Branching Network Research Articles

On the Interaction between Player Heterogeneity and Partner Heterogeneity in Two-Way Flow Strict Nash Networks

This paper brings together analyses of two-way flow Strict Nash networks under exclusive player heterogeneity assumption and exclusive partner heterogeneity assumption. This is achieved through examining how the interactions between these two assumptions influence important properties of Strict Nash networks. Built upon the findings of Billand et al (2011) and Galleotti et al (2006), which assume exclusive partner heterogeneity and exclusive player heterogeneity respectively, I provide a proposition that generalizes the results of these two models by stating that: (i) Strict Nash network consists of multiple non-empty components as in Galleotti et al (2006), and (ii) each non-empty component is a branching or Bi network as in Billand et al (2011). This proposition requires that a certain restriction on link formation cost (called Uniform Partner Ranking), which encloses exclusive partner heterogeneity and exclusive player heterogeneity as a specific case, is satisfied. In addition, this paper shows that value heterogeneity plays a relatively less important role in changing the shapes of Strict Nash networks.

216 HORMONAL REGULATION OF CLAUDIN-4 TIGHT JUNCTION MOLECULE IN MOUSE PLACENTA

Tight junctions (TJ) are composed of a branching network of sealing strands. TJ regulate paracellular conductance and ionic selectivity. TJ components include the peripheral protein ZO-1, junctional adhesion molecules (JAM) and the integral proteins such as occludin and claudin. Claudins are a family of proteins that are the most important components in the tight junctions. The established paracellular transport barriers that control transportation of molecules within intercellular space. The present study focused on the expression of claudin, suggesting as major working molecules in the paracellular transport system. To study the regulation and roles of claudin family, we examined expression of mouse placental claudin family. Fifteen pregnant C57/BL6 mice were used in this study and TJ proteins including Claudin-1 to Claudin-24 expressions by real-time RT–PCR and Western blotting. The mice were divided into 3 groups depending on the gestational day (on Days 12, 16, and 20 of gestation).The localization of TJ proteins were examined by immunohistochemistry. After we identified the fluctuation of claudin expression during pregnancy, we assumed that the hormones are one regulator for claudin family. Therefore, we performed an in vivo study with hormone receptor antagonists (ICI 182, 780, and RU-486) for examining hormonal effect on claudin expression in the placenta. Forty-nine mice were divided into 7 groups. The changes of claudin expression were examined with real-time RT-PCR and Western blotting. In the transcription levels, Claudin-1, claudin-2, claudin-4, and Claudin-5 expression levels were relatively high compared to others in the claudin family in all periods of the pregnancy. The claudin-4 expression, which reduces permeability of ions, increased over a period of time. However, caludin-5 expression that is the responsive protein for a decrease in paracellular conductance, were decreased. Claudin-1 and -4 have been known as responsive genes for a decrease in paracellular conductance. On the other hand, claudin 2 and 5 have been known as increasing paracellular conductance. In addition, immunohistochemistry was performed to identify their localization for inferring permeability in placenta. In summary, we analysed the claudin expressions and presented possible important claudins among its family. Furthermore, their localization was also examined in the mouse placenta. In addition, the regulation of critically expressed claudins by pregnancy-associated hormones, E2 and P4, was examined. These results may provide functional and structural roles of claudins and their involvement in the maternal-fetal interaction and in the transportation of placental materials.

Novel roles of perivascular nerves on neovascularization.

Neovascularization, including angiogenesis, arteriogenesis and vasculogenesis, occurs in physiological and pathological state. Efficient and controlled reconstruction of functional vascular network is necessary. Nerves and blood vessels establish intricate branching network in every organ which share anatomical and functional characteristics. Nerves direct vessel branching patterns and arterial differentiation in the developmental embryonic limb skin. Various neurotransmitters exert antiapoptotic, chemotactic and proliferative effect on EC and SMC, and modulate all the phases of neovascularization. Hence, we proposed that the perivascular nerves may play critical roles in neovascularization.

Infiltrating angiolipoma of the lower lip: A case report and literature review.

Infiltrating angiolipoma (IAL) is a rare lesion and is a clinicopathological variant of angiolipoma. IAL occurs most commonly in the trunk and extremities, it is rarely found in the head and neck regions and extremely rare in the oral cavity. This study presents the case of a 74-year-old female with IAL of the lower lip. To the best of our knowledge, this is the first case of IAL arising in the lower lip to be reported. Microscopically, IAL was unencapsulated and mature lipocytes were separated by a branching network of proliferating small vessels that infiltrated the adjacent tissues. Therefore, complete excision was difficult to perform. Magnetic resonance imaging has been reported to be valuable in determining the extent of the tumor and asserting a preoperative diagnosis. According to previous studies, the recurrence rate of IAL following surgical extirpation is 35–50%. Furthermore, the levels of mRNA expression of the vascular endothelial growth factor (VEGF) family members in the tumor were investigated. VEGF-A and -B expression were detected, however, VEGF-C and -D were expressed at extremely low levels. Excisional biopsy was performed under local anesthesia. During four years of follow-up, no evidence of tumor recurrence had been identified. An operating microscope may be utilized for the total removal of an IAL to minimize damage to normal tissues. This report indicates that mast cell-derived VEGF may be responsible for the enhanced vascularity in the tumor. We would therefore consider careful extirpation with no wide safety margin to be the procedure of choice, except when the tumor invades irregularly into the muscles.

Abstract 3152: Integrin α6β1 dependent collective cell migration in prostate cancer metastasis

Abstract Investigating the metastasis tactics of cancer cells show some cancers migrate using epithelial to mesenchymal transition (EMT) while others, such as prostate cancer, use collective migration similar to embryonic tubulogenesis. In human tissue specimens, collective migration originates from pre-malignant prostate intraepithelial neoplasia (PIN), occurs in invasive adenocarcinoma and persists in prostate cancer metastatic bone lesions. Successful collective migration requires cell attachment to the surrounding extracellular matrix (ECM), via adhesion receptors, specifically integrins. In prostate cancer, the laminin binding integrins α6β1 and α3β1 are expressed throughout disease progression including metastases. The laminin receptor α6β1 has been shown to be a determinant of prostate tumor cell aggressiveness. Integrin α6β1 undergoes a post-translational modification mediated by the serine protease, urokinase plasminogen activator (uPA) and its receptor uPAR, resulting in a variant form called α6pβ1. In this study, we optimized the growth and retrieval of tumor cells from 3-dimensional matrigel cultures, to determine the role of integrin α6β1, α6pβ1 and α3β1 in DU145 prostate tumor cell collective migration. The DU145 prostate tumor cells embedded in growth factor reduced matrigel, grew robust networks within 24 hours and contained extensive branching structures. The network formation was shown to be dependent on integrin α6β1 expression as determined by specific knockdown of α6β1 over a 24 hour period using 25nM siRNA targeting. Interestingly, the knockdown of α3β1 integrin had no observable effect on the networks. The networks produced by the DU145 cells contained pericellular proteolysis activity along the branches of collective cells as well as at the leading tips of the branches. Laminin 332, its receptor integrin α6β1, and uPAR co-localized on the membranes between cells traveling collectively. Induced production of integrin α6pβ1 increased branching network formation, while blockage of integrin α6pβ1 production impaired collective migration via reduced network formation. Taken together, these observations suggest that collective cell migration through tubulogenesis requires cell adhesion to laminin via integrin α6β1 and production of the α6pβ1 structural variant facilitates this process. Ongoing work is using the model to identify candidate molecular effectors of tubulogenesis as well as pharmacological approaches to block the process and prevent tumor progression. Supported in part by NIH grants CA 23074 and CA 159406. Citation Format: Cynthia S. Rubenstein, Jaime Gard, Raymond B. Nagle, Terry H. Landowski, Anne E. Cress. Integrin α6β1 dependent collective cell migration in prostate cancer metastasis. [abstract]. In: Proceedings of the 105th Annual Meeting of the American Association for Cancer Research; 2014 Apr 5-9; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2014;74(19 Suppl):Abstract nr 3152. doi:10.1158/1538-7445.AM2014-3152

A practical introduction to skeletons for the plant sciences

Before the availability of digital photography resulting from the invention of charged couple devices in 1969, the measurement of plant architecture was a manual process either on the plant itself or on traditional photographs. The introduction of cheap digital imaging devices for the consumer market enabled the wide use of digital images to capture the shape of plant networks such as roots, tree crowns, or leaf venation. Plant networks contain geometric traits that can establish links to genetic or physiological characteristics, support plant breeding efforts, drive evolutionary studies, or serve as input to plant growth simulations. Typically, traits are encoded in shape descriptors that are computed from imaging data. Skeletons are one class of shape descriptors that are used to describe the hierarchies and extent of branching and looping plant networks. While the mathematical understanding of skeletons is well developed, their application within the plant sciences remains challenging because the quality of the measurement depends partly on the interpretation of the skeleton. This article is meant to bridge the skeletonization literature in the plant sciences and related technical fields by discussing best practices for deriving diameters and approximating branching hierarchies in a plant network.

Multi-objective Design Optimization of Branching, Multifloor, Counterflow Microheat Exchangers

Heat removal capacity, coolant pumping power requirement, and surface temperature nonuniformity are three major challenges facing single-phase flow microchannel compact heat exchangers. In this paper multi-objective optimization has been performed to increase heat removal capacity, and decrease pumping power and temperature nonuniformity in complex networks of microchannels. Three-dimensional (3D) four-floor configurations of counterflow branching networks of microchannels were optimized to increase heat removal capacity from surrounding silicon substrate (15 × 15 × 2 mm). Each floor has four different branching subnetworks with opposite flow direction with respect to the next one. Each branching subnetwork has four inlets and one outlet. Branching patterns of each of these subnetworks could be different from the others. Quasi-3D conjugate heat transfer analysis has been performed by developing a software package which uses quasi-1D thermofluid analysis and a 3D steady heat conduction analysis. These two solvers were coupled through their common boundaries representing surfaces of the cooling microchannels. Using quasi-3D conjugate analysis was found to require one order of magnitude less computing time than a fully 3D conjugate heat transfer analysis while offering comparable accuracy for these types of application. The analysis package is capable of generating 3D branching networks with random topologies. Multi-objective optimization using modeFRONTIER software was performed using response surface approximation and genetic algorithm. Diameters and branching pattern of each subnetwork and coolant flow direction on each floor were design variables of multi-objective optimization. Maximizing heat removal capacity, while minimizing coolant pumping power requirement and temperature nonuniformity on the hot surface, were three simultaneous objectives of the optimization. Pareto-optimal solutions demonstrate that thermal loads of up to 500 W/cm2 can be managed with four-floor microchannel cooling networks. A fully 3D thermofluid analysis was performed for one of the optimal designs to confirm the accuracy of results obtained by the quasi-3D simulation package used in this paper.

Changing Agents

It issomething of atruism in the field of book history that it's easy enough to produce detailed case-studies of books and their makers and readers, but very difficult indeed to synthesise these fragments into any sort of greater whole. This is especially true now that heroic bibliographical work has yielded such wonders as the English Short Title Catalogue (ESTC). Now attention increasingly turns to interpretative questions about how books occupy their place in cultures and societies and how they do the work they do. Consensus emerges slowly from a fog of detail. In recent decades work by historians such as D. F. McKenzie and theorists such as Jerome McGann has shown us how messy the work of making books is. Books are collaborative projects shaped by the actions of many people, amongst which those of authors can be of more or less importance. Meanwhile scholars including David McKitterick and Harold Love have successfully challenged the idea that print and manuscript have always been starkly separate modes of production. We now know that that the invention of printing in Europe wasn't a moment of rupture in which manuscript circulation was rendered obsolete, but the beginning of a complex process of coexistence for printed and hand-written texts. Turning to questions of use rather than production, pioneers in the history of reading like Roger Chartier have been followed by an industrious tribe toiling to piece together the history of how different people at different times have used books in different ways. Their aim is to show us that books depend on branching networks of people and practices and that meaning blossoms from those connections. The growing popularity of e-books makes these questions particularly pressing as all sorts of readers ask whether the end of the physical book is nigh. Those who must publish or perish wonder what publishing will look like in a world of open access.

New methods for reconstructing geographical effects on dispersal rates and routes from large-scale radiocarbon databases

We introduce a methodology for reconstructing geographical effects on dispersal and diffusion patterns, using georeferenced archaeological radiocarbon databases. Fast Marching methods for modelling front propagation enable geographical scenarios to be explored regarding barriers, corridors, and favoured and unfavoured habitat types. The use of genetic algorithms as optimal search tools also enables the derivation of new geographical scenarios, and is especially useful in high-dimensional parameter spaces that cannot be characterized exhaustively due to computer runtime constraints. Model selection is guided by goodness-of-fit statistics for observed and predicted radiocarbon dates.We also introduce an important additional model output, namely, modelled phylogenies of the dispersing population or diffusing cultural entity, based on branching networks of shortest or 'least cost' paths. These 'dispersal trees' can be used as an additional tool to evaluate dispersal scenarios, based on their degree of congruence with phylogenies of the dispersing population reconstructed independently from other kinds of information.We illustrate our approach with a case study, the spread of the Neolithic transition in Europe, using a database from the literature (Pinhasi, Fort and Amerman 2005). Our methods find support for a geographical model in which dispersal is limited by an altitudinal cut-off and in which there is a climate-related latitudinal gradient in rate of spread. This model leads to a deceleration in front propagation rate with geodesic distance, which is also consistent with models of the propagation of the Neolithic transition under space competition with pre-existing populations of hunter-gatherers. Our genetic algorithms meanwhile searched the parameter space and found support for an alternative model involving fast spread along the northern Mediterranean coast and the Danube/Rhine riverine corridor. Both these models outperformed the geography-free Great Circle distance model, and both also outperformed another, almost geography-free, model that constrains dispersal to land to and near-offshore coastal waters. The adjusted coefficient of determination for modelled and observed radiocarbon dates for first arrival supports the GA-derived model; the shortest path network analysis, however, gives greater support to the model with altitudinal cut-off and latitudinal gradient in dispersal rate, since it produces branching 'dispersal trees' that are more congruent with these archaeological sites' clade memberships (as defined by archaeological material culture).

Continual in situ monitoring of pore water stable isotopes in the subsurface

Abstract. Stable isotope signatures provide an integral fingerprint of origin, flow paths, transport processes, and residence times of water in the environment. However, the full potential of stable isotopes to quantitatively characterize subsurface water dynamics is yet unfolded due to the difficulty in obtaining extensive, detailed, and repeated measurements of pore water in the unsaturated and saturated zone. This paper presents a functional and cost-efficient system for non-destructive continual in situ monitoring of pore water stable isotope signatures with high resolution. Automatic controllable valve arrays are used to continuously extract diluted water vapor in soil air via a branching network of small microporous probes into a commercial laser-based isotope analyzer. Normalized liquid-phase isotope signatures are then obtained based on a specific on-site calibration approach along with basic corrections for instrument bias and temperature dependent isotopic fractionation. The system was applied to sample depth profiles on three experimental plots with varied vegetation cover in southwest Germany. Two methods (i.e., based on advective versus diffusive vapor extraction) and two modes of sampling (i.e., using multiple permanently installed probes versus a single repeatedly inserted probe) were tested and compared. The results show that the isotope distribution along natural profiles could be resolved with sufficiently high accuracy and precision at sampling intervals of less than four minutes. The presented in situ approaches may thereby be used interchangeably with each other and with concurrent laboratory-based direct equilibration measurements of destructively collected samples. It is thus found that the introduced sampling techniques provide powerful tools towards a detailed quantitative understanding of dynamic and heterogeneous shallow subsurface and vadose zone processes.

Bank branch location and stability during distress

Purpose – The purpose of this paper is to examine the impact of bank branch location on the likelihood of bank failure during the most recent financial crisis. Design/methodology/approach – This paper estimates the probit regression to identify the causes of bank failures and attempts to determine the role of branch location in bank performance. Findings – Using data from failed and surviving banks in Georgia and Florida, this paper finds that diversifying the balance sheet and operating in more competitive markets reduced failure rates, but branching intensity, measured by number of branches and distance of branches from the home office did not significantly reduce the probability of failure. This suggests that, at least in today ' s market, it is not important to bank stability to have a branching network a significant distance from the home office. Originality/value – This paper carefully considers the role of branch location in the likelihood of bank failure during financial distress. As such, it contributes to the historical policy debate regarding regulation prohibiting or minimizing banks ' ability to branch. It also contributes to our understanding of how banks structure their branching networks in the contemporary banking environment.

Properties of Branch Length Similarity Entropy on the Network in Rk

Branching network is one of the most universal phenomena in living or non-living systems, such as river systems and the bronchial trees of mammals. To topologically characterize the branching networks, the Branch Length Similarity (BLS) entropy was suggested and the statistical methods based on the entropy have been applied to the shape identification and pattern recognition. However, the mathematical properties of the BLS entropy have not still been explored in depth because of the lack of application and utilization requiring advanced mathematical understanding. Regarding the mathematical study, it was reported, as a theorem, that all BLS entropy values obtained for simple networks created by connecting pixels along the boundary of a shape are exactly unity when the shape has infinite resolution. In the present study, we extended the theorem to the network created by linking infinitely many nodes distributed on the bounded or unbounded domain in Rk for k ≥ 1. We proved that all BLS entropies of the nodes in the network go to one as the number of nodes, n, goes to infinite and its convergence rate is 1 - O(1= ln n), which was confirmed by the numerical tests.

A new Ediacaran fossil with a novel sediment displacive life habit

Nilpenia rossi new genus new species, described here from the Ediacara Member (Rawnsley Quartzite, South Australia), provides evidence of a Precambrian macroscopic sessile sediment-dweller. Nilpenia, ranging up to 30 cm in diameter, consists of two zones, a complex central area surrounded by radiating, dichotomously branching structures that decrease in diameter from the center to the outer edges. Other elements of the Ediacara Biota are interpreted to have been mat-encrusters but Nilpenia uniquely grew within the upper millimeters of the actual sediment displacing sediment with growth. This sediment surface was rippled and cohesive and may well have included an endobenthic mat. The branching network on the upper surface of the organisms would have been in contact with the water. The phylogenetic relationships of the Ediacara biota are not well constrained and Nilpenia is no exception. However, the morphology and ecology of Nilpenia represent a novel growth strategy present in the Ediacaran and not common today.

Galactosyltransferase 4 is a major control point for glycan branching in N-linked glycosylation.

ABSTRACTProtein N-glycosylation is a common post-translational modification that produces a complex array of branched glycan structures. The levels of branching, or antennarity, give rise to differential biological activities for single glycoproteins. However, the precise mechanism controlling the glycan branching and glycosylation network is unknown. Here, we constructed quantitative mathematical models of N-linked glycosylation that predicted new control points for glycan branching. Galactosyltransferase, which acts on N-acetylglucosamine residues, was unexpectedly found to control metabolic flux through the glycosylation pathway and the level of final antennarity of nascent protein produced in the Golgi network. To further investigate the biological consequences of glycan branching in nascent proteins, we glycoengineered a series of mammalian cells overexpressing human chorionic gonadotropin (hCG). We identified a mechanism in which galactosyltransferase 4 isoform regulated N-glycan branching on the nascent protein, subsequently controlling biological activity in an in vivo model of hCG activity. We found that galactosyltransferase 4 is a major control point for glycan branching decisions taken in the Golgi of the cell, which might ultimately control the biological activity of nascent glycoprotein.

Bridging Integrator 1 (BIN1)-Induced T-Tubule Formation in Cardiomyocytes

The T-tubule system is a branching network of membrane invaginations essential for efficient Ca2+-induced Ca2+ release in myocytes. Significant remodeling of this system has been observed during heart failure (HF), resulting in delayed Ca2+ release at sites lacking T-tubules. Despite its considerable role in HF aetiology, the signaling mechanisms behind T-tubule remodeling remain largely unknown. Bridging integrator 1 (BIN1) has recently drawn considerable interest due to its altered expression during HF and ability to tubulate membranes. In rats examined 6 weeks following myocardial infarction, BIN1 transcription was significantly elevated in animals with compensated or end-stage HF, compared to SHAM operated controls. Although overall T-tubule density was unchanged, confocal imaging of isolated cells stained with di-8-ANEPPS confirmed that the transverse pattern of T-tubules was lost in failing cardiomyocytes, as indicated by reduced peak power in fast Fourier transforms. Interestingly, between-peak power was increased, consistent with the increased fraction of longitudinal tubules visible in failing cardiomyocytes. The role of BIN1 in T-tubule growth was investigated using HL-1 cells, a differentiated murine cardiac cell line lacking both intrinsic BIN1 and T-tubules. When transfected with hBIN1, HL-1 cells developed BIN1-positive invaginations as early as 12 hours following transfection. Whereas BIN1 transcript and protein levels rapidly rose to a peak 24 hours following transfection, BIN1-generated tubules gradually increased in density up until 48 hours after transfection. Additionally, early Ca2+ release at sites containing BIN1-positive tubules indicated that these structures improve Ca2+ release synchrony across the cell. We propose that BIN1 is a crucial regulator of T-tubule development in both healthy and failing cardiomyocytes. In the setting of heart failure, increased BIN1 expression may promote growth of longitudinal tubules that compensate for loss of transverse elements, thereby improving calcium homeostasis in this disease.

Commensal borings from the Middle Devonian of central New York: ecologic and taxonomic review ofClionoides, Clionolithes, andCanaliparvan. ichnogen

The examination of 730 borings within 88 brachiopod hosts form the Middle Devonian of central New York State revealed four ichnospecies belonging to three ichnogenera that have taxonomic histories riddled with confusion, controversy and contradiction. New observations of the ichnotaxa question long-held views of a simple morphologic differentiation between sponge borings and worm borings.ClionoidesFenton and Fenton, 1932 is here considered a sponge boring, which is comprised of a complex, multi-dimensional system of tunnels, shafts, canals, microterraced bowl-shaped structures and cone extensions, and is a senior synonym ofPaleosabella(McCoy 1855) andVermiforichnusCameron, 1969a.ClionolithesClarke, 1908 is a sponge boring possessing a rosette, branching network extending from a central node and is a senior synonym ofNododendrinaVogel et al., 1987 andRamodendrinaVogel et al., 1987. The creation ofCanaliparva circularisn. ichnogen. n. ichnosp. is needed to accommodate simple, vertically oriented, U-shaped tunnels that are indicative of worm activity. Paleoecologic evidence supports a commensal relationship between the endoliths and hosts based upon boring site frequencies in the hosts, boring patterns and five inter-specific co-occurrences between traces. These new data suggest greater diversity and ecologic complexity in ichnofaunal paleocommunities from the Middle Devonian than previously recognized.

128 EXPRESSIONS OF MOUSE TIGHT JUNCTION MOLECULES IN PLACENTA – CLAUDINS AND OTHER PARACELLULAR TRANSPORT MOLECULES

Tight junctions (TJ) are composed of a branching network of sealing strands. Tight junctions regulate paracellular conductance and ionic selectivity. The TJ components include the peripheral protein ZO-1, junctional adhesion molecules (JAM), and integral proteins, such as occludin and claudin. Claudins, a family of proteins, are the most important components in TJ. They establish paracellular transport barriers, which control transportation of molecules within intercellular space. The current study focused on expression of claudin, suggesting claudin as a major working molecule in the paracellular transport system. In order to study the mechanisms and roles of the claudin family, the expression levels of claudin family in various organs should be determined. In this study, we examined expression of the mouse placental claudin family. Pregnant C57/BL6 mice (n = 5) were used in this study, and compared with β-actin, expression of TJ proteins, including Claudin-1 to Claudin-24, JAM-a, Zo-1, and occludin, tricellulin, and MarvelD3 was examined. In the transcription levels, Claudin-1 and -4 proteins were predominantly expressed. Claudin-1 and -4 have been known as a responsive gene for a direct decrease in paracellular conductance by selective reduction of the permeability of Na+ ions. On the other hand, Claudin-2, Claudin-3, Claudin-5, Cludin-11, and Claudin-12 showed ~33% expression compared with Claudin-1. Claudin-6 and Claudin-7 showed ~20% relative expression compared to Claudin 1. Claudin-10a and Claudin-16 were not detectable by real-time RT-PCR under our experimental conditions. Other claudin proteins showed low expression. Because the transcriptional levels of TJ genes were expressed variously, protein levels and their localization in the placenta will be further evaluated by immunostaining and Western blot assay. This study will provide data on expression of TJ genes and their localization in the mouse placenta, which may contribute to assuming the roles of these TJ genes regarding maternal-fetal ion transportation in the placenta.

The Influence of Branch Order on Optimal Leaf Vein Geometries: Murray’s Law and Area Preserving Branching

Models that predict the form of hierarchical branching networks typically invoke optimization based on biomechanical similitude, the minimization of impedance to fluid flow, or construction costs. Unfortunately, due to the small size and high number of vein segments found in real biological networks, complete descriptions of networks needed to evaluate such models are rare. To help address this we report results from the analysis of the branching geometry of 349 leaf vein networks comprising over 1.5 million individual vein segments. In addition to measuring the diameters of individual veins before and after vein bifurcations, we also assign vein orders using the Horton-Strahler ordering algorithm adopted from the study of river networks. Our results demonstrate that across all leaves, both radius tapering and the ratio of daughter to parent branch areas for leaf veins are in strong agreement with the expectation from Murray’s law. However, as veins become larger, area ratios shift systematically toward values expected under area-preserving branching. Our work supports the idea that leaf vein networks differentiate roles of leaf support and hydraulic supply between hierarchical orders.

A conceptual structure for heat transfer imitating the transporting principle of plant leaf

Due to the high efficiency in water transportation, the plant branching networks were widely investigated and used in designing the microchannel of mass flow and heat dissipation for electronic components. However, in current studies of fractal tree-like networks used in microchannel design, the wall was always regarded as a non-porous structure, and the porous tissue surrounding the network was overlooked, which is actually contrary to the real plant branching system, where water can penetrate into the surrounding tissue through the permeable wall. In this paper, the branching network with permeable wall and the porous media are designed to form a conceptual structure based on the real architecture of plant leaf. The effect of the permeable wall and the porous media on the performance of heat dissipation and flow is analyzed. The results show that, the permeable wall and the porous media play a very important role in heat spreader design.

Identification of butterfly based on their shapes when viewed from different angles using an artificial neural network

Identification of butterfly species is essential because they are directly associated with crop plants used for human and animal consumption. However, the widely used reliable methods for butterfly identification are not efficient due to complicated butterfly shapes. We previously developed a novel shape recognition method that uses branch length similarity (BLS) entropy, which is a simple branching network consisting of a single node and branches. The method has been successfully applied to recognize battle tanks and characterize human faces with different emotions. In the present study, we used the BLS entropy profile (an assemble of BLS entropies) as an input feature in a feed-forward back-propagation artificial neural network to identify butterfly species according to their shapes when viewed from different angles (for vertically adjustable angle, θ=±10°, ±20°, …, ±60° and for horizontally adjustable angle, φ=±10°, ±20°, …, ±60°). In the field, butterfly images are generally captured obliquely by camera due to butterfly alignment and viewer positioning, which generates various shapes for a given specimen. To generate different shapes of a butterfly when viewed from different angles, we projected the shapes captured from top-view to a plane rotated through angles θ and φ. Projected shapes with differing θ and φ values were used as training data for the neural network and other shapes were used as test data. Experimental results showed that our method successfully identified various butterfly shapes. In addition, we briefly discuss extension of the method to identify more complicated images of different butterfly species.