Quantifying loopy network architectures

Biology presents many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a hierarchically-nested architecture containing closed loops at many different levels. Although a number of methods have been proposed to measure aspects of the structure of such networks, a robust metric to quantify their hierarchical organization is still lacking. We present an algorithmic framework, the hierarchical loop decomposition, that allows mapping loopy networks to binary trees, preserving in the connectivity of the trees the architecture of the original graph. We apply this framework to investigate computer generated graphs, such as artificial models and optimal distribution networks, as well as natural graphs extracted from digitized images of dicotyledonous leaves and vasculature of rat cerebral neocortex. We calculate various metrics based on the Asymmetry, the cumulative size distribution and the Strahler bifurcation ratios of the corresponding trees and discuss the relationship of these quantities to the architectural organization of the original graphs. This algorithmic framework decouples the geometric information (exact location of edges and nodes) from the metric topology (connectivity and edge weight) and it ultimately allows us to perform a quantitative statistical comparison between predictions of theoretical models and naturally occurring loopy graphs.Comment: 17 pages, 8 figures. During preparation of this manuscript the authors became aware of the work of Mileyko at al., concurrently submitted for publicatio

Drop Traffic in Microfluidic Ladder Networks with Fore-Aft Structural Asymmetry

We investigate the dynamics of pairs of drops in microfluidic ladder networks with slanted bypasses, which break the fore-aft structural symmetry. Our analytical results indicate that unlike symmetric ladder networks, structural asymmetry introduced by a single slanted bypass can be used to modulate the relative drop spacing, enabling them to contract, synchronize, expand, or even flip at the ladder exit. Our experiments confirm all these behaviors predicted by theory. Numerical analysis further shows that while ladder networks containing several identical bypasses are limited to nearly linear transformation of input delay between drops, mixed combination of bypasses can cause significant non-linear transformation enabling coding and decoding of input delays.Comment: 4 pages, 5 figure

Biomimetic transferable surface for a real time control over wettability and photoerasable writing with water drop lens

We demonstrate a transferable device that can turn wettability of surfaces to sticky or slippy, as per requirement. It is composed of polymeric yarn with a fibrous structure, which can be lifted and placed on any surface to render it the unique wettability properties. We introduce Polyvinylidenefluoride (PVDF) random fiber as biomimetic rose petal surface. When it is decorated with PVDF nanofibers yarns, the random mesh transform from rose petal sticky state into grass leaf slippy state. When it is placed on sticky, hydrophilic metal coin, it converts the surface of the coin to super hydrophobic. Adjustments in the yarn system, like interyarn spacing, can be done in real time to influence its wettability, which is a unique feature. Next, we load the polymer with a photochromic compound for chemical restructuring. It affects the sliding angle of water drop and makes the fibers optically active. We also demonstrate a “water droplets lens” concept that enables erasable writing on photochromic rose petal sticky fibrous surface. The droplet on a highly hydrophobic surface acts as a ball lens to concentrate light onto a hot spot; thereby we demonstrate UV light writing with water lenses and visible light erasing

New constraints on atmospheric CO2 concentration for the Phanerozoic

Earth's atmospheric CO2 concentration (ca) for the Phanerozoic Eon is estimated from proxies and geochemical carbon cycle models. Most estimates come with large, sometimes unbounded uncertainty. Here, we calculate tightly constrained estimates of ca using a universal equation for leaf gas exchange, with key variables obtained directly from the carbon isotope composition and stomatal anatomy of fossil leaves. Our new estimates, validated against ice cores and direct measurements of ca, are less than 1000 ppm for most of the Phanerozoic, from the Devonian to the present, coincident with the appearance and global proliferation of forests. Uncertainties, obtained from Monte Carlo simulations, are typically less than for ca estimates from other approaches. These results provide critical new empirical support for the emerging view that large (~2000-3000 ppm), long-term swings in ca do not characterize the post-Devonian and that Earth's long-term climate sensitivity to ca is greater than originally thought. Key Points A novel CO2 proxy calculates past atmospheric CO2 with improved certainty CO2 is unlikely to have exceeded ~1000 ppm for extended periods post Devonian Earth's long-term climate sensitivity to CO2 is greater than originally thought

Phenotypic Plasticity of Leaf Shape along a Temperature Gradient in Acer rubrum

Both phenotypic plasticity and genetic determination can be important for understanding how plants respond to environmental change. However, little is known about the plastic response of leaf teeth and leaf dissection to temperature. This gap is critical because these leaf traits are commonly used to reconstruct paleoclimate from fossils, and such studies tacitly assume that traits measured from fossils reflect the environment at the time of their deposition, even during periods of rapid climate change. We measured leaf size and shape in Acer rubrum derived from four seed sources with a broad temperature range and grown for two years in two gardens with contrasting climates (Rhode Island and Florida). Leaves in the Rhode Island garden have more teeth and are more highly dissected than leaves in Florida from the same seed source. Plasticity in these variables accounts for at least 6–19 % of the total variance, while genetic differences among ecotypes probably account for at most 69–87 %. This study highlights the role of phenotypic plasticity in leaf-climate relationships. We suggest that variables related to tooth count and leaf dissection in A. rubrum can respond quickly to climate change, which increases confidence in paleoclimate methods that use these variables

Leaf Morphology, Taxonomy and Geometric Morphometrics: A Simplified Protocol for Beginners

Taxonomy relies greatly on morphology to discriminate groups. Computerized geometric morphometric methods for quantitative shape analysis measure, test and visualize differences in form in a highly effective, reproducible, accurate and statistically powerful way. Plant leaves are commonly used in taxonomic analyses and are particularly suitable to landmark based geometric morphometrics. However, botanists do not yet seem to have taken advantage of this set of methods in their studies as much as zoologists have done. Using free software and an example dataset from two geographical populations of sessile oak leaves, we describe in detailed but simple terms how to: a) compute size and shape variables using Procrustes methods; b) test measurement error and the main levels of variation (population and trees) using a hierachical design; c) estimate the accuracy of group discrimination; d) repeat this estimate after controlling for the effect of size differences on shape (i.e., allometry). Measurement error was completely negligible; individual variation in leaf morphology was large and differences between trees were generally bigger than within trees; differences between the two geographic populations were small in both size and shape; despite a weak allometric trend, controlling for the effect of size on shape slighly increased discrimination accuracy. Procrustes based methods for the analysis of landmarks were highly efficient in measuring the hierarchical structure of differences in leaves and in revealing very small-scale variation. In taxonomy and many other fields of botany and biology, the application of geometric morphometrics contributes to increase scientific rigour in the description of important aspects of the phenotypic dimension of biodiversity. Easy to follow but detailed step by step example studies can promote a more extensive use of these numerical methods, as they provide an introduction to the discipline which, for many biologists, is less intimidating than the often inaccessible specialistic literature

Classification of Camellia (Theaceae) Species Using Leaf Architecture Variations and Pattern Recognition Techniques

Leaf characters have been successfully utilized to classify Camellia (Theaceae) species; however, leaf characters combined with supervised pattern recognition techniques have not been previously explored. We present results of using leaf morphological and venation characters of 93 species from five sections of genus Camellia to assess the effectiveness of several supervised pattern recognition techniques for classifications and compare their accuracy. Clustering approach, Learning Vector Quantization neural network (LVQ-ANN), Dynamic Architecture for Artificial Neural Networks (DAN2), and C-support vector machines (SVM) are used to discriminate 93 species from five sections of genus Camellia (11 in sect. Furfuracea, 16 in sect. Paracamellia, 12 in sect. Tuberculata, 34 in sect. Camellia, and 20 in sect. Theopsis). DAN2 and SVM show excellent classification results for genus Camellia with DAN2's accuracy of 97.92% and 91.11% for training and testing data sets respectively. The RBF-SVM results of 97.92% and 97.78% for training and testing offer the best classification accuracy. A hierarchical dendrogram based on leaf architecture data has confirmed the morphological classification of the five sections as previously proposed. The overall results suggest that leaf architecture-based data analysis using supervised pattern recognition techniques, especially DAN2 and SVM discrimination methods, is excellent for identification of Camellia species