Narrow Results

The Temporal Sampling Framework (TSF) theorizes that the characteristic phonological difficulties of dyslexia are caused by an atypical oscillatory sampling at one or more temporal rates. The LEEDUCA study conducted a series of Electroencephalography (EEG) experiments on children listening to amplitude modulated (AM) noise with slow-rythmic prosodic (0.5–1Hz), syllabic (4–8Hz) or the phoneme (12–40Hz) rates, aimed at detecting differences in perception of oscillatory sampling that could be associated with dyslexia. The purpose of this work is to check whether these differences exist and how they are related to children’s performance in different language and cognitive tasks commonly used to detect dyslexia. To this purpose, temporal and spectral inter-channel EEG connectivity was estimated, and a denoising autoencoder (DAE) was trained to learn a low-dimensional representation of the connectivity matrices. This representation was studied via correlation and classification analysis, which revealed ability in detecting dyslexic subjects with an accuracy higher than 0.8, and balanced accuracy around 0.7. Some features of the DAE representation were significantly correlated ($p<0.005$) with children’s performance in language and cognitive tasks of the phonological hypothesis category such as phonological awareness and rapid symbolic naming, as well as reading efficiency and reading comprehension. Finally, a deeper analysis of the adjacency matrix revealed a reduced bilateral connection between electrodes of the temporal lobe (roughly the primary auditory cortex) in DD subjects, as well as an increased connectivity of the F7 electrode, placed roughly on Broca’s area. These results pave the way for a complementary assessment of dyslexia using more objective methodologies such as EEG.

An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicates the intrinsic limitations of spectral methods when it comes to the task of measuring frequencies. Other examples, one from medicine and one from bifurcation theory, are given, which also exhibit these limitations of spectral methods. For two methods of spectral estimation it is verified that the particular way end points are treated, which is specific to each method, is, for long enough time series, not relevant for the main result.

In this article, we study the empirical power of Bartlett's Kolmogorov–Smirnov test statistic derived from cumulative periodograms in detecting chaos. In our study, we simulated 10 000 time series of i.i.d. standard normal random variable, logistic map and Gaussian chaotic map of various lengths with and without measurement errors. The empirical power was assessed for the original series and its order transformed series. Although our results showed that the Bartlett's test statistic was not a powerful test statistic in detecting chaos when it is applied directly to the original series generated by the logistic map and the Gaussian chaotic map, the order transformation technique can significantly increase the power of the Bartlett's test statistic.

A stationary time series is said to be long-range dependent (LRD) if its autocovariance function decays as a power of the lag, in such a way that the sum (over all lags) of the autocovariances diverges. The asymptotic rate of decay is determined by a parameter H, called the Hurst parameter. The time series is said to be short-range dependent (H = 1/2) if the sum converges. It is commonly believed that a random permutation of a sequence maintains the marginal distribution of each element but destroys the dependence, and in particular, that a random permutation of an LRD sequence creates a new sequence whose estimate of Hurst parameter H is close to 1/2. This paper provides a theoretical basis for investigating these claims. In reality, a complete random permutation does not destroy the covariances, but merely equalizes them. The common value of the equalized covariances depends on the length N of the original sequence and it decreases to 0 as N → ∞. Using the periodogram method, we explain why one is led to think, mistakenly, that the randomized sequence yields an "estimated H close to 1/2.".

Bucket random permutations (shuffling) are used to modify the dependence structure of a time series, and this may destroy long-range dependence, when it is present. Three types of bucket permutations are considered here: external, internal and two-level permutations. It is commonly believed that (1) an external random permutation destroys the long-range dependence and keeps the short-range dependence, (2) an internal permutation destroys the short-range dependence and keeps the long-range dependence, and (3) a two-level permutation distorts the medium-range dependence while keeping both the long-range and short-range dependence. This paper provides a theoretical basis for investigating these claims. It extends the study started in Ref. 1 and analyze the effects that these random permutations have on a long-range dependent finite variance stationary sequence both in the time domain and in the frequency domain.

The aim of this paper is to make inference about a general class of time series models including fractional Brownian motion. The spectral of these processes is supported on lines not parallel to the diagonal $T_1(x)=x$, $T_j(x)={\alpha }_{j}x\pm {\beta }_j$, $j=2,\dots ,m$, in spectral square $[0,2\pi )\times [0,2\pi )$, and this class includes stationary, cyclostationary, almost cyclostationary time series and specially fractional Brownian motions. First, the periodogram of these processes is defined and auxiliary operator is applied to explore the distribution of the periodogram. Then the asymptotical estimation for the spectral density function is proposed and asymptotical Wishart function is found. Finally, the validity of the theoretical results is studied using simulated data sets.

We propose an asymptotically unbiased and consistent estimate of the bispectrum of a stationary continuous-time process X = {X(t)}_t∈ℝ. The estimate is constructed from observations obtained by a random sampling of the time by {X(τ_k)}_k∈ℤ, where {τ_k}_k∈ℤ is a sequence of real random variables, generated from a Poisson counting process. Moreover, we establish the asymptotic normality of the constructed estimate.