BACKGROUND Neurally adjusted ventilatory assist (NAVA) is a partial ventilatory support mode where positive pressure is provided in relation to diaphragmatic electrical activity (EAdi). Central inspiratory activity is normally not monotonous, but it demonstrates short-term variability and complexity. The authors reasoned that NAVA should produce a more "natural" or variable breathing pattern th...

Estimating the entropy of finite strings has applications in areas such as event detection, similarity measurement or in the performance assessment of compression algorithms. This report compares a variety of computable information measures for finite strings that may be used in entropy estimation. These include Shannon’s n-block entropy, the three variants of the Lempel-Ziv production complexi...

In this contribution, we introduce the concepts of logical entropy and logical mutual information of experiments in the intuitionistic fuzzy case, and study the basic properties of the suggested measures. Subsequently, by means of the suggested notion of logical entropy of an IF-partition, we define the logical entropy of an IF-dynamical system. It is shown that the logical entropy of IF-dynami...

For an ergodic p.m.p. action G y (X,μ) of a countable group G, we define the Rokhlin entropy hRok G (X,μ) to be the infimum of the Shannon entropies of countable generating partitions. It is known that for free ergodic actions of amenable groups this notion coincides with classical Kolmogorov– Sinai entropy. It is thus natural to view Rokhlin entropy as a close analogue to classical entropy. Un...

We prove that the Kolmogorov-Sinai entropy of the Chirikov-Standard map Tλf : (x, y) 7→ (2x − y + λf(x), x) with f(x) = sin(x) with respect to the invariant Lebesgue measure on the two-dimensional torus is bounded below by log(λ/2) − C(λ) with C(λ) = arcsinh(1/λ) + log(2/ √ 3). For λ > λ0 = (8/(6 − 3 √ 3)) = 3.1547..., the entropy of Tλ sin is positive. This result is stable in Banach spaces of...

¿From the analyticity properties of the equation governing infinitesimal perturbations, it is shown that all stability properties of spatially extended 1D systems can be derived from a single function that we call entropy potential since it gives directly the Kolmogorov-Sinai entropy density. Such a function allows determining also Lyapunov spectra in reference frames where timelike and space-l...

In this exposition we prove an existence theorem for a quantum mechanical dynamical entropy based on von-Neumann’s measurement theory. To that end we introduced a Shannon type of information associated with a quantum channel or measurement based on Araki’s relative entropy. This is an invariance for the dynamics which generalizes Kolmogorov-Sinai ’s notion of dynamical entropy of a measure pres...