Branching Geometry Research Articles

FROM STITCHES TO DIGITS AND BACK: COMPUTATIONAL CROCHETING OF BRANCHING GEOMETRIES

Crocheting is a hands-on craft that involves repetitive manipulation of a single continuous thread with a hook-like tool to generate surfaces and 3D forms. In a previous study, we have presented a parametric model [1] that generates crochet patterns of NURBS surfaces using a 10-stitches-by-10-rows swatch to account for all the physical variables that affect the crocheted object (i.e., yarn thickness, hook size, crafter’s grip). The dimensions of the previously crocheted tension swatches were used as the inputs of the crochet pattern generator algorithm, alongside the desired NURBS geometry, to generate individualized crochet patterns. These crochet patterns are text-based representations, similar to g-code in additive manufacturing, enabling the documentation and communication of the step-by-step hands-on crocheting process. Following these crochet patterns, the users can crochet physical objects with the same dimensions and form as their digitally modeled counterparts. 
 This paper presents the second stage of this research in which we expanded this computational framework to enable crocheting of parametric branching geometries with multiple components by multiple crafters. While the components of the branching geometries can be crocheted by a single user, it is also possible to have different users crochet the components since the tension swatch can capture crafter-specific variables. As a proof-of-concept, a branching structure made of 14 unique components is designed and crocheted by two students of architecture as part of the Advanced Digital Fabrication course at the Pennsylvania State University. The students each crocheted 7 components based on their individual inputs while maintaining the dimensions and form of the digitally designed branching geometry. The findings suggest the possibility of a collective and distributed crocheting platform which can be used to create crocheted artifacts in various scales. This can be considered an alternative way to transition from the digital to the physical without relying on digital fabrication tools.

A Novel Path Generation Approach for Robotic Spatial Printing of Branching Geometry

Although robotic spatial printing (RSP) has demonstrated a new way of fabricating building components with a good stiffness-to-weight ratio, the complexity of the applied geometries is still limited. Among them are branching geometries, which refer to the bio-inspired branching structures (BIBSs) in the building industry. This paper presents a cutting-edge approach to tackle this bottleneck problem, in which we propose an automated printing path generation (APPG) approach for the RSP of branching geometries, including an original hierarchical framework of printing node permutations and a linear workflow that incorporates five core algorithms: the heat method, graph generation, graph traversal, curve adjustment, and lattice generation. Through the execution of this workflow, a lattice structure and its corresponding printing path can be generated. This work is validated by the simulation of three prototypes: two-branch geometry, multi-branch geometry, and multi-level-branch geometry. Printing expenses are compared with each of the related algorithms to validate the efficiency of this proposed approach. Along with the appropriate APPG solutions, an analytical tool for topological type is also presented in this paper.

Tree Information Modeling: A Data Exchange Platform for Tree Design and Management

Trees integrated into buildings and dense urban settings have become a trend in recent years worldwide. Without a thoughtful design, conflicts between green and gray infrastructures can take place in two aspects: (1) tree crown compete with living space above ground; (2) built underground environment, the other way round, affect tree’s health and security. Although various data about urban trees are collected by different professions for multiple purposes, the communication between them is still limited by unmatched scales and formats. To address this, tree information modeling (TIM) is proposed in this study, aiming at a standardized tree description system in a high level of detail (LoD). It serves as a platform to exchange data and share knowledge about tree growth models. From the perspective of architects and landscape designers, urban trees provide ecosystem services (ESS) not only through their overall biomass, shading, and cooling. They are also related to various branching forms and crown density, forming new layers of urban living space. So, detailed stem, branch and even root geometry is the key to interacting with humans, building structures and other facilities. It is illustrated in this paper how these detailed data are collected to initialize a TIM model with the help of multiple tools, how the topological geometry of stem and branches in TIM is interpreted into an L-system (a common syntax to describe tree geometries), allowing implementation of widely established tree simulations from other professions. In a vision, a TIM-assisted design workflow is framed, where trees are regularly monitored and simulated under boundary conditions to approach target parameters by design proposals.

Thermal control of parallelly connected thermoelectric coolers in a uniform temperature field

The possibility of using a set of thermoelectric devices to control the thermal regime of a number of thermo-dependent and heat-loaded elements of radio-electronic equipment, which are subject to increased requirements for reliability indicators and dynamic characteristics, is considered. A mathematical model of a thermoelectric device has been developed for a uniform temperature field, a typical range of power dissipation of the products used, a range of standard values of the supply voltage, and a fixedgeometry of thermoelement legs. A relation is obtained for determining the relative operating current depending on the relative temperature difference at a given supply voltage, the geometry of the thermoelement branches, and the magnitude of the thermal load. The region of real values of the relative operating current in the zone of relative temperature differences is determined for a given geometry of branches and thermal load. An analysis is made of the relationship between the relative operating current of a single-stage thermoelectric cooler and the coefficient of performance, the amount of energy expended, the heat-removing capacity of the radiator, the time to reach a stationary mode, and the probability of failure-free operation. The dependence ofthe relative failure rate and the probability of failure-free operation, the amount of energy expended, the heat-removing capacity of the radiator, and the number of thermoelements on the supply voltage of the thermoelectric cooler has been studied. This made it possible to evaluate the control features and identify the effectiveness of the control actions when the coolers are connected in parallel in a uniform temperature field. The possibility of choosing the optimal supply voltage is shown, taking into account a number of restrictive factors in terms of weight, size, energy, dynamic and reliability characteristics of a complex of thermoelectric coolers as part of systems for ensuring thermal regimes of heat-loaded radio-electronic equipment.

Use of the volume-averaged Murray's deviation method for the characterization of branching geometry in liver fibrosis: a preliminary study on vascular circulation.

Vascular changes in liver fibrosis can result in increased intrahepatic vascular resistance and impaired blood circulation. This can hinder the recovery from fibrosis and may eventually lead to portal hypertension, a major cirrhosis complication. This report proposed a volume-averaged Murray's deviation method to characterize intrahepatic circulation in the liver during fibrosis and its subsequent regression via X-ray phase-contrast computed tomography (PCCT). Liver fibrosis was induced in 24 Sprague-Dawley rats by exposure to carbon tetrachloride (CCl4) for up to 10 weeks, after which, spontaneous regression commenced and continued until week 30. High-resolution three-dimensional (3D) imaging of the livers was performed with PCCT. The values of Murray's deviation based on the volume-averaged and the conventional diameter-based methods were compared. After that, the intrahepatic circulation at different stages of fibrosis was evaluated using the volume-averaged method. The increase in collagen during liver fibrosis was assessed by pathological analyses. A comparison of the 2 methods showed that with an increase in the number of diameter measurements, the value of Murrary's deviation obtained using the diameter-based method gradually approaches those of the volume-averaged method, with minimal variations. The value of Murray's deviation increased with the development of fibrosis. After reversal, the value rapidly decreased and approached that of the normal state in both the main branches (1.05±0.17, 1.17±0.21, 1.34±0.18, and 1.17±0.19 in the normal, moderate, severe, and regressive groups, respectively; P<0.05 between the severe group and other groups) and the small branches (1.05±0.09, 1.42±0.48, 1.79±0.57, and 1.18±0.28 in the normal, moderate, severe, and regressive group, respectively; P<0.05 between adjacent groups). An analysis of Murray's deviation and the pathological results showed that the vascular circulation in this disease model was consistent with the progression and recovery from fibrosis. This study showed the validity of the volume-averaged method for calculating Murray's deviation and demonstrated that it could accurately evaluate the blood circulation state of the liver during fibrosis and its subsequent regression. Thus, the volume-averaged method of calculating Murray's deviation may be an objective and valuable staging criterion to evaluate intrahepatic circulation during liver fibrosis.

Survival in branching cellular populations

We analyze evolutionary dynamics in a confluent, branching cellular population, such as in a growing duct, vasculature, or in a branching microbial colony. We focus on the coarse-grained features of the evolution and build a statistical model that captures the essential features of the dynamics. Using simulations and analytic approaches, we show that the survival probability of strains within the growing population is sensitive to the branching geometry: Branch bifurcations enhance survival probability due to an overall population growth (i.e., “inflation”), while branch termination and the small effective population size at the growing branch tips increase the probability of strain extinction. We show that the evolutionary dynamics may be captured on a wide range of branch geometries parameterized just by the branch diameter N0 and branching rate b. We find that the survival probability of neutral cell strains is largest at an “optimal” branching rate, which balances the effects of inflation and branch termination. We find that increasing the selective advantage s of the cell strain mitigates the inflationary effect by decreasing the average time at which the mutant cell fate is determined. For sufficiently large selective advantages, the survival probability of the advantageous mutant decreases monotonically with the branching rate.

A method of three-dimensional branching geometry to differentiate the intrahepatic vascular type in early-stage liver fibrosis using X-ray phase-contrast CT

PurposeDifferentiating the intrahepatic vascular type is essential for the early diagnosis of liver fibrosis. X-ray phase-contrast computed tomography (PCCT) is a label-free, high-resolution imaging modality for imaging vascular networks in a whole liver lobe. This study explores the use of three-dimensional (3D) branching geometry to differentiate between the hepatic vein (HV) and portal vein (PV) in early-stage liver fibrosis with PCCT. MethodBile duct ligation surgery was conducted in mice to induce early-stage liver fibrosis. The individual liver lobes of mice were imaged using PCCT, and morphological characteristics, including vascular diameter, cross-sectional area, eccentricity, branch angle, bifurcation index, area ratio and junction exponent, were investigated in 3D modality. These characteristics were used to differentiate the HV from the PV, and their performance was evaluated through receiver operating characteristic (ROC) curve analysis. ResultsPCCT revealed a 3D vascular structure of the liver lobes. For intact lobes, the differentiation method between the HV and PV using the junction exponent had an AUC of 0.99 (95% CI: 0.98–1.00). Moreover, the AUCs of the junction exponent for 15, 10, and 5 branches in dissected lobes for differentiation were 0.98 (95% CI: 0.94–1.00), 0.86 (95% CI: 0.73–0.99) and 0.82 (95% CI: 0.67–0.97), respectively. ConclusionThe method of 3D branching geometry using the junction exponent could differentiate the HV from PV in early-stage liver fibrosis via the PCCT, which provides the foundation for further analysis of liver fibrosis.

A Review of Recent Research on Bio-inspired Structures and Materials

As result of advancements in DNA technology, nearly any two- or three-dimensional architecture may now be precisely built. The selection of DNA sequences creates new opportunities to predictably generate the structure and size of anodized monomolecular assemblies, which is crucial for successful self-assembly. Designer nucleoside analogues can be added to DNA nonmaterial’s to further functionalize them with accessible groups that affect their activity. This article highlights the latest developments young discipline a rundown of potential future directions and uses. The ability to create nearly any three dimensional geometry using a DNA-based scaffolding approach is a significant benefit; the only real restriction is the researcher's creativity. Examples of building blocks include engineered Holliday junctions, DNA scissoring, ion-triggered switches, DNA tube regulation DNA linkers, and Small-molecule-mediated DNA junction induction. A self-assembled crystalline DNA structure developed by Seaman, others is undoubtedly a recent key structure in three-dimensional design. [3] Tensor triangles, which are composed of three connected non-coplanar double helices of DNA, are essentially hard 3D triangular units. They come together with the addition of sticky vertices, eventually forming a symmetric 3D lattice. Surprisingly, at temperatures when genomic DNA is entirely reduced, the DNA will be unusually branched, with small sticky ends combining into a highly ordered substance if branch geometry and connector stiffness promote crystallization. Can be long (usually viral) DNA strands joined main strands to produce well-defined anodized as illustrated by Rothmans' pioneering work on DNA origami tiles. The successful fabrication of smiling faces on well-known maps and surfaces is proof that DNA origami only needs a few hundred basic strands to form. [12] Because rectangular origami tiles may be connected together by hanging DNA around the edges, they are now beginning to play a significant assembly line. Grasp the crucial elements DNA is involved in the construction of origami superstructures requires an understanding of origami tile design.

Experimental Film Cooling Effectiveness of Three-Hole-Branch Circular Holes

A three-hole-branch geometry for film cooling is proposed. Each branch is made up of a streamwise 30°-angled circular hole with a circular hole of the same diameter on each side of it. These three holes share the same inlet area on the coolant supply side. Three side hole inclination angles of 30°, 37.5°, and 45° and three branch angles (the angle between the main and side holes) generated nine configurations that were tested for four blowing ratios of 0.5, 1, 1.5, and 2. To their benefits, these straight-through circular holes could easily be laser drilled on the airfoils or other gas turbine hot section surfaces. For comparative evaluation of these film hole geometries, the commonly used 7°-7°-7° diffusion hole geometry with the same inlet hole diameter was tested as a baseline under otherwise identical conditions. The pressure-sensitive paint (PSP) technique was utilized to test these geometries for their film cooling effectiveness. Depending on the branch geometry, for the same amount of coolant, some configurations were found to be superior to the baseline case for stream- or spanwise film cooling distributions while for the steeper side hole angles, these branched holes did not perform as well as the baseline case. The main conclusion is that the three holes with the same inclination angle of 30° exhibited the best film cooling effectiveness performance including the baseline geometry.

Cancer as a Model System for Testing Metabolic Scaling Theory

Biological allometries, such as the scaling of metabolism to mass, are hypothesized to result from natural selection to maximize how vascular networks fill space yet minimize internal transport distances and resistance to blood flow. Metabolic scaling theory argues two guiding principles—conservation of fluid flow and space-filling fractal distributions—describe a diversity of biological networks and predict how the geometry of these networks influences organismal metabolism. Yet, mostly absent from past efforts are studies that directly, and independently, measure metabolic rate from respiration and vascular architecture for the same organ, organism, or tissue. Lack of these measures may lead to inconsistent results and conclusions about metabolism, growth, and allometric scaling. We present simultaneous and consistent measurements of metabolic scaling exponents from clinical images of lung cancer, serving as a first-of-its-kind test of metabolic scaling theory, and identifying potential quantitative imaging biomarkers indicative of tumor growth. We analyze data for 535 clinical PET-CT scans of patients with non-small cell lung carcinoma to establish the presence of metabolic scaling between tumor metabolism and tumor volume. Furthermore, we use computer vision and mathematical modeling to examine predictions of metabolic scaling based on the branching geometry of the tumor-supplying blood vessel networks in a subset of 56 patients diagnosed with stage II-IV lung cancer. Examination of the scaling of maximum standard uptake value with metabolic tumor volume, and metabolic tumor volume with gross tumor volume, yield metabolic scaling exponents of 0.64 (0.20) and 0.70 (0.17), respectively. We compare these to the value of 0.85 (0.06) derived from the geometric scaling of the tumor-supplying vasculature. These results: (1) inform energetic models of growth and development for tumor forecasting; (2) identify imaging biomarkers in vascular geometry related to blood volume and flow; and (3) highlight unique opportunities to develop and test the metabolic scaling theory of ecology in tumors transitioning from avascular to vascular geometries.

Fitting Splines to Axonal Arbors Quantifies Relationship Between Branch Order and Geometry.

Neuromorphology is crucial to identifying neuronal subtypes and understanding learning. It is also implicated in neurological disease. However, standard morphological analysis focuses on macroscopic features such as branching frequency and connectivity between regions, and often neglects the internal geometry of neurons. In this work, we treat neuron trace points as a sampling of differentiable curves and fit them with a set of branching B-splines. We designed our representation with the Frenet-Serret formulas from differential geometry in mind. The Frenet-Serret formulas completely characterize smooth curves, and involve two parameters, curvature and torsion. Our representation makes it possible to compute these parameters from neuron traces in closed form. These parameters are defined continuously along the curve, in contrast to other parameters like tortuosity which depend on start and end points. We applied our method to a dataset of cortical projection neurons traced in two mouse brains, and found that the parameters are distributed differently between primary, collateral, and terminal axon branches, thus quantifying geometric differences between different components of an axonal arbor. The results agreed in both brains, further validating our representation. The code used in this work can be readily applied to neuron traces in SWC format and is available in our open-source Python package brainlit: http://brainlit.neurodata.io/.

Construction of Initial Data Sets for Lorentzian Manifolds with Lightlike Parallel Spinors

Lorentzian manifolds with parallel spinors are important objects of study in several branches of geometry, analysis and mathematical physics. Their Cauchy problem has recently been discussed by Baum, Leistner and Lischewski, who proved that the problem locally has a unique solution up to diffeomorphisms, provided that the intial data given on a space-like hypersurface satisfy some constraint equations. In this article we provide a method to solve these constraint equations. In particular, any curve (resp. closed curve) in the moduli space of Riemannian metrics on M with a parallel spinor gives rise to a solution of the constraint equations on Mtimes (a,b) (resp. Mtimes S^1).

Low Cost Automatic Reconstruction of Tree Structure by AdQSM with Terrestrial Close-Range Photogrammetry

The quantitative structure model (QSM) contains the branch geometry and attributes of the tree. AdQSM is a new, accurate, and detailed tree QSM. In this paper, an automatic modeling method based on AdQSM is developed, and a low-cost technical scheme of tree structure modeling is provided, so that AdQSM can be freely used by more people. First, we used two digital cameras to collect two-dimensional (2D) photos of trees and generated three-dimensional (3D) point clouds of plot and segmented individual tree from the plot point clouds. Then a new QSM-AdQSM was used to construct tree model from point clouds of 44 trees. Finally, to verify the effectiveness of our method, the diameter at breast height (DBH), tree height, and trunk volume were derived from the reconstructed tree model. These parameters extracted from AdQSM were compared with the reference values from forest inventory. For the DBH, the relative bias (rBias), root mean square error (RMSE), and coefficient of variation of root mean square error (rRMSE) were 4.26%, 1.93 cm, and 6.60%. For the tree height, the rBias, RMSE, and rRMSE were—10.86%, 1.67 m, and 12.34%. The determination coefficient (R2) of DBH and tree height estimated by AdQSM and the reference value were 0.94 and 0.86. We used the trunk volume calculated by the allometric equation as a reference value to test the accuracy of AdQSM. The trunk volume was estimated based on AdQSM, and its bias was 0.07066 m3, rBias was 18.73%, RMSE was 0.12369 m3, rRMSE was 32.78%. To better evaluate the accuracy of QSM’s reconstruction of the trunk volume, we compared AdQSM and TreeQSM in the same dataset. The bias of the trunk volume estimated based on TreeQSM was −0.05071 m3, and the rBias was −13.44%, RMSE was 0.13267 m3, rRMSE was 35.16%. At 95% confidence interval level, the concordance correlation coefficient (CCC = 0.77) of the agreement between the estimated tree trunk volume of AdQSM and the reference value was greater than that of TreeQSM (CCC = 0.60). The significance of this research is as follows: (1) The automatic modeling method based on AdQSM is developed, which expands the application scope of AdQSM; (2) provide low-cost photogrammetric point cloud as the input data of AdQSM; (3) explore the potential of AdQSM to reconstruct forest terrestrial photogrammetric point clouds.

Efficient metadata mining of web-accessible neural morphologies

Advancements in neuroscience research have led to steadily accelerating data production and sharing. The online community repository of neural reconstructions NeuroMorpho.Org grew from fewer than 1000 digitally traced neurons in 2006 to more than 140,000 cells today, including glia that now constitute 10.1% of the content. Every reconstruction consists of a detailed 3D representation of branch geometry and connectivity in a standardized format, from which a collection of morphometric features is extracted and stored. Moreover, each entry in the database is accompanied by rich metadata annotation describing the animal subject, anatomy, and experimental details. The rapid expansion of this resource in the past decade was accompanied by a parallel rise in the complexity of the available information, creating both opportunities and challenges for knowledge mining. Here, we introduce a new summary reporting functionality, allowing NeuroMorpho.Org users to efficiently download digests of metadata and morphometrics from multiple groups of similar cells for further analysis. We demonstrate the capabilities of the tool for both glia and neurons and present an illustrative statistical analysis of the resulting data.

Respiratory-induced changes in renovisceral branch vessel morphology after fenestrated thoracoabdominal aneurysm repair with the BeGraft balloon-expandable covered stent

ObjectiveWe evaluated the respiratory-induced changes in branch vessel geometry after thoracoabdominal fenestrated endovascular aneurysm repair (fEVAR) with the Bentley BeGraft graft (Innomed GmbH, Hechingen, Germany) as the covered bridging stent. MethodsPatients treated with fEVAR for thoracoabdominal aortic aneurysms with a custom-made Zenith fenestrated endograft (Cook Medical Europe Ltd, Limerick, Ireland) and Bentley BeGraft peripheral stents were prospectively recruited. Using SimVascular software (Open-Source Medical Software Corp, San Diego, CA), the pre- and postoperative aortic and branch contours were segmented from computed tomography angiograms performed during inspiratory and expiratory breath-holds. The centerlines were extracted from the lumen contours, from which the branch take-off angles, distal stent angles, and peak branch curvature changes were computed. Paired, two-tailed t tests were performed to compare the pre- and postoperative deformations. ResultsRenovisceral vessel geometry was evaluated in 12 patients undergoing fEVAR with a total of 46 target vessels (10 celiac arteries, 12 superior mesenteric arteries [SMAs], 24 renal arteries). Implantation of BeGraft bridging stents was associated with a significant reduction in respiration-induced changes in vessel branch angulation (Δ5.3° ± 3.9° vs Δ12.0° ± 8.3° [postoperative vs preoperative]; P = .001) and mean curvature (0.72 ± 0.22 cm−1 vs 0.53 ± 0.18 cm−1) in the renal arteries, without significant changes in the celiac arteries or SMAs. No significant difference was found in end-stent angle motion in the renal arteries (P = .77), celiac arteries (P = .34), or SMAs (P = .55). The maximum local vessel curvature change decreased after fEVAR in the SMAs (Δ0.28 cm−1 vs Δ0.47 cm−1; P = .04) but was unchanged in the celiac (P = .61) and renal (P = .51) arteries. ConclusionsImplantation of the BeGraft as a bridging stent in fEVAR was associated with decreased respiratory-induced deformation in the renal branch take-off angulation and mean renal artery curvature, with reduced maximum curvature bending in the SMA compared with the preoperative anatomy. However, the BeGraft allowed for celiac and renal artery bending similar to that in the native preoperative state. These findings suggest that the use of BeGraft peripheral stents with fEVAR will closely mimic the native arterial branch geometry and vessel conformability caused by relatively aggressive respiratory motion.

Functional Optimality of the Highly Conserved Arp2/3‑Mediated 70° Branching Angle

Actin-based motility is widespread among eukaryotic cells. Many distinct cell types must undergo migration reliably in order to perform a variety of biological functions. However, the fundamental mechanism by which actin produces force, the Brownian ratchet, carries with it an inherent stochasticity. We aimed to understand how robust migration behavior can arise from stochastic actin polymerization in the context of lamellipodial motility. In previous experimental and theoretical efforts, we developed a stochastic model of the leading edge that faithfully recapitulates the stable lamellipodial shape dynamics observed in migrating cells. The stability of this minimal model, in the absence of additional feedback mechanisms, necessarily implies that lamellipodial maintenance is an intrinsic property of branched actin growth against a membrane. In the present work, we performed a theoretical exploration into the biophysical mechanisms underlying stability in our model. Surprisingly, we find that membrane tension is dispensable for maintaining a stable leading edge, and instead identify lateral filament spreading, mediated by the inherent geometry of branched actin growth, as the critical contributor to lamellipodial stability. Furthermore, we find that the genetically encoded branch geometry (the Arp2/3-mediated 70-80° branching angle, conserved from protists to mammals) maximally suppresses leading edge shape and actin density fluctuations. Taken together, these results contextualize two long-standing experimental observations: First, they suggest that the essential lamellipodial maintenance role of the Arp2/3 complex is rooted in its ability to facilitate filament spreading and suppress stochastic fluctuations. Second, the results hint that the high conservation of the Arp2/3-mediated branching angle may stem from its capacity to optimally perform this smoothing effect. In conclusion, we find that the branched structure of actin at the leading edge naturally quells stochastic fluctuations, thereby representing a novel biological noise-suppression mechanism based entirely on system geometry.

Micromagnetic Simulation of Coercivity of Alnico Magnets

A branch connecting two neighboring ferromagnetic α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -phase rods is one of the geometric factors that contributes to degradation of alnico's normally high coercivity. This letter investigates the effects of various branch geometries and dimensions on the coercivity of alnico comprehensively by using a micromagnetic simulator when the branch is assumed to be connected in either H- or U-shaped alnico structure and the magnetization reversal of the ferromagnetic α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -phase rod occurs by quasi-coherent rotation or curling. For the H-shaped structure, high coercivity is realized by adopting the middle-branch-connected (MBC) structure with a long branch length and width for quasi-coherent rotation, regardless of the branch thickness. For curling, the same geometric parameters are suggested except for a thick branch thickness. For the U-shaped structure with quasi-coherent rotation, a short branch thickness, width, and length, and MBC position lead a high coercivity. For curling, a short branch width but long length and edge-bridge-connected position result in a high coercivity, regardless of the branch thickness.

Determination of the Fractal Dimension of the Active Fault Data along the East Anatolian Fault Zone

The current study has analyzed active fault data along the East Anatolian Fault Zone (EAFZ) applying both manual (classic) and modern versions of the box counting method. The EAFZ active fault dataset used for analysis was taken from the Geoscience Map Viewer and the Drawing Editor from the website of the General Directorate of Mineral Research and Exploration. The study covered an area stretching from Karlıova in the north to Kırıkhan in the south. The fractal analysis of the earthquake surface rupture and the Holocene fault data was performed. Fractal dimensions of the EAFZ active-fault data were calculated for 15 boxes and compared with correlation coefficient values. The calculated fractal dimension values were found to vary with the density of the active-fault data falling into the boxes. The maximum fractal dimension value D1 was determined for Karlıova and its surroundings, which can be associated with the fault density due to the branching geometry.

Branching principles of animal and plant networks identified by combining extensive data, machine learning and modelling.

Branching in vascular networks and in overall organismic form is one of the most common and ancient features of multicellular plants, fungi and animals. By combining machine-learning techniques with new theory that relates vascular form to metabolic function, we enable novel classification of diverse branching networks—mouse lung, human head and torso, angiosperm and gymnosperm plants. We find that ratios of limb radii—which dictate essential biologic functions related to resource transport and supply—are best at distinguishing branching networks. We also show how variation in vascular and branching geometry persists despite observing a convergent relationship across organisms for how metabolic rate depends on body mass.

Towards a classification of rank r mathcal{N} = 2 SCFTs. Part II. Special Kahler stratification of the Coulomb branch

We study the stratification of the singular locus of four dimensional mathcal{N} = 2 Coulomb branches. We present a set of self-consistency conditions on this stratification which can be used to extend the classification of scale-invariant rank 1 Coulomb branch geometries to two complex dimensions, and beyond. The calculational simplicity of the arguments presented here stems from the fact that the main ingredients needed — the rank 1 deformation patterns and the pattern of inclusions of rank 2 strata — are discrete topological data which satisfy strong self-consistency conditions through their relationship to the central charges of the SCFT. This relationship of the stratification data to the central charges is used here, but is derived and explained in a companion paper [1] by one of the authors. We illustrate the use of these conditions by re-analyzing many previously-known examples of rank 2 SCFTs, and also by finding examples of new theories. The power of these conditions stems from the fact that for Coulomb branch stratifications a conjecturally complete list of physically allowed “elementary slices” is known. By contrast, constraining the possible elementary slices of symplectic singularities relevant for Higgs branch stratifications remains an open problem.