An algorithm for determining the distribution of maximal entropy subject to constraints is presented. The method provides an alternative to the conventional procedure which requires the numerical solution of a set of implicit nonlinear equations for the Lagrange multipliers. Here they are determined by seeking a minimum of a concave function, a procedure which readily lends itself to computatio...

We construct a natural extension for each of Nakada’s α-continued fraction transformations and show the continuity as a function of α of both the entropy and the measure of the natural extension domain with respect to the density function (1+ xy). For 0 < α ≤ 1, we show that the product of the entropy with the measure of the domain equals π/6. We show that the interval (3 − √ 5)/2 ≤ α ≤ (1 + √ ...

Maximum entropy methods have proven to be a powerful tool for reconstructing data from incomplete measurements or in the presence of noise. In this note, we apply the method to the reconstruction computed tomography data derived from backprojection over a finite set of angles. In this case, one derives quite simple formulae which may be easily implemented on computer.

We consider distributions of ordered random vectors with given one-dimensional marginal distributions. We give an elementary necessary and sufficient condition for the existence of such a distribution with finite entropy. In this case, we give explicitly the density of the unique distribution which achieves the maximal entropy and compute the value of its entropy. This density is the unique one...

This note extends some results of Nishiyama [Ann. Probab. 28 (2000) 685–712]. A maximal inequality for stochastic integrals with respect to integer-valued random measures which may have infinitely many jumps on compact time intervals is given. By using it, a tightness criterion is obtained; if the so-called quadratic modulus is bounded in probability and if a certain entropy condition on the pa...

We consider the problem of minimax estimation of the entropy of a density over Lipschitz balls. Dropping the usual assumption that the density is bounded away from zero, we obtain the minimax rates (n lnn)− s s+d + n for 0 < s ≤ 2 in arbitrary dimension d, where s is the smoothness parameter and n is the number of independent samples. Using a two-stage approximation technique, which first appro...

We show that the one-sided Dyck shift has a unique tail invariant topologically σ-finite measure (up to scaling). This invariant measure of the one sided Dyck turns out to be a shift-invariant probability. Furthermore, it is one of the two ergodic probabilities obtaining maximal entropy. For the two sided Dyck shift we show that there are exactly three ergodic double-tail invariant probabilitie...

BACKGROUND The aim of this study was to investigate the independent effect of remifentanil on the approximate entropy (ApEn) in frontoparietal montages. The authors investigated which montages were relevant to assess the remifentanil effect on the electroencephalogram. Spectral edge frequency and the canonical univariate parameter were used as comparators. METHODS Twenty-eight healthy volunte...

In this note we show that the periodic points of an expansive Zd action on a compact abelian group are uniformly distributed with respect to Haar measure if the action has completely positive entropy. In the general expansive case, we show that any measure obtained as the distribution of periodic points along some sequence of periods necessarily has maximal entropy but need not be Haar measure. §

We study the quantitative behavior of Poincaré recurrence. In particular, for an equilibrium measure on a locally maximal hyperbolic set of a C diffeomorphism f , we show that the recurrence rate to each point coincides almost everywhere with the Hausdorff dimension d of the measure, that is, inf{k > 0 : fx ∈ B(x, r)} ∼ r. This result is a non-trivial generalization of work of Boshernitzan conc...