Universal analytic properties of noise. Introducing the J-Matrix formalism

We propose a new method in the spectral analysis of noisy time-series data for damped oscillators. From the Jacobi three terms recursive relation for the denominators of the Pad\'e Approximations built on the well-known Z-transform of an infinite time-series, we build an Hilbert space operator, a J-Operator, where each bound state (inside the unit circle in the complex plane) is simply associated to one damped oscillator while the continuous spectrum of the J-Operator, which lies on the unit circle itself, is shown to represent the noise. Signal and noise are thus clearly separated in the complex plane. For a finite time series of length 2N, the J-operator is replaced by a finite order J-Matrix J_N, having N eigenvalues which are time reversal covariant. Different classes of input noise, such as blank (white and uniform), Gaussian and pink, are discussed in detail, the J-Matrix formalism allowing us to efficiently calculate hundreds of poles of the Z-transform. Evidence of a universal behaviour in the final statistical distribution of the associated poles and zeros of the Z-transform is shown. In particular the poles and zeros tend, when the length of the time series goes to infinity, to a uniform angular distribution on the unit circle. Therefore at finite order, the roots of unity in the complex plane appear to be noise attractors. We show that the Z-transform presents the exceptional feature of allowing lossless undersampling and how to make use of this property. A few basic examples are given to suggest the power of the proposed method.Comment: 14 pages, 8 figure

1974

History of Golf (1) The Nine Toughest Holes in the World (2) Stockie Madness (3) Bartender, One More Round for Pythium (3) Panel: 1973 Turf Problems in Review - 1974 Possible Remedies (A1-A12) Movement of Water to a Holding Pond (A13) Maintenance of Low Budget, Short Season Golf Courses (A16) Turfgrass Fertilization (A18) Determining Turfgrass Fertilizer Needs (A25) Shortage of Plant Food and How to Adjust to Supply and Cost (A29) Panel: Tricalcium Arsenate - Use and Abuse (A33-A46) Operating and Maintaining Municipal Golf Courses (A48) Maintenance of a High Budget Golf Course (A51) Trends in Agricultural Education and Where Are the Emphases (A58) Maintenance of Municipal Parks and Recreation Areas (A60) Maintenance of Grass Tennis Courts (A63) Transition from Natural to Artificial Turf (A67) Plant materials for Outlying Areas (A71) Care of University Grounds (A76) Maintenance of Industrial Sites (A79) Turfgrass Diseases and Systemic Fungicides (A81) A Look at the Future (A 84) Watering of Golf Course Turf (A92

Taking Children's Voices in Disaster Risk Reduction a Step Forward

Disaster risk reduction (DRR) continues to gain momentum globally and locally, but there is a notable void in the DRR literature on the role of children in community-level disaster risk management in Zimbabwe. Children are among the most vulnerable groups when disasters occur, yet their voices in disaster risk reduction are rarely heard. Using a qualitative methodology, this article examines the extent to which children are involved in disaster risk reduction in Muzarabani District, Zimbabwe. Despite evidence of the potential positive impact that children can have on DRR, their involvement in risk reduction planning in Zimbabwe is negligible. To achieve greater resilience to disasters requires that children's voices are heard and recognized as central to improved disaster risk reduction

Intergovernmental fiscal transfers as pork barrel

This paper uses a simultaneous equations model to analyze increases in intergovernmental fiscal transfers and associated vote changes in Portuguese legislative elections. The results suggest that election year increases in transfers by the central government to municipalities secure added votes, and that these transfers are targeted at jurisdictions where the government faces the risk of losing support.COMPETE; QREN; FEDERFundação para a Ciência e a Tecnologia (FCT