We aimed to evaluate the effects of mental workload variations, as a function of the road environment, on the brain activity of army drivers performing combat and non-combat scenarios in a light multirole vehicle dynamic simulator. Forty-one non-commissioned officers completed three standardized driving exercises with different terrain complexities (low, medium, and high) while we recorded their electroencephalographic (EEG) activity. We focused on variations in the theta EEG power spectrum, a well-known index of mental workload. We also assessed performance and subjective ratings of task load. The theta EEG power spectrum in the frontal, temporal, and occipital areas were higher during the most complex scenarios. Performance (number of engine stops) and subjective data supported these findings. Our findings strengthen previous results found in civilians on the relationship between driver mental workload and the theta EEG power spectrum. This suggests that EEG activity can give relevant insight into mental workload variations in an objective, unbiased fashion, even during real training and/or operations. The continuous monitoring of the warfighter not only allows instantaneous detection of over/underload but also might provide online feedback to the system (either automated equipment or the crew) to take countermeasures and prevent fatal errors.

Fourier parameters display the spectral content of a signal and provide explicit representations in the frequency domain. In the case of electroencephalograms, the FFT algorithm was the only quantifying method used until the 1970s, but this analysis is not conclusive in most pathologies. Fractal techniques provide new tools for the processing of signals whose traces have a sophisticated geometric complexity. The fractal dimension is computed easily in our work by means of explicit formulae involving the time samples. In this paper we obtain, under some hypotheses, an exact relation between the Fourier Transform of a signal and its Fractal Dimension. In the last part of the paper, an electroencephalographic application involving fractal and spectral parameters is described.

Inspired by the ideas of R. Kannan, we define the new concepts of mutual Kannan contractivity and mutual contractivity between two self-maps on a metric space that generalize the concepts of the Kannan map and contraction. We give some examples and deduce the properties of the operators satisfying this type of condition; in particular, we study the case where the space is normed, and the maps are linear. Then we generalize some theorems proposed by this author on the existence of a fixed point of one operator or a common fixed point for two operators. Our results first prove the existence of a common fixed point of a set of self-maps of any cardinal number (countable or uncountable) satisfying the conditions of Kannan type in metric spaces. The same is proved for a set of maps satisfying the mutual relations of classical contractivity. We prove in both cases the convergence of iterative schemes involving operators with mutual relations of contractivity, proposing sufficient conditions for the iteration of the operators on any element of the space to converge to the common fixed point when a different operator is taken in each step. The results obtained are applied to operators acting on real functions, coming from the fractal convolution with the null function.

This article explores the properties of fractal interpolation functions with variable scaling parameters, in the context of smooth fractal functions. The first part extends the Barnsley–Harrington theorem for differentiability of fractal functions and the fractal analogue of Hermite interpolation to the present setting. The general result is applied on a special class of iterated function systems in order to develop differentiability of the so-called $\boldsymbol{{\it\alpha}}$ -fractal functions. This leads to a bounded linear map on the space ${\mathcal{C}}^{k}(I)$ which is exploited to prove the existence of a Schauder basis for ${\mathcal{C}}^{k}(I)$ consisting of smooth fractal functions.

In this paper, we introduce the notion of cyclic generalized iterated function system (GIFS), which is a family of functions f₁, f₂,…,f_M : X^k→X, where each f_i is a cyclic generalized φ-contraction (contractive) map on a collection of subsets {B_j}^p_j=1 of a complete metric space (X,d) respectively, and k, M, p are natural numbers. When B_j,j = 1, 2,…,p are closed subsets of X, we show the existence of attractor of this cyclic GIFS, and investigate its properties. Further, we extend our ideas to cyclic countable GIFS.

Dynamical systems and fractal theory methodologies have been proved useful for the modeling and analysis of experimental datasets and, in particular, for electroencephalographic signals. The computation of the fractal dimension of approximation curves in the plane enables the assignment of numerical values to bioelectric recordings in order to discriminate between different states of the observed system. The procedure does not require the stationarity of the signals nor extremely long segments of data. In previous works, we checked that this parameter is a good index for brain activity. In this paper, we consider this measurement in order to quantify the geometric complexity of the brain waves in states of rest and during vehicle driving simulation in different scenarios. This work presents evidence that the fractal dimension allows the detection of the brain bioelectric changes produced in the areas that carry out the different driving simulation tasks, increasing with their complexity.