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Pituitary growth hormone (GH)-secreting cells regulate growth and metabolism in animals and humans. To secrete highly ordered GH pulses (up to 1,000-fold rise in hormone levels in vivo), the pituitary GH cell population needs to mount coordinated responses to GH secretagogues, yet GH cells display an apparently heterogeneous scattered distribution in 2D histological studies. To address this paradox, we analyzed in 3D both positioning and signaling of GH cells using reconstructive, two-photon excitation microscopy to image the entire pituitary in GH-EGFP transgenic mice. Our results unveiled a homologous continuum of GH cells connected by adherens junctions that wired the whole gland and exhibited the three primary features of biological networks: robustness of architecture across lifespan, modularity correlated with pituitary GH contents and body growth, and connectivity with spatially stereotyped motifs of cell synchronization coordinating cell activity. These findings change our view of GH cells, from a collection of dispersed cells to a geometrically connected homotypic network of cells whose local morphology and connectivity can vary, to alter the timing of cellular responses to promote more coordinated pulsatile secretion. This large-scale 3D view of cell functioning provides a powerful approach to identify and understand other networks of endocrine cells that are thought to be scattered in situ. Many dispersed endocrine systems exhibit pulsatile outputs. We suggest that cell positioning and associated cell-cell connection mechanisms will be critical parameters that determine how well such systems can deliver a coordinated secretory pulse of hormone to their target tissues. biological rhythms | endocrinology | systems biology | connectivity | calcium

The need to assess subtle, potentially exploitable changes in serial structure is paramount in the analysis of financial data. Herein, we demonstrate the utility of approximate entropy (ApEn), a model-independent measure of sequential irregularity, toward this goal, by several distinct applications. We consider both empirical data and models, including composite indices (Standard and Poor's 500 and Hang Seng), individual stock prices, the random-walk hypothesis, and the Black-Scholes and fractional Brownian motion models. Notably, ApEn appears to be a potentially useful marker of system stability, with rapid increases possibly foreshadowing significant changes in a financial variable.

Despite many diverse theories that address closely related themes - e.g., probability theory, algorithmic complexity, cryptoanalysis, and pseudorandom number generation - a near-void remains in constructive methods certified to yield the desired 'random' output. Herein, we provide explicit techniques to produce broad sets of both highly irregular finite and normal infinite sequences, based on constructions and properties derived from approximate entropy (ApEn), a computable formulation of sequential irregularity. Furthermore, for infinite sequences, we considerably refine normality, by providing methods for constructing diverse classes of normal numbers, classified by the extent to which initial segments deviate from maximal irregularity.

Although they lie at the conceptual core of a wide range of scientific questions, the notions of irregular or 'random' arrangement and the process of randomization itself have never been unambiguously defined. Algorithmic implementation of these concepts requires a combinatorial, rather than a probability-theoretic, formulation. We introduce vector versions of approximate entropy to quantify the degrees of irregularity of planar (and higher dimensional) arrangements. Selection rules, applied to the elements of irregular permutations, define randomization in strictly combinatorial terms. These concepts are developed in the context of Latin square arrangements and valid randomization of them. Conflicts and tradeoffs between the objectives of irregular arrangements and valid randomization are highlighted. Extensions to broad classes of designs, and a diverse range of scientific applications are indicated, including lattice-based models in physics and signal detection in seismology and physiology.

The effects of surgical and hormonal gonadal suppression on the orderliness of growth hormone (GH) secretion were investigated in male and female rats. Serum GH concentration was determined at specific time intervals in the study animals. The relative degree of disorder in GH secretion from maximum to minimum is given in the following order: intact female, hormonally suppressed female, ovariectomized female, orchiectomized male, hormonally suppressed male and intact male.

The need to assess the randomness of a single sequence, especially a finite sequence, is ubiquitous, yet is unaddressed by axiomatic probability theory. Here, we assess randomness via approximate entropy (ApEn), a computable measure of sequential irregularity, applicable to single sequences of both (even very short) finite and infinite length. We indicate the novelty and facility of the multidimensional viewpoint taken by ApEn, in contrast to classical measures. Furthermore and notably, for finite length, finite state sequences, one can identify maximally irregular sequences, and then apply ApEn to quantify the extent to which given sequences differ from maximal irregularity, via a set of deficit ([def.sub.m]) functions. The utility of these [def.sub.m] functions which we show allows one to considerably refine the notions of probabilistic independence and normality, is featured in several studies, including (i) digits of e, [Pi], [square root of 2], and [square root of 3], both in base 2 and in base 10, and (ii) sequences given by fractional parts of multiples of irrationals. We prove companion analytic results, which also feature in a discussion of the role and validity of the almost sure properties from axiomatic probability theory insofar as they apply to specified sequences and sets of sequences (in the physical world). We conclude by relating the present results and perspective to both previous and subsequent studies.

A computable framework is established for the randomness notion for arbitrary length sequences, where short sequences are not defined by the Kolmogorov and Usphenski theory and leaves an option for closer classification to a random state. An infinite sequence model for randomness is also established, where retention of finite properties allow a computable random sequence. Approximate entropy is used refine computational concepts.

Porksen, Niels, Claus Juhl, Malene Hollingdal, Steve M. Pincus, Jeppe Sturis, Johannes D. Veldhuis, and Ole Schmitz. Concordant induction of rapid in vivo pulsatile insulin secretion by recurrent punctuated glucose infusions. Am. J. Physiol. Endocrinol. Metab. 278: E162-E170, 2000.--Insulin is largely secreted as serial secretory bursts superimposed on basal release, insulin secretion is regulated through changes of pulse mass and frequency, and the insulin release pattern affects insulin action. Coordinate insulin release is preserved in the isolated perfused pancreas, suggesting intrapancreatic coordination. However, occurrence of glucose concentration oscillations may influence the process in vivo, as it does for ultradian oscillations. To determine if rapid pulsatile insulin release may be induced by minimal glucose infusions and to define the necessary glucose quantity, we studied six healthy individuals during brief repetitive glucose infusions of 6 and 2 mg [multiplied by] [kg.sup.-1] [multiplied by] [min.sup.-1] for 1 min every 10 min. The higher dose completely synchronized pulsatile insulin release at modest plasma glucose changes (~0.3 mM = ~5%), with large (~100%) amplitude insulin pulses at every single glucose induction (n = 54) at a lag time of 2 min (P [is less than] 0.05), compared with small (10%) and rare (n = 3) uninduced insulin excursions. The smaller glucose dose induced insulin pulses at lower significance levels and with considerable breakthrough insulin release. Periodicity shift from either 7- to 12-min or from 12- to 7-min intervals between consecutive glucose (6 mg [multiplied by] [kg.sup.-1] [multiplied by] [min.sup.-1]) infusions in six volunteers revealed rapid frequency changes. The orderliness of insulin release as estimated by approximate entropy (1.459 [+ or -] 0.009 vs. 1.549 [+ or -] 0.027, P = 0.016) was significantly improved by glucose pulse induction (n = 6; 6 mg [multiplied by] [kg.sup.-1] [multiplied by] [min.sup.-1]) compared with unstimulated insulin profiles (n = 7). We conclude that rapid in vivo oscillations in glucose may be an important regulator of pulsatile insulin secretion in humans and that the use of an intermittent pulsed glucose induction to evoke defined and recurrent insulin secretory signals may be a useful tool to unveil more subtle defects in [Beta]-cell glucose sensitivity. C-peptide; oscillations; fasting; [Beta]-cell