Recurrence plot statistics and the effect of embedding

Recurrence plots provide a graphical representation of the recurrent patterns in a timeseries, the quantification of which is a relatively new field. Here we derive analytical expressions which relate the values of key statistics, notably determinism and entropy of line length distribution, to the correlation sum as a function of embedding dimension. These expressions are obtained by deriving the transformation which generates an embedded recurrence plot from an unembedded plot. A single unembedded recurrence plot thus provides the statistics of all possible embedded recurrence plots. If the correlation sum scales exponentially with embedding dimension, we show that these statistics are determined entirely by the exponent of the exponential. This explains the results of Iwanski and Bradley (Chaos 8 [1998] 861-871) who found that certain recurrence plot statistics are apparently invariant to embedding dimension for certain low-dimensional systems. We also examine the relationship between the mutual information content of two timeseries and the common recurrent structure seen in their recurrence plots. This allows time-localized contributions to mutual information to be visualized. This technique is demonstrated using geomagnetic index data; we show that the AU and AL geomagnetic indices share half their information, and find the timescale on which mutual features appear

Tunable microwave signal generator with an optically-injected 1310nm QD-DFB laser

Tunable microwave signal generation with frequencies ranging from below 1 GHz to values over 40 GHz is demonstrated experimentally with a 1310nm Quantum Dot (QD) Distributed-Feedback (DFB) laser. Microwave signal generation is achieved using the period 1 dynamics induced in the QD DFB under optical injection. Continuous tuning in the positive detuning frequency range of the quantum dot's unique stability map is demonstrated. The simplicity of the experimental configuration offers promise for novel uses of these nanostructure lasers in Radio-over-Fiber (RoF) applications and future mobile networks. © 2013 Optical Society of America

Evaluating Management Options to Increase Roadside Carbon Sequestration

We estimated the amount of carbon sequestered along Montana Department of Transportation (MDT) roads and tested 3 different highway right-of-way (ROW) management techniques to increase carbon stocks. Using Geographic Information System techniques, the total ROW acreage owned by MDT was found to sequester 75,292 metric tons of carbon per year and to consist mostly of grasslands (70%). From 2016-2018 we tested 3 ROW management techniques to increase carbon stocks- increase mowing height, plant woody shrubs, or add legumes to reclamation seed mixes of disturbed soils - at 3 sites (Three Forks [3F], Bear Canyon [BC], and Bozeman Pass [BP]) along Interstate 90 in southwestern Montana. Soil samples generally averaged 0.75–1.5% soil organic carbon (SOC) at the 3F site, 2.5–4% SOC at the BC site, and 1.5–2.5% SOC at the BP site. Average SOC levels were always lower in 2018 than in 2016. Soil respiration rates were generally highest in June or July at the BC site, averaging ~4 μmol CO2 m-2 second-1. Soil respiration rates were lower at the BC site in November 2016, at the BP site in June 2018, and at the 3F site in July 2018 (all ~2–3 μmol CO2 m-2 s-1). Aboveground biomass carbon estimates generally mirrored belowground SOC estimates. Taken together, our findings suggest that of the three treatments implemented (raised mowing height, shrub planting, and disturbance), minimizing disturbance to soils likely makes the greatest contribution to the medium- and long-term carbon-storage potential of these roadside soils

Towards a genome-wide transcriptogram: the Saccharomyces cerevisiae case

A genome modular classification that associates cellular processes to modules could lead to a method to quantify the differences in gene expression levels in different cellular stages or conditions: the transcriptogram, a powerful tool for assessing cell performance, would be at hand. Here we present a computational method to order genes on a line that clusters strongly interacting genes, defining functional modules associated with gene ontology terms. The starting point is a list of genes and a matrix specifying their interactions, available at large gene interaction databases. Considering the Saccharomyces cerevisiae genome we produced a succession of plots of gene transcription levels for a fermentation process. These plots discriminate the fermentation stage the cell is going through and may be regarded as the first versions of a transcriptogram. This method is useful for extracting information from cell stimuli/responses experiments, and may be applied with diagnostic purposes to different organisms

Recurrence quantification analysis of global stock markets

This study investigates the presence of deterministic dependencies in international stock markets using recurrence plots and recurrence quantification analysis (RQA). The results are based on a large set of free float-adjusted market capitalization stock indices, covering a period of 15 years. The statistical tests suggest that the dynamics of stock prices in emerging markets is characterized by higher values of RQA measures when compared to their developed counterparts. The behavior of stock markets during critical financial events, such as the burst of the technology bubble, the Asian currency crisis, and the recent subprime mortgage crisis, is analyzed by performing RQA in sliding windows. It is shown that during these events stock markets exhibit a distinctive behavior that is characterized by temporary decreases in the fraction of recurrence points contained in diagonal and vertical structures.Recurrence plot, Recurrence quantification analysis, Nonlinear dynamics, International stock markets