Time reversal, symbolic series and irreversibility of human heartbeat

We study the time reversal properties of time series by means of a ternary coding of the differentiated series. For the symbolic series obtained in this way we show that suitable pairs of ternary words have the same probability if the time series is reversible. This provides tests in which time reversibility is rejected if the estimated probabilities are significantly different. We apply one of these tests to the human heartbeat series extracted from 24 h Holter recordings of 19 healthy subjects. Data analysis shows a highly significant prevalence of irreversibility. Our symbolic approach to time reversal gives further support to the suitability of non-linear modeling of the normal heartbeat.     

The Neumann problem for the Hénon equation,trace inequalities and Steklov eigenvalues

We consider the Neumann problem for the Hénon equation. We obtain existence results and we analyze the symmetry properties of the ground state solutions. We prove that some symmetry and variational properties can be expressed in terms of eigenvalues of a Steklov problem. Applications are also given to extremals of certain trace inequalities.     

On the categorical structure of H

The categorical structure of H² is shown to be a particular instance of the cokernel of a morphism between symmetric categorical groups.