Complementarity in classical dynamical systems

The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an \emph{ad hoc} partition of an underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed.Comment: 18 pages, no figure

A Passive Monitoring System in Assisted Living Facilities: 12-Month Comparative Study

The GE QuietCare® passive monitoring system uses advanced motion sensor technology that learns the daily living patterns of senior community residents and sends alerts when certain out-of-the-ordinary events occur. This study compared falls, hospitalizations, care level changes, and resident attrition between two similar assisted living facilities where one facility adopted the QuietCare® monitoring system and the other did not over a 12-month period. Average falls per week were significantly lower in the QuietCare® facility than the control facility. There was also a trend toward fewer weekly hospitalizations in the QuietCare® facility. There was higher resident retention at the QuietCare® facility. This study provides evidence of direct benefits to both the resident and the facility for the use of QuietCare®. There was a significant reduction in the number of falls, as well as a general facility performance improvement measured by care level consistency and higher resident retention rates

Log-linear Poisson autoregression

We consider a log-linear model for time series of counts. This type of model provides a framework where both negative and positive association can be taken into account. In addition time dependent covariates are accommodated in a straightforward way. We study its probabilistic properties and maximum likelihood estimation. It is shown that a perturbed version of the process is geometrically ergodic, and, under some conditions, it approaches the non-perturbed version. In addition, it is proved that the maximum likelihood estimator of the vector of unknown parameters is asymptotically normal with a covariance matrix that can be consistently estimated. The results are based on minimal assumptions and can be extended to the case of log-linear regression with continuous exogenous variables. The theory is applied to aggregated financial transaction time series. In particular, we discover positive association between the number of transactions and the volatility process of a certain stock

Nonlinear Poisson autoregression

We study statistical properties of a class of non-linear models for regression analysis of count time series. Under mild conditions, it is shown that a perturbed version of the model is geometrically ergodic and possesses moments of any order. This result turns out to be instrumental on deriving large sample properties of the maximum likelihood estimators of the regression parameters. The theory is illustrated with examples

On weak dependence conditions for Poisson autoregressions

We consider generalized linear models for regression modeling of count time series. We give easily verifiable conditions for obtaining weak dependence for such models. These results enable the development of maximum likelihood inference under minimal conditions. Some examples which are useful to applications are discussed in detail

Asymptotic Inference for Unit Roots in Spatial Triangular Autoregression

A spatial autoregressive process with two parameters is investigated both in the stable and in the unstable case. It is shown that the limiting distribution of the least squares estimator of these parameters is normal and the rate of convergence is n(3/2) if one of the key parameters equals zero and n otherwise