Computing algebraic transfer entropy and coupling directions via transcripts.

Most random processes studied in nonlinear time series analysis take values on sets endowed with a group structure, e.g., the real and rational numbers, and the integers. This fact allows to associate with each pair of group elements a third element, called their transcript, which is defined as the product of the second element in the pair times the first one. The transfer entropy of two such processes is called algebraic transfer entropy. It measures the information transferred between two coupled processes whose values belong to a group. In this paper, we show that, subject to one constraint, the algebraic transfer entropy matches the (in general, conditional) mutual information of certain transcripts with one variable less. This property has interesting practical applications, especially to the analysis of short time series. We also derive weak conditions for the 3-dimensional algebraic transfer entropy to yield the same coupling direction as the corresponding mutual information of transcripts. A related issue concerns the use of mutual information of transcripts to determine coupling directions in cases where the conditions just mentioned are not fulfilled. We checked the latter possibility in the lowest dimensional case with numerical simulations and cardiovascular data, and obtained positive results.

Information directionality in coupled time series using transcripts.

In ordinal symbolic dynamics, transcripts describe the algebraic relationship between ordinal patterns. Using the concept of transcript, we exploit the mathematical structure of the group of permutations to derive properties and relations among information measures of the symbolic representations of time series. These theoretical results are then applied for the assessment of coupling directionality in dynamical systems, where suitable coupling directionality measures are introduced depending only on transcripts. These measures improve the reliability of the information flow estimates and reduce to well-established coupling directionality quantifiers when some general conditions are satisfied. Furthermore, by generalizing the definition of transcript to ordinal patterns of different lengths, several of the commonly used information directionality measures can be encompassed within the same framework.

Scaling relations between trabecular bone volume fraction and microstructure at different skeletal sites.

In this study, we investigated the scaling relations between trabecular bone volume fraction (BV/TV) and parameters of the trabecular microstructure at different skeletal sites. Cylindrical bone samples with a diameter of 8mm were harvested from different skeletal sites of 154 human donors in vitro: 87 from the distal radius, 59/69 from the thoracic/lumbar spine, 51 from the femoral neck, and 83 from the greater trochanter. µCT images were obtained with an isotropic spatial resolution of 26µm. BV/TV and trabecular microstructure parameters (TbN, TbTh, TbSp, scaling indices (< > and σ of α and αz), and Minkowski Functionals (Surface, Curvature, Euler)) were computed for each sample. The regression coefficient ß was determined for each skeletal site as the slope of a linear fit in the double-logarithmic representations of the correlations of BV/TV versus the respective microstructure parameter. Statistically significant correlation coefficients ranging from r=0.36 to r=0.97 were observed for BV/TV versus microstructure parameters, except for Curvature and Euler. The regression coefficients ß were 0.19 to 0.23 (TbN), 0.21 to 0.30 (TbTh), -0.28 to -0.24 (TbSp), 0.58 to 0.71 (Surface) and 0.12 to 0.16 (<α>), 0.07 to 0.11 (<αz>), -0.44 to -0.30 (σ(α)), and -0.39 to -0.14 (σ(αz)) at the different skeletal sites. The 95% confidence intervals of ß overlapped for almost all microstructure parameters at the different skeletal sites. The scaling relations were independent of vertebral fracture status and similar for subjects aged 60-69, 70-79, and >79years. In conclusion, the bone volume fraction-microstructure scaling relations showed a rather universal character.

Randomized placebo-controlled human pilot study of cold atmospheric argon plasma on skin graft donor sites.

Cold atmospheric plasma has already been shown to decrease the bacterial load in chronic wounds. However, until now it is not yet known if plasma treatment can also improve wound healing. We aimed to assess the impact of cold atmospheric argon plasma on the process of donor site healing. Forty patients with skin graft donor sites on the upper leg were enrolled in our study. The wound sites were divided into two equally sized areas that were randomly assigned to receive either plasma treatment or placebo (argon gas) for 2 minutes. Donor site healing was evaluated independently by two blinded dermatologists, who compared the wound areas with regard to reepithelialization, blood crusts, fibrin layers, and wound surroundings. From the second treatment day onwards, donor site wound areas treated with plasma (n = 34) showed significantly improved healing compared with placebo-treated areas (day 1, p = 0.25; day 2, p = 0.011; day 3, p < 0.001; day 4, p < 0.001; day 5, p = 0.004; day 6, p = 0.008; day 7, p = 0.031). Positive effects were observed in terms of improved reepithelialization and fewer fibrin layers and blood crusts, whereas wound surroundings were always normal, independent of the type of treatment. Wound infection did not occur in any of the patients, and no relevant side effects were observed. Both types of treatment were well tolerated. The mechanisms contributing to these clinically observed effects should be further investigated.

Reproducibility of trabecular bone structure measurements of the distal radius at 1.5 and 3.0 T magnetic resonance imaging.

The purpose of this study was to assess and compare the reproducibility of trabecular bone structure measurements of the distal radius at 1.5 and 3.0 T magnetic resonance imaging (MRI). Root mean square reproducibility errors ranged from 0.69% to 4.94% at 1.5 T MRI and from 0.38% to 5.80% at 3.0 T MRI. Thus, reproducibility errors of trabecular bone structure measurements are overall in an acceptable range and similar at 1.5 and 3.0 T MRI.

Transcripts: an algebraic approach to coupled time series.

Ordinal symbolic dynamics is based on ordinal patterns. Its tools include permutation entropy (in metric and topological versions), forbidden patterns, and a number of mathematical results that make this sort of symbolic dynamics appealing both for theoreticians and practitioners. In particular, ordinal symbolic dynamics is robust against observational noise and can be implemented with low computational cost, which explains its increasing popularity in time series analysis. In this paper, we study the perhaps less exploited aspect so far of ordinal patterns: their algebraic structure. In a first part, we revisit the concept of transcript between two symbolic representations, generalize it to N representations, and derive some general properties. In a second part, we use transcripts to define two complexity indicators of coupled dynamics. Their performance is tested with numerical and real world data.

Label-free live-cell imaging with confocal Raman microscopy.

Confocal Raman spectroscopy is a noninvasive alternative to established cell imaging methods because it does not require chemical fixation, the use of fluorescent markers, or genetic engineering. In particular, single live-cell, high-resolution imaging by confocal Raman microscopy is desirable because it allows further experiments concerning the individually investigated cells. However, to derive meaningful images from the spectroscopic data, one must identify cell components within the dataset. Using immunofluorescence images as a reference, we derive Raman spectral signatures by means of information measures to identify cell components such as the nucleus, the endoplasmic reticulum, the Golgi apparatus, and mitochondria. The extracted signatures allow us to generate representations equivalent to conventional (immuno)fluorescence images with more than three cell components at a time, exploiting the Raman spectral information alone.

Characterizing synchronization in time series using information measures extracted from symbolic representations.

We present a methodology to characterize synchronization in time series based on symbolic representations. Each time series is mapped onto a sequence of p -dimensional delay vectors that are subsequently transformed into symbols by means of a rank-ordering of their values. Based on these representations, we propose a transcription scheme between symbols of the respective time series to study synchronization properties. Group-theoretical considerations and the use of information measures allow us to classify regimes of synchronization and to assess its strength. We apply our method to a prototype nonlinear system, which reveals a rich variety of coupled dynamics. We investigate in detail the robustness of the derived synchronization measure against noise and compare its value with that of the established measures.

Advances of 3T MR imaging in visualizing trabecular bone structure of the calcaneus are partially SNR-independent: analysis using simulated noise in relation to micro-CT, 1.5T MRI, and biomechanical strength.

PURPOSE: To investigate differences in magnetic resonance imaging (MRI) of trabecular bone at 1.5T and 3.0T and to specifically study noise effects on the visualization and quantification of trabecular architecture using conventional histomorphometric and nonlinear measures of bone structure. MATERIALS AND METHODS: Sagittal MR images of 43 calcaneus specimens (donor age: 81 +/- 10 years) were acquired at 1.5T and 3.0T using gradient echo sequences. Noise was added to obtain six sets of images with decreasing signal-to-noise ratios (SNRs). Micro-CT images were obtained from biopsies taken from 37 calcaneus samples and bone strength was determined. Morphometric and nonlinear structure parameters were calculated in all datasets. RESULTS: Originally, SNR was 1.5 times higher at 3.0T. In the simulated image sets, SNR was similar at both fields. Trabecular dimensions measured by microCT were adequately estimated by MRI, with residual errors (e(r)), ranging from 16% to 2.7% at 3.0T. Comparing e(r) at similar SNR, 3.0T consistently displayed lower errors than 1.5T (eg, bone fraction at SNR approximately 4: e(r)[3.0T] = 15%; e(r)[1.5T] = 21%, P < 0.05). CONCLUSION: The advances of 3.0T compared to 1.5T in visualizing trabecular bone structure are partially SNR-independent. The better performance at 3.0T may be explained by pronounced susceptibility, enhancing the visualization of thin trabecular structures.

Nonlinear volatility of river flux fluctuations.

We study the spectral properties of the magnitudes of daily river flux increments, the volatility. The volatility series exhibits (i) strong seasonal periodicity and (ii) power-law correlations for time scales less than 1 yr. We test the nonlinear properties of the river flux increment series by randomizing its Fourier phases and find that the surrogate volatility series (i) has almost no seasonal periodicity and (ii) is weakly correlated for time scales less than 1 yr. We quantify the degree of nonlinearity by measuring (i) the amplitude of the power spectrum at the seasonal peak and (ii) the correlation power-law exponent of the volatility series.

First-order irreversible phase transitions in a nonequilibrium system: mean-field analysis and simulation results.

First-order irreversible phase transitions (IPT's) between an active regime and an absorbing state are studied in a single-component, two-dimensional interacting particle system by means of both simulations and a mean-field analysis. Several features obtained using the mean-field approximation such as the presence of a first-order IPT and hysteresis effects, are in excellent agreement with simulation results. In addition, extensive epidemic simulations show that the dynamical critical behavior of the system is by no means scale invariant.