The paper relates to possible connection between spectrum power-law decay and correlation dimension estimation for electroencephalogram (EEG). EEG signals recorded during relaxed wakefulness were analysed. Power-law decay of about 2.28 prevailing over the exponential falling off was established when exponent from the whole EEG spectrum was taken. The correlation dimension was also estimated. Th...

For 0 < λ < 1/e the Julia set of λez is an uncountable union of pairwise disjoint simple curves tending to infinity [Devaney and Krych 1984], the Hausdorff dimension of this set is two [McMullen 1987], but the set of curves without endpoints has Hausdorff dimension one [Karpińska 1999]. We show that these results have three-dimensional analogues when the exponential function is replaced by a qu...

We solve Talagrand’s entropy problem: the L2-covering numbers of every uniformly bounded class of functions are exponential in its shattering dimension. This extends Dudley’s theorem on classes of {0, 1}valued functions, for which the shattering dimension is the VapnikChervonenkis dimension. In convex geometry, the solution means that the entropy of a convex body K is controlled by the maximal ...

between the front and reverse side images due to differences between both images caused by factors like document skews, different scales during image capture, and warped surfaces at books' spine areas. We are currently working on the development of a computer-assisted method to do the image overlay. Abstract—In this paper, the problem of estimating the intrinsic dimension of a data set is inves...

We consider a mass-conservative fragmentation of the unit interval. The main purpose of this work is to specify the Hausdorff dimension of the set of locations having exactly an exponential decay. The study relies on an additive martingale which arises naturally in this setting, and a class of Lévy processes constrained to stay in a finite interval.

Within learning theory teaching has been studied in various ways. In a common variant the teacher has to teach all learners that are restricted to output only consistent hypotheses. The complexity of teaching is then measured by the maximum number of mistakes a consistent learner can make until successful learning. This is equivalent to the so-called teaching dimension. However, many interestin...

The general structure of a q-analogue of the Zassenhaus formula, the dual of the Baker-Campbell-Hausdorff formula for combining exponential operators, is derived and the first few terms of the disentanglement of a q-exponential operator are explicitly given.

Necessary and suffident conditions are derived for the existence ofH, controllers for a dass of linear, time-invariant enerslieed plants which is arciuded by the assoznptions genera if y made in the solution of H, problems. The assumptions relaxed in this work concern the comnarative dimensions of the dent's i n ~ u t = and ontput spaces.

We test recent claims that causal (driver/response) relationships can be deduced from interdependencies between simultaneously measured time series. We apply two recently proposed interdependence measures which should give similar results as cross predictabilities used by previous authors. The systems which we study are asymmetrically coupled simple models (Lorenz, Roessler, and Henon models), ...

this paper presents a fuzzy approach to the prediction of highly nonlinear timeseries.the optimized mamdani-type fuzzy system denoted sqp-flc is applied forthe input-output modeling of measured data. in order to tune fuzzy membershipfunctions, a sequential quadratic programming (sqp) method is employed. theproposed method is evaluated and validated on a highly complex time series, dailygold pri...