Paired Time Series Research Articles

Patterns of GH output and their synchrony with short-term height increments influence stature and growth performance in normal children.

GH is the principal hormone driving growth throughout childhood, but the mechanism by which changing GH secretion is translated into height (Ht) remains undefined. We previously demonstrated that variability in urinary GH (uGH) output over weeks is an important statistical determinant of stature in normal children. We now examine the relationship between the temporal pattern of uGH output and growth using approximate entropy (ApEn) in 29 healthy prepubertal children, monitored serially three times a week from September to June [13 males and 16 females; age, 5.7-7.8 yr; Ht SD score, -2.9 to +2.3; median, 85 measurements per subject]. ApEn is a measure of process irregularity, with low values indicating strong regularity or subpattern persistence and high values indicating greater irregularity. The bivariate extension of this method, cross (X)-ApEn, provides a measure of the strength of interaction between two paired time series (joint signal synchrony). Low values of X-ApEn indicate synchrony, whereas high values indicate asynchrony. Weekly Ht gain, weight (Wt) gain, and uGH output showed significant orderliness in 20 of 29, 26 of 29, and 29 of 29 subjects, respectively, with weekly changes in uGH output being significantly more ordered than Ht gain (P < 0.001) and Wt gain (P < 0.01). ApEn(GH) was positively correlated with Ht gain over the whole year (r = 0.42) and Ht velocity SD score (r = 0.42; both, P < 0.05). Thus, increased irregularity in successive weekly GH output was associated with increased Ht gain and growth rate. There was significant synchrony between Ht and uGH, Wt and uGH, and Ht and Wt in 16 of 29, 22 of 29, and 25 of 29 subjects, respectively, as measured by X-ApEn. The degree of synchrony between Ht and GH output [X-ApEn(Ht:GH)] was inversely correlated with Ht SD score (r = -0.45) and Ht velocity SD score (r = -0.40; both P < 0.05), indicating that increased joint signal synchrony between Ht and GH accompanies tall stature and increased growth rate. These results extend the concept that variability in GH output over time is an important determinant of growth in normal children by indicating that an irregular temporal pattern of GH contributes to growth. Furthermore, synchrony between GH output and short-term Ht increments is associated with tall stature and good growth.

Patterns of GH Output and Their Synchrony with Short-Term Height Increments Influence Stature and Growth Performance in Normal Children

GH is the principal hormone driving growth throughout childhood, but the mechanism by which changing GH secretion is translated into height (Ht) remains undefined. We previously demonstrated that variability in urinary GH (uGH) output over weeks is an important statistical determinant of stature in normal children. We now examine the relationship between the temporal pattern of uGH output and growth using approximate entropy (ApEn) in 29 healthy prepubertal children, monitored serially three times a week from September to June [13 males and 16 females; age, 5.7–7.8 yr; Ht sd score, −2.9 to +2.3; median, 85 measurements per subject]. ApEn is a measure of process irregularity, with low values indicating strong regularity or subpattern persistence and high values indicating greater irregularity. The bivariate extension of this method, cross (X)-ApEn, provides a measure of the strength of interaction between two paired time series (joint signal synchrony). Low values of X-ApEn indicate synchrony, whereas high values indicate asynchrony. Weekly Ht gain, weight (Wt) gain, and uGH output showed significant orderliness in 20 of 29, 26 of 29, and 29 of 29 subjects, respectively, with weekly changes in uGH output being significantly more ordered than Ht gain (P < 0.001) and Wt gain (P < 0.01). ApEn(GH) was positively correlated with Ht gain over the whole year (r = 0.42) and Ht velocity sd score (r = 0.42; both, P < 0.05). Thus, increased irregularity in successive weekly GH output was associated with increased Ht gain and growth rate. There was significant synchrony between Ht and uGH, Wt and uGH, and Ht and Wt in 16 of 29, 22 of 29, and 25 of 29 subjects, respectively, as measured by X-ApEn. The degree of synchrony between Ht and GH output[ X-ApEn(Ht:GH)] was inversely correlated with Ht sd score (r = −0.45) and Ht velocity sd score (r =− 0.40; both P < 0.05), indicating that increased joint signal synchrony between Ht and GH accompanies tall stature and increased growth rate. These results extend the concept that variability in GH output over time is an important determinant of growth in normal children by indicating that an irregular temporal pattern of GH contributes to growth. Furthermore, synchrony between GH output and short-term Ht increments is associated with tall stature and good growth.

Soil carbon protection in podocarp/hardwood forest, and effects of conversion to pasture and exotic pine forest

A combination of paired site, time series, and survey approaches were used to estimate the effect of land use change on mineral soil carbon (C), and to identify factors associated with variation. Land-uses compared included podocarp/hardwood forest, improved pasture, and pine plantation. Soil C was significantly related to soil pH that ranged between 3.9–5.9 (0–0.05 m), 3.6–6.0 (0.05–0.10 m), and 4.5–6.1 (0.10–0.50 m) in indigenous forest. Time series data obtained by periodically re-sampling soil (0–0.10 m) in permanent plots in a pine forest previously under pasture showed that mineral soil C decrease by approximately 4 Mg ha −1 by the end of the first rotation. The time series data compared closely with mean results obtained at paired-site throughout New Zealand. Soil C concentration was highly variable in all land-uses, and the evidence suggests that chemical stabilisation of C occurred under acid conditions in native forest, through complexation with Al, and that effects persisted long after conversion of the native forest to other land-uses. The implications of these findings for the design of sampling protocols for soil C are discussed.

Assessing the Economic Preconditions for a Yen Bloc

Stabilising Asia-Pacific exchange rates by establishing a system of pegs, bands or target zones around the Japanese yen requires the compromise of domestic policy autonomy. The cost of doing so is least when members reaction to economic shocks are symmetric. This study considers which currencies meet this necessary precondition. To assess regional disturbance symmetry the Blanchard and Quah (1989) procedure is employed to distinguish temporary from permanent shocks for paired aggregate output and price time-series. Disturbance correlations between Japan and other Asia-Pacific nations are calculated. Supply-side disturbance correlations are relatively weak and suggest the economic preconditions for a yen bloc are not in place.

Disruption of the Young-Adult Synchrony between Luteinizing Hormone Release and Oscillations in Follicle-Stimulating Hormone, Prolactin, and Nocturnal Penile Tumescence (NPT) in Healthy Older Men*

The healthy human male hypothalamo-pituitary-gonadal axis exhibits age-dependent loss of coordinate LH-testosterone secretion. A putative independent defect in Leydig-cell steroidogenesis with aging would confound the attribution of such LH-testosterone asynchrony to a hypothalamo-pituitary locus per se. Accordingly, here we appraise by sampling every 2.5 min overnight the joint synchrony of moment-to-moment LH release with simultaneously monitored pituitary FSH secretion, prolactin release, and nocturnal penile tumescence (NPT) oscillations, as a neurophysiological correlate of sleep regulation) in 10 young (ages 21-34) and 8 older (ages 62-72) healthy men. Joint synchrony for paired LH-FSH, LH-prolactin, and LH-NPT observations in young vs. older individuals was quantified by the cross-approximate entropy (cross-ApEn) statistic, with larger cross-ApEn values indicating greater two-variable asynchrony. Concomitantly, we assessed (possible) univariate changes with age for each of LH, FSH, prolactin, and NPT, as quantified by approximate entropy (ApEn). Hormone assays were performed by random-access direct chemiluminescence analyzer. Overnight mean (+/- SEM) serum LH concentrations (IU/L) were equivalent in older (3.1 +/- 0.31 IU/L) and younger (2.9 +/- 0.29) men, as were their serum total testosterone concentrations; viz., 425 +/- 48 (older) and 523 +/- 40 (younger) ng/dL. However, all three sets of paired time-series were significantly more asynchronous in the older cohort. First, cross-ApEn of paired LH-FSH release was significantly higher (or more asynchronous) in older subjects; viz., 1.902 +/- 0.022 in older men vs. 1.607 +/- 0.058 in younger individuals (P = 0.0005). Second, cross-ApEn of paired LH and prolactin release was 1.744 +/- 0.085 in older volunteers vs. 1.346 +/- 0.084 in younger subjects (P = 0.0046). Third, and most notably, cross-ApEn for the joint LH-NPT observation time-series was significantly greater in older subjects at 1.771 +/- 0.056 vs. 1.223 +/- 0.086 (young) (P = 0.0001), thereby denoting loss of coordination between (neural) signals directing intermittent LH secretion and those governing sleep-associated penile tumescence in older men. Among one-variable results, only ApEn of LH release was significantly higher in older individuals at 1.323 +/- 0.058 vs. 0.897 +/- 0.089 in younger subjects (P = 0.0019), signifying greater disorderliness of the LH secretory process in aged men. Individual ApEn values of FSH and prolactin release and NPT were age-invariant. In ensemble, the present clinical experiments indicate that, within the aging male reproductive axis, bihormonal network disruption is more pronounced than individual signal disruption. We suggest that abrogation of joint synchrony among hypothalamically directed pituitary hormones and a neurogenically organized sexual response (nocturnal penile tumescence) can be unified thematically under an hypothesis of disrupted central nervous system hypothalamo-pituitary network coordination in human aging. Such implicit disarray of multinodal communication is of consequence both scientifically and clinically, especially in proposing aging theories and intervention strategies.

A Difference Estimator for Testing Equality of Variances for Paired Time Series

A difference estimator of the standard error for the difference in variances of paired time series is proposed. The difference estimator uses the independence of periodogram ordinates to remove nuisance parameters. The difference estimator is easier to compute than one centered on the smoothed periodogram, but shares the same small sample shortcomings for non‐normal series

Correlation dimension for paired discrete time series

We present a method for detecting the dimension of a dynamical system encompassing simultaneously two distinct discrete time series. This method is an extension of the technique introduced by Grassberger and Procaccia for single time series and allows to evaluate the common correlation dimension of the chaotic attractor. The method is applied to some mathematical models and to multiple single-neuron spike trains

Randomized Intervention Analysis and the Interpretation of Whole‐Ecosystem Experiments

Randomized intervention analysis (RIA) is used to detect changes in a manipulated ecosystem relative to an undisturbed reference system. It requires paired time series of data from both ecosystems before and after manipulation. RIA is not affected by non—normal errors in data. Monte Carlo simulation indicated that, even when serial autocorrelation was substantial, the true P value (i.e., from nonoautocorrelated data) was &lt;.05 when the P value from autocorrelated data was &lt;.01. We applied RIA to data from 12 lakes (3 manipulated and 9 reference ecosystems) over 3 yr. RIA consistently indicated changes after major manipulations and only rarely indicated changes in ecosystems that were not manipulated. Less than 3% of the data sets we analyzed had equivocal results because of serial autocorrelation. RIA appears to be a reliable method for determining whether a nonrandom change has occurred in a manipulated ecosystem. Ecological arguments must be combined with statistical evidence to determine whether the changes demonstrated by RIA can be attributed to a specific ecosystem manipulation.