Geometry of River Networks II: Distributions of Component Size and Number

The structure of a river network may be seen as a discrete set of nested sub-networks built out of individual stream segments. These network components are assigned an integral stream order via a hierarchical and discrete ordering method. Exponential relationships, known as Horton's laws, between stream order and ensemble-averaged quantities pertaining to network components are observed. We extend these observations to incorporate fluctuations and all higher moments by developing functional relationships between distributions. The relationships determined are drawn from a combination of theoretical analysis, analysis of real river networks including the Mississippi, Amazon and Nile, and numerical simulations on a model of directed, random networks. Underlying distributions of stream segment lengths are identified as exponential. Combinations of these distributions form single-humped distributions with exponential tails, the sums of which are in turn shown to give power law distributions of stream lengths. Distributions of basin area and stream segment frequency are also addressed. The calculations identify a single length-scale as a measure of size fluctuations in network components. This article is the second in a series of three addressing the geometry of river networks.Comment: 16 pages, 13 figures, 4 tables, Revtex4, submitted to PR

A complementary view on the growth of directory trees

Trees are a special sub-class of networks with unique properties, such as the level distribution which has often been overlooked. We analyse a general tree growth model proposed by Klemm {\em et. al.} (2005) to explain the growth of user-generated directory structures in computers. The model has a single parameter $q$ which interpolates between preferential attachment and random growth. Our analysis results in three contributions: First, we propose a more efficient estimation method for $q$ based on the degree distribution, which is one specific representation of the model. Next, we introduce the concept of a level distribution and analytically solve the model for this representation. This allows for an alternative and independent measure of $q$. We argue that, to capture real growth processes, the $q$ estimations from the degree and the level distributions should coincide. Thus, we finally apply both representations to validate the model with synthetically generated tree structures, as well as with collected data of user directories. In the case of real directory structures, we show that $q$ measured from the level distribution are incompatible with $q$ measured from the degree distribution. In contrast to this, we find perfect agreement in the case of simulated data. Thus, we conclude that the model is an incomplete description of the growth of real directory structures as it fails to reproduce the level distribution. This insight can be generalised to point out the importance of the level distribution for modeling tree growth.Comment: 16 pages, 7 figure

Temporal reproduction and its neuroanatomical correlates in adults with attention deficit hyperactivity disorder and their unaffected first-degree relatives

Background: Little is known about time perception, its putative role as cognitive endophenotype, and its neuroanatomical underpinnings in adults with attention deficit hyperactivity disorder (ADHD). Method: Twenty adults with ADHD, 20 unaffected first-degree relatives and 20 typically developing controls matched for age and gender undertook structural magnetic resonance imaging scans. Voxel-based morphometry with DARTEL was performed to obtain regional grey-matter volumes. Temporal processing was investigated as a putative cognitive endophenotype using a temporal reproduction paradigm. General linear modelling was employed to examine the relationship between temporal reproduction performances and grey-matter volumes. Results: ADHD participants were impaired in temporal reproduction and unaffected first-degree relatives performed in between their ADHD probands and typically developing controls. Increased grey-matter volume in the cerebellum was associated with poorer temporal reproduction performance. Conclusions: Adults with ADHD are impaired in time reproduction. Performances of the unaffected first-degree relatives are in between ADHD relatives and controls, suggesting that time reproduction might be a cognitive endophenotype for adult ADHD. The cerebellum is involved in time reproduction and might play a role in driving time performances

Dynamic Analysis of Vascular Morphogenesis Using Transgenic Quail Embryos

Background: One of the least understood and most central questions confronting biologists is how initially simple clusters or sheet-like cell collectives can assemble into highly complex three-dimensional functional tissues and organs. Due to the limits of oxygen diffusion, blood vessels are an essential and ubiquitous presence in all amniote tissues and organs. Vasculogenesis, the de novo self-assembly of endothelial cell (EC) precursors into endothelial tubes, is the first step in blood vessel formation [1]. Static imaging and in vitro models are wholly inadequate to capture many aspects of vascular pattern formation in vivo, because vasculogenesis involves dynamic changes of the endothelial cells and of the forming blood vessels, in an embryo that is changing size and shape. Methodology/Principal Findings: We have generated Tie1 transgenic quail lines Tg(tie1:H2B-eYFP) that express H2B-eYFP in all of their endothelial cells which permit investigations into early embryonic vascular morphogenesis with unprecedented clarity and insight. By combining the power of molecular genetics with the elegance of dynamic imaging, we follow the precise patterning of endothelial cells in space and time. We show that during vasculogenesis within the vascular plexus, ECs move independently to form the rudiments of blood vessels, all while collectively moving with gastrulating tissues that flow toward the embryo midline. The aortae are a composite of somatic derived ECs forming its dorsal regions and the splanchnic derived ECs forming its ventral region. The ECs in the dorsal regions of the forming aortae exhibit variable mediolateral motions as they move rostrally; those in more ventral regions show significant lateral-to-medial movement as they course rostrally. Conclusions/Significance: The present results offer a powerful approach to the major challenge of studying the relative role(s) of the mechanical, molecular, and cellular mechanisms of vascular development. In past studies, the advantages of the molecular genetic tools available in mouse were counterbalanced by the limited experimental accessibility needed for imaging and perturbation studies. Avian embryos provide the needed accessibility, but few genetic resources. The creation of transgenic quail with labeled endothelia builds upon the important roles that avian embryos have played in previous studies of vascular development

Interaction of perceptual grouping and crossmodal temporal capture in tactile apparent-motion

Previous studies have shown that in tasks requiring participants to report the direction of apparent motion, task-irrelevant mono-beeps can "capture'' visual motion perception when the beeps occur temporally close to the visual stimuli. However, the contributions of the relative timing of multimodal events and the event structure, modulating uni- and/or crossmodal perceptual grouping, remain unclear. To examine this question and extend the investigation to the tactile modality, the current experiments presented tactile two-tap apparent-motion streams, with an SOA of 400 ms between successive, left-/right-hand middle-finger taps, accompanied by task-irrelevant, non-spatial auditory stimuli. The streams were shown for 90 seconds, and participants' task was to continuously report the perceived (left-or rightward) direction of tactile motion. In Experiment 1, each tactile stimulus was paired with an auditory beep, though odd-numbered taps were paired with an asynchronous beep, with audiotactile SOAs ranging from -75 ms to 75 ms. Perceived direction of tactile motion varied systematically with audiotactile SOA, indicative of a temporal-capture effect. In Experiment 2, two audiotactile SOAs-one short (75 ms), one long (325 ms)-were compared. The long-SOA condition preserved the crossmodal event structure (so the temporal-capture dynamics should have been similar to that in Experiment 1), but both beeps now occurred temporally close to the taps on one side (even-numbered taps). The two SOAs were found to produce opposite modulations of apparent motion, indicative of an influence of crossmodal grouping. In Experiment 3, only odd-numbered, but not even-numbered, taps were paired with auditory beeps. This abolished the temporal-capture effect and, instead, a dominant percept of apparent motion from the audiotactile side to the tactile-only side was observed independently of the SOA variation. These findings suggest that asymmetric crossmodal grouping leads to an attentional modulation of apparent motion, which inhibits crossmodal temporal-capture effects

Tomato: a crop species amenable to improvement by cellular and molecular methods

Tomato is a crop plant with a relatively small DNA content per haploid genome and a well developed genetics. Plant regeneration from explants and protoplasts is feasable which led to the development of efficient transformation procedures. In view of the current data, the isolation of useful mutants at the cellular level probably will be of limited value in the genetic improvement of tomato. Protoplast fusion may lead to novel combinations of organelle and nuclear DNA (cybrids), whereas this technique also provides a means of introducing genetic information from alien species into tomato. Important developments have come from molecular approaches. Following the construction of an RFLP map, these RFLP markers can be used in tomato to tag quantitative traits bred in from related species. Both RFLP's and transposons are in the process of being used to clone desired genes for which no gene products are known. Cloned genes can be introduced and potentially improve specific properties of tomato especially those controlled by single genes. Recent results suggest that, in principle, phenotypic mutants can be created for cloned and characterized genes and will prove their value in further improving the cultivated tomato.

Geometry of River Networks I: Scaling, Fluctuations, and Deviations

This article is the first in a series of three papers investigating the detailed geometry of river networks. Large-scale river networks mark an important class of two-dimensional branching networks, being not only of intrinsic interest but also a pervasive natural phenomenon. In the description of river network structure, scaling laws are uniformly observed. Reported values of scaling exponents vary suggesting that no unique set of scaling exponents exists. To improve this current understanding of scaling in river networks and to provide a fuller description of branching network structure, we report here a theoretical and empirical study of fluctuations about and deviations from scaling. We examine data for continent-scale river networks such as the Mississippi and the Amazon and draw inspiration from a simple model of directed, random networks. We center our investigations on the scaling of the length of sub-basin's dominant stream with its area, a characterization of basin shape known as Hack's law. We generalize this relationship to a joint probability density and show that fluctuations about scaling are substantial. We find strong deviations from scaling at small scales which can be explained by the existence of linear network structure. At intermediate scales, we find slow drifts in exponent values indicating that scaling is only approximately obeyed and that universality remains indeterminate. At large scales, we observe a breakdown in scaling due to decreasing sample space and correlations with overall basin shape. The extent of approximate scaling is significantly restricted by these deviations and will not be improved by increases in network resolution.Comment: 16 pages, 13 figures, Revtex4, submitted to PR

Emergent Imaging and Geospatial Technologies for Soil Investigations

Soil survey investigations and inventories form the scientific basis for a wide spectrum of agronomic and environmental management programs. Soil data and information help formulate resource conservation policies of federal, state, and local governments that seek to sustain our agricultural production system while enhancing environmental quality on both public and private lands. The dual challenges of increasing agricultural production and ensuring environmental integrity require electronically available soil inventory data with both spatial and attribute quality. Meeting this societal need in part depends on development and evaluation of new methods for updating and maintaining soil inventories for sophisticated applications, and implementing an effective framework to conceptualize and communicate tacit knowledge from soil scientists to numerous stakeholders

Fast fluorescence microscopy for imaging the dynamics of embryonic development

Live imaging has gained a pivotal role in developmental biology since it increasingly allows real-time observation of cell behavior in intact organisms. Microscopes that can capture the dynamics of ever-faster biological events, fluorescent markers optimal for in vivo imaging, and, finally, adapted reconstruction and analysis programs to complete data flow all contribute to this success. Focusing on temporal resolution, we discuss how fast imaging can be achieved with minimal prejudice to spatial resolution, photon count, or to reliably and automatically analyze images. In particular, we show how integrated approaches to imaging that combine bright fluorescent probes, fast microscopes, and custom post-processing techniques can address the kinetics of biological systems at multiple scales. Finally, we discuss remaining challenges and opportunities for further advances in this field