The analysis of uni- or multivariate time series provides crucial information to describe, understand, and predict climatic variability. The discovery and implementation of a number of novel methods for extracting useful information from time series has recently revitalized this classical eld of study. Considerable progress has also been made in interpreting the information so obtained in terms of dynamical systems theory.

Using the ideas of generalized linear stability theory, the authors examine the potential role that tropical variability on synoptic–intraseasonal timescales can play in controlling variability on seasonal–interannual timescales. These ideas are investigated using an intermediate coupled ocean–atmosphere model of the El Niño– Southern Oscillation (ENSO). The variability on synoptic–intraseasonal timescales is treated as stochastic noise that acts as a forcing function for variability at ENSO timescales. The spatial structure is computed that the stochastic noise forcing must have in order to enhance the variability of the system on seasonal–interannual timescales. These structures are the so-called stochastic optimals of the coupled system, and they bear a good resemblence to variability that is observed in the real atmosphere on synoptic and intraseasonal timescales. When the coupled model is subjected to a stochastic noise forcing composed of the stochastic optimals, variability on seasonal–interannual timescales develops that has spectral characteristics qualitatively similar to those seen in nature. The stochastic noise forcing produces perturbations in the system that can grow rapidly. The response of the system to the stochastic optimals is to induce perturbations that bear a strong resemblence to westerly and easterly wind bursts frequently observed in the western tropical Pacific. In the model, these ‘‘wind bursts’’ can act as efficient precursors for ENSO episodes if conditions are favorable. The response of the system to

Multivariate gait data have traditionally been challenging to analyze. Part 1 of this review explored applications of fuzzy, multivariate statistical and fractal methods to gait data analysis. Part 2 extends this critical review to the applications of artificial neural networks and wavelets to gait data analysis. The review concludes with a practical guide to the selection of alternative gait data analysis methods. Neural networks are found to be the most prevalent non-traditional methodology for gait data analysis in the last 10 years. Interpretation of multiple gait signal interactions and quantitative comparisons of gait waveforms are identified as important data analysis topics in need of further research.

Long-memory noise is common to many areas of signal processing and can seriously confound estimation of linear regression model parameters and their standard errors. Classical autoregressive moving average (ARMA) methods can adequately address the problem of linear time invariant, short-memory errors but may be inefficient and/or insufficient to secure type 1 error control in the context of fractal or scale invariant noise with a more slowly decaying autocorrelation function. Here we introduce a novel method, called wavelet-generalized least squares (WLS), which is (to a good approximation) the best linear unbiased (BLU) estimator of regression model parameters in the context of long-memory errors. The method also provides maximum likelihood (ML) estimates of the Hurst exponent

People sometimes solve problems with a unique process called insight, accompanied by an ‘‘Aha!’ ’ experience. It has long been unclear whether different cognitive and neural processes lead to insight versus noninsight solutions, or if solutions differ only in subsequent subjective feeling. Recent behavioral studies indicate distinct patterns of performance and suggest differential hemispheric involvement for insight and noninsight solutions. Subjects solved verbal problems, and after each correct solution indicated whether they solved with or without insight. We observed two objective neural correlates of insight. Functional magnetic resonance imaging (Experiment 1) revealed increased activity in the right hemisphere anterior superior temporal gyrus for insight relative to noninsight solutions. The same region was active during initial solving efforts. Scalp electroencephalogram recordings (Experiment 2) revealed a sudden burst of high-frequency (gamma-band) neural activity in the same area beginning 0.3 s prior to insight solutions. This right anterior temporal area is associated with making connections across distantly related information during comprehension. Although all problem solving relies on a largely shared cortical network, the sudden flash of insight occurs when solvers engage distinct neural and cognitive processes that allow them to see connections that previously eluded them.

Introduction The bivariate relationship between two time series is often of crucial interest in atmospheric science. For example, the Madden--Julian oscillation (MJO) [3] was found using bivariate spectral analysis between the station pressure and zonal wind components at Canton Island -- specifically the co-spectrum and magnitude squared coherence. We introduce the wavelet covariance and correlation between two time series based upon the maximal overlap DWT [6] and Daubechies families of wavelets [1, Sec. 6.2]. Key points include 4 the wavelet covariance decomposes the usual covariance on a scale by scale basis, 4 approximate confidence intervals may be calculated for estimators of the wavelet covariance and correlation, and 4 the wavelet cross-covariance and cross-correlation are used to investigate lead/lag relationships. We apply these wavelet estimators to the bivariate analysis of the Southern Oscillation Index (SOI), an

A new physically based prediction scheme for 20–30-day variability shows promise in monsoon regions for agricultural planning, disaster mitigation, and flood forecasting. During the summer of 2002, drought conditions persisted over India from mid-June to mid-July following a later-than-average arrival of seasonal monsoon rain. By the end of that summer, the average summer Indian rainfall totaled 711 mm or 19% below normal. With the exception of the area near the foothills of the Himalayas in the very north of India, where above-average rainfall occurred, most of India was in deficit, with the state of Rajasthan 64 % below normal. Figure 1 provides a geographical reference for the locations discussed in the text. The summer of 2002 was the sixth driest in 130 yr (Table 1).

: We formulate a nonparametric technique for estimating the mean-value function of a nonhomogeneous Poisson process having a long-term trend or some cyclic e#ect(s) that may lack familiar trigonometric characteristics such as symmetry over the corresponding cycle(s). This multiresolution procedure begins at the lowest level of resolution by estimating any long-term trend in the target counting process; then at progressively higher levels of resolution, the procedure yields estimates of the cyclic behavior associated with progressively smaller cycle lengths. We also formulate an e#cient algorithm for generating realizations of such counting processes. Keywords: Counting processes; Multiresolution estimation procedure; Simulation 1 Introduction In many simulation studies, we encounter arrival processes having a long-term trend or multiply periodic behavior. A prominent recent example is found in a large-scale simulation model of the organ procurement and transplantation network of the Un...

The discrete wavelet transform has be used extensively in the field of Statistics, mostly in the area of "denoising signals" or nonparametric regression. This thesis provides a new application for the discrete wavelet transform, assessing nonstationary events in time series -- especially long memory processes. Long memory processes are those which exhibit substantial correlations between events separated by a long period of time. Departures from stationarity in these heavily autocorrelated time series, such as an abrupt change in the variance at an unknown location or "bursts" of increased variability, can be detected and accurately located using discrete wavelet transforms -- both orthogonal and overcomplete. A cumulative sum of squares method, utilizing a Kolomogorov-Smirnov-type

Spatial outliers are the spatial objects with distinct features from their surrounding neighbors. Detection of spatial outliers helps reveal important and valuable information from large spatial data sets. In the field of meteorology, for example, spatial outliers can be associated with disastrous natural events such as tornadoes, hurricane, and forest fires. Previous study of spatial outlier mainly focuses on point data. However, in the meteorological data or other applications, spatial outliers are frequently represented in region, i.e., a group of points, with two dimensions or even three dimensions, and the previous point-based approaches may not be appropriate to be used. As region outliers are commonly multi-scale objects, wavelet analysis is an effective tool to study them. In this paper, we propose a wavelet analysis based approach to detect region outliers. We discuss the region outlier detection problem and design a suite of algorithms to effectively discover them. The algorithms were implemented and evaluated with a real-world meteorological data set.