Discriminating dynamical from additive noise in the Van der Pol oscillator

We address the distinction between dynamical and additive noise in time series analysis by making a joint evaluation of both the statistical continuity of the series and the statistical differentiability of the reconstructed measure. Low levels of the latter and high levels of the former indicate the presence of dynamical noise only, while low values of the two are observed as soon as additive noise contaminates the signal. The method is presented through the example of the Van der Pol oscillator, but is expected to be of general validity for continuous-time systems.Comment: 12 pages (Elsevier LaTeX class), 4 EPS figures, submitted to Physica D (4 july 2001

Photodegradation disproportionately impacts biodegradation of semi‐labile DOM in streams

Exposure of dissolved organic matter (DOM) to sunlight can increase or decrease the fraction that is biodegradable (BDOM), but conceptual models fail to explain this dichotomy. We investigated the effect of sunlight exposure on BDOM, addressing three knowledge gaps: (1) how fractions of DOM overlap in their susceptibility to degradation by sunlight and microbes, (2) how the net effect of sunlight on BDOM changes with photon dose, and (3) how rates of DOM photodegradation and biodegradation compare in a stream. Stream waters were exposed to sunlight, and then fed through bioreactors designed to separate labile and semi‐labile pools within BDOM. The net effects of photodegradation on DOM biodegradability, while generally positive, represented the balance between photochemical production and removal of BDOM that was mediated by photon dose. By using sunlight exposure times representative of sunlight exposures in a headwater stream and bioreactors colonized with natural communities and scaled to whole‐stream dynamics, we were able to relate our laboratory findings to the stream. The impact of sunlight exposure on rates of DOM biodegradation in streams was calculated using rates of light absorption by chromophoric DOM, apparent quantum yields for photomineralization and photochemical alteration of BDOM, and mass transfer coefficients for labile and semi‐labile DOM. Rates of photochemical alteration of labile DOM were an order of magnitude lower than rates of biodegradation of labile DOM, but for semi‐labile DOM, these rates were similar, suggesting that sunlight plays a substantial role in the fate of semi‐labile DOM in streams.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/153758/1/lno11244.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/153758/2/lno11244_am.pd

Book Reviews

Book Reviews by Charles S. Desmond, Godfrey P. Schmidt, Robert E. Sullivan, Louis C. Kaplan, and Paul C. Bartholomew

Detecting Determinism in High Dimensional Chaotic Systems

A method based upon the statistical evaluation of the differentiability of the measure along the trajectory is used to identify in high dimensional systems. The results show that the method is suitable for discriminating stochastic from deterministic systems even if the dimension of the latter is as high as 13. The method is shown to succeed in identifying determinism in electro-encephalogram signals simulated by means of a high dimensional system.Comment: 8 pages (RevTeX 3 style), 5 EPS figures, submitted to Phys. Rev. E (25 apr 2001

Using Topological Statistics to Detect Determinism in Time Series

Statistical differentiability of the measure along the reconstructed trajectory is a good candidate to quantify determinism in time series. The procedure is based upon a formula that explicitly shows the sensitivity of the measure to stochasticity. Numerical results for partially surrogated time series and series derived from several stochastic models, illustrate the usefulness of the method proposed here. The method is shown to work also for high--dimensional systems and experimental time seriesComment: 23 RevTeX pages, 14 eps figures. To appear in Physical Review