dados.

Application of wavelets to the study of political history

\The idea that social processes develop in a cyclical manner is somewhat like a `Lorelei'. Researchers are lured to it because of its theoretical promise, only to become entangled in (if not wrecked by) messy problems of empirical inference. The reasoning leading to hypotheses of some kind of cycle is often elegant enough, yet the data from repeated observations rarely display the supposed cyclical pattern. (...) In addition, various `schools' seem to exist which frequently arrive at di erent conclusions on the basis of the same data." (van der Eijk and Weber 1987:271). Much of the empirical controversies around these issues arise because of three distinct problems: the coexistence of cycles of di erent periodicities, the possibility of transient cycles and the existence of cycles without xed periodicity. In some cases, there are no reasons to expect any of these phenomena to be relevant. Seasonality caused by Christmas is one such example (Wen 2002). In such cases, researchers mostly rely on spectral analysis and Auto-Regressive Moving-Average (ARMA) models to estimate the periodicity of cycles.1 However, and this is particularly true in social sciences, sometimes there are good theoretical reasons to expect irregular cycles. In such cases, \the identi cation of periodic movement in something like the vote is a daunting task all by itself. When a pendulum swings with an irregular beat (frequency), and the extent of the swing (amplitude) is not constant, mathematical functions like sine-waves are of no use."(Lebo and Norpoth 2007:73) In the past, this di culty has led to two di erent approaches. On the one hand, some researchers dismissed these methods altogether, relying on informal alternatives that do not meet rigorous standards of statistical inference. Goldstein (1985 and 1988), studying the severity of Great power wars is one such example. On the other hand, there are authors who transfer the assumptions of spectral analysis (and ARMA models) into fundamental assumptions about the nature of social phenomena. This type of argument was produced by Beck (1991) who, in a reply to Goldstein (1988), claimed that only \ xed period models are meaningful models of cyclic phenomena".We argue that wavelet analysis|a mathematical framework developed in the mid-1980s (Grossman and Morlet 1984; Goupillaud et al. 1984) | is a very viable alternative to study cycles in political time-series. It has the advantage of staying close to the frequency domain approach of spectral analysis while addressing its main limitations. Its principal contribution comes from estimating the spectral characteristics of a time-series as a function of time, thus revealing how its di erent periodic components may change over time. The rest of article proceeds as follows. In the section \Time-frequency Analysis", we study in some detail the continuous wavelet transform and compare its time-frequency properties with the more standard tool for that purpose, the windowed Fourier transform. In the section \The British Political Pendulum", we apply wavelet analysis to essentially the same data analyzed by Lebo and Norpoth (2007) and Merrill, Grofman and Brunell (2011) and try to provide a more nuanced answer to the same question discussed by these authors: do British electoral politics exhibit cycles? Finally, in the last section, we present a concise list of future directions.

Haar wavelets-based approach for quantifying credit portfolio losses

This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelet basis functions and calculate the coefficients of the approximation by inverting its Laplace transform. The Wavelet Approximation (WA) method is specially suitable for non-smooth distributions, often arising in small or concentrated portfolios, when the hypothesis of the Basel II formulas are violated. To test the methodology we consider the Vasicek one-factor portfolio credit loss model as our model framework. WA is an accurate, robust and fast method, allowing to estimate VaR much more quickly than with a Monte Carlo (MC) method at the same level of accuracy and reliability.

IPH response to PPS 12: Draft Policy HS 3 (Amended) Travellers Accommodation

The Amendment to Policy HS 3 of PPS 12 furthers the Minister’s commitment to meeting the distinctive accommodation needs of travellers. The existing policy HS 3 contained in PPS 12 provides for grouped housing, serviced sites, and transit sites for travellers within, adjoining or in close proximity to settlements. However, outside settlements there is only limited provision for grouped housing and transit sites – not serviced sites. This amendment provides policy for serviced sites for travellers outside settlements.