Time series irreversibility: a visibility graph approach

We propose a method to measure real-valued time series irreversibility which combines two differ- ent tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the in and out degree distributions of the associated graph. The method is computationally effi- cient, does not require any ad hoc symbolization process, and naturally takes into account multiple scales. We find that the method correctly distinguishes between reversible and irreversible station- ary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic pro- cesses (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv) dissipative chaotic maps in the presence of noise. Two alternative graph functionals, the degree and the degree-degree distributions, can be used as the Kullback-Leibler divergence argument. The former is simpler and more intuitive and can be used as a benchmark, but in the case of an irreversible process with null net current, the degree-degree distribution has to be considered to identifiy the irreversible nature of the series.Comment: submitted for publicatio

Multilayered feed forward Artificial Neural Network model to predict the average summer-monsoon rainfall in India

In the present research, possibility of predicting average summer-monsoon rainfall over India has been analyzed through Artificial Neural Network models. In formulating the Artificial Neural Network based predictive model, three layered networks have been constructed with sigmoid non-linearity. The models under study are different in the number of hidden neurons. After a thorough training and test procedure, neural net with three nodes in the hidden layer is found to be the best predictive model.Comment: 19 pages, 1 table, 3 figure

Dual element (¹⁵N/ ¹⁴N, ¹³C/ ¹²C) isotope analysis of glyphosate and AMPA by derivatization-gas chromatography isotope ratio mass spectrometry (GC/IRMS) combined with LC/IRMS.

To assess sources and degradation of the herbicide glyphosate [N-(phosphonomethyl) glycine] and its metabolite AMPA (aminomethylphosphonic acid), concentration measurements are often inconclusive and even (13)C/(12)C analysis alone may give limited information. To advance isotope ratio analysis of an additional element, we present compound-specific (15)N/(14)N analysis of glyphosate and AMPA by a two step derivatization in combination with gas chromatography/isotope ratio mass spectrometry (GC/IRMS). The N-H group was derivatized with isopropyl chloroformate (iso-PCF), and remaining acidic groups were subsequently methylated with trimethylsilyldiazomethane (TMSD). Iso-PCF treatment at pH <10 gave too low (15)N/(14)N ratios indicating an incomplete derivatization; in contrast, too high (15)N/(14)N ratios at pH >10 indicated decomposition of the derivative. At pH 10, and with an excess of iso-PCF by 10-24, greatest yields and accurate (15)N/(14)N ratios were obtained (deviation from elemental analyzer-IRMS: -0.2 ± 0.9 % for glyphosate; -0.4 ± 0.7 % for AMPA). Limits for accurate δ(15)N analysis of glyphosate and AMPA were 150 and 250 ng injected, respectively. A combination of δ(15)N and δ(13)C analysis by liquid chromatography/isotope ratio mass spectrometry (LC/IRMS) (1) enabled an improved distinction of commercial glyphosate products and (2) showed that glyphosate isotope values during degradation by MnO2 clearly fell outside the commercial product range. This highlights the potential of combined carbon and nitrogen isotopes analysis to trace sources and degradation of glyphosate