Branching Network Research Articles

Mitochondrial Network Branching Enables Rapid Protein Spread with Slower Mitochondrial Dynamics

Mitochondrial network structure is controlled by the dynamical processes of fusion and fission, which merge and split mitochondrial tubes into structures including branches and loops. To investigate the impact of mitochondrial network dynamics and structure on the spread of proteins and other molecules through mitochondrial networks, we used stochastic simulations of two distinct quantitative models that each included mitochondrial fusion and fission, and particle diffusion via the network. Better-connected mitochondrial networks and networks with faster dynamics exhibit more rapid particle spread on the network, with little further improvement once a network has become well connected. As fragmented networks gradually become better connected, particle spread either steadily improves until the networks become well connected for slow-diffusing particles or plateaus for fast-diffusing particles. We compared model mitochondrial networks with both end-to-end and end-to-side fusion, which form branches, to nonbranching model networks that lack end-to-side fusion. To achieve the optimum (most rapid) spread that occurs on well-connected branching networks, nonbranching networks require much faster fusion and fission dynamics. Thus, the process of end-to-side fusion, which creates branches in mitochondrial networks, enables rapid spread of particles on the network with relatively slow fusion and fission dynamics. This modeling of protein spread on mitochondrial networks builds toward mechanistic understanding of how mitochondrial structure and dynamics regulate mitochondrial function. Published by the American Physical Society 2024

Resource‐adaptive and OOD‐robust inference of deep neural networks on IoT devices

AbstractEfficiently executing inference tasks of deep neural networks on devices with limited resources poses a significant load in IoT systems. To alleviate the load, one innovative method is branching that adds extra layers with classification exits to a pre‐trained model, enabling inputs with high‐confidence predictions to exit early, thus reducing inference cost. However, branching networks, not originally tailored for IoT environments, are susceptible to noisy and out‐of‐distribution (OOD) data, and they demand additional training for optimal performance. The authors introduce BrevisNet, a novel branching methodology designed for creating on‐device branching models that are both resource‐adaptive and noise‐robust for IoT applications. The method leverages the refined uncertainty estimation capabilities of Dirichlet distributions for classification predictions, combined with the superior OOD detection of energy‐based models. The authors propose a unique training approach and thresholding technique that enhances the precision of branch predictions, offering robustness against noise and OOD inputs. The findings demonstrate that BrevisNet surpasses existing branching techniques in training efficiency, accuracy, overall performance, and robustness.

Obstructed Branching Networks: A Constructal Approach in Fluid Flow Investigation

Tree flow networks are common in both natural and manufactured systems. The organization of the flow hierarchy passes through the dimensional evolution of the form that is linked to the function. Thus, the objective of comparing bifurcated tube networks obtained by the constructal design method, where part of the structure is obstructed, aims to understand the effects on fluid flow and the prediction of evolutionary deviations in its function. This study compares designs of 3D tree networks with various homothety reduction factors for sizes, having tubes obstructed in some locals of the network. In this computational fluid dynamics study, the geometric constraint applied to these networks is the equal total volume of tubes at each branch level. The evaluation is based on the flow resistance of the networks. This study shows, among other things, that the performance of tree designs is highly dependent on geometric characteristics and the branching level where the obstructions are applied. The effect of the number and position of tubes obstructed in the network, as well as the alignment of the tubes across the network branching levels, on the asymmetry of fluid flow through the network is also studied. It is recommended that the results presented be considered when designing networks for engineering systems.

Understanding the effects of mineralization and structure on the mechanical properties of tendon-bone insertion using mesoscale computational modeling

Tendon-bone fibrocartilaginous insertion, or enthesis, is a specialized interfacial region that connects tendon and bone, effectively transferring forces while minimizing stress concentrations. Previous studies have shown that insertion features gradient mineralization and branching fiber structure, which are believed to play critical roles in its excellent function. However, the specific structure-function relationship, particularly the effects of mineralization and structure at the mesoscale fiber level on the properties and function of insertion, remains poorly understood. In this study, we develop mesoscale computational models of the distinct fiber organization at tendon-bone insertions, capturing the branching network from tendon to interface fibers and the different mineralization scales. We specifically analyze three key descriptors: the mineralization scale of interface fibers, the mean, and relative standard deviation of the local branching angles of interface fibers. Tensile test simulations on insertion models with varying mineralization scales of interface fibers and structures are performed to mimic the primary loading condition applied to the insertion. We measure and analyze five representative mechanical properties: Young's modulus, strength, toughness, resilience, and failure strain. Our results reveal that mechanical properties are significantly influenced by the three key descriptors, with tradeoffs observed between mutually exclusive properties. For instance, strength and resilience plateau beyond a certain mineralization scale, while failure strain and Young's modulus exhibit monotonic decreasing and increasing trends, respectively. Consequently, there exists an optimal mineralization scale for toughness due to these tradeoffs. By analyzing the mesoscale deformation and failure mechanisms from simulation trajectories, we identify three fracture regimes closely related to the trends in mechanical properties, supporting the observed tradeoffs. Additionally, we examine in detail the effects of the mean and relative standard deviation of local branching angles on mechanical properties and deformation mechanisms. Overall, our study enhances the fundamental understanding of the composition-structure-function relationships at the tendon-bone insertion, complementing recent experimental studies. The mechanical insights from our work have the potential to guide the future biomimetic design of fibrillar adhesives and interfaces for joining soft and hard materials.

Fractal permeability model for power-law fluids in embedded tree-like branching networks based on the fractional-derivative theory

The investigation of permeability in tree-like branching networks has attracted widespread attention. However, most studies about fractal models for predicting permeability in tree-like branching networks include empirical constants. This paper investigates the flow characteristics of power-law fluids in the dual porosity model of porous media in embedded tree-like branching networks. Considering the inherent properties of power-law fluids, non-Newtonian behavior effects, and fractal properties of porous media, a power-law fluids rheological equation is introduced based on the fractional-derivative theory and fractal theory. Then, an analytical formula for predicting the effective permeability of power-law fluids in dual porous media is derived. This analytical formula indicates the influences of fractal dimensions and structural parameters on permeability. With increasing length ratio, bifurcation series, and bifurcation angle, as well as decreasing power-law exponent and diameter ratio, the effective permeability decreases to varying degrees. The derived analytical model does not include empirical constants and is consistent with the non-Newtonian properties of power-law fluids, indicating that the model is an effective method for describing the flow process of complex non-Newtonian fluids in porous media in natural systems and engineering. Therefore, this study is of great significance to derive analytical solutions for the permeability of power-law fluids in embedded tree-like bifurcation networks.

Systematic design of tree-like branching network microchannel heat sinks for enhanced heat transfer with nanofluids

Branched or tree-shaped networks of microchannels are often preferred heatsink designs for microelectronic cooling due to their ability to offer a substantially large surface area-to-volume ratio. Designing an optimized tree-shaped heatsink in terms of hydrothermal performance poses challenges due to the intricate geometry and small-scale fluid–structure interactions involved, making prototyping challenging. We propose a systematically designed microchannel network heat exchanger inspired by tree branching patterns, aiming for ease in rapid prototyping and improved flow distributions offering enhanced thermal performance. Starting from a simpler geometrical consideration, we systematically improve the design by introducing a pin fin at the junction for improved flow distribution and then by imparting a converging angle in the channel for enhanced thermal performance. Additionally, we conduct an entropy generation analysis to examine the thermal performance of various nanofluid concentrations within the proposed device and witness significant thermal performance improvement that can benefit the thermal management of microelectronic components and other cooling applications.

Fractal study on the permeability of power-law fluid in a rough and damaged tree-like branching network

Fractal study on the permeability of power-law fluid in a rough and damaged tree-like branching network

Alleviating imbalanced problems of reinforcement learning when applying in real-time power network dispatching and control

Real-time power network dispatching and control (PDC) presents unique challenges that traditional methods cannot effectively address due to the consideration of temporal dynamic factors. Reinforcement learning (RL) has been introduced and proven to be effective. However, given the vast space for solutions, there is an urgent need to enhance the performance of RL further. Analyzing the characteristics of the power network to improve the performance of RL holds significant potential. This article presents a comprehensive analysis of power network characteristics, including imbalanced state distribution and the imbalanced action operation frequency, along with their impact on applying RL in real-time PDC to guide the algorithm design. Guided by the analysis, the paper proposes the Balance Deep Q-Network (DQN) algorithm to mitigate the negative impact of the imbalanced problems on algorithm performance. A K-means-based predefined curriculum learning (KPCL) module is proposed to address the state imbalance issue. It allows for differentiated access to operation scenarios based on their hardness, ensuring a balanced exploration of operation scenarios while maintaining diversity during training. An Option DQN module is proposed to tackle the action imbalance problem, utilizing a branching network structure and hierarchical action selection to reduce the coupling between actions with different usage frequencies, thereby enhancing the accuracy of action value estimation. The effectiveness of the Balance DQN algorithm is demonstrated through extensive experiments conducted on the Grid2Op platform with 14-bus and 36-bus cases. The results indicate that Balance DQN can efficiently alleviate the negative impacts of imbalanced problems on RL for real-time PDC agents and achieve good performance in both cases.

Study on the water transport performance of the fractal tree-like structure of nonwoven cotton fabrics

Fractal branching networks are structures that are ubiquitous in nature, possessing multiple transport characteristics, and have been the subject of long-term attention by many researchers. Currently, in the field of textiles, research on the ability of tree-like structures to enhance the water transport property of fabrics is mostly focused on the thickness direction of the fabric. However, there is little research on the liquid water transfer rate in the horizontal direction. In this article, the water transport performance of liquid water in tree-like fractal nonwoven fabrics with different shapes (tree-like and rectangular) was investigated, and the liquid water transport rate was measured using the horizontal wicking method. It was found that when the sum of the cube of the branch width was equal to the cube of the main stem width, the water transport efficiency of liquid water in the fabric is optimal. At the same time, a summary of the experimental data was made by comparing the water transport property of fabrics with corresponding equal areas but different widths or heights. It was found that for nonwoven fabrics with the same area size, tree-like structures can transport liquid water to a farther distance in the same amount of time. Furthermore, the liquid water transport ability of tree-like nonwoven fabrics in the horizontal direction was simulated using finite element analysis in COMSOL Multiphysics, and the results were in good agreement with the experimental values.

Treegraph: tree architecture from terrestrial laser scanning point clouds

AbstractAccurate quantification of tree architecture is critical to interpreting the growth, health and functioning of trees and forests. Terrestrial laser scanning (TLS) offers millimetre‐level point cloud data, but current approaches to 3D tree reconstruction from TLS point clouds primarily focus on retrieving total volume at tree scale for aboveground biomass (AGB) estimation. Few methods have been designed specifically to provide tree architectural properties, including branch‐level morphology and topology, rather than AGB; derived topological traits have tended to be a compromise, and of secondary importance to volume. We present Treegraph, a new approach explicitly designed to retrieve the architectural traits of trees at multiple scales, from the whole tree scale down to individual branches and internodes, using TLS data with limited assumptions about tree form. It provides morphological traits such as branch length and diameter, alongside topological traits including parent–daughter connections of branches and internodes, furcation (branching) number and branch order. We compare Treegraph‐derived morphological and topological traits with manual measurements of branches from eight destructively harvested trees, yielding RMSE values of 0.60 m (5.96%) for branch length, 2.99 cm (33.45%) for branch diameter, 0.46 (19.38%) for furcation number and 0.08 m (33.16%) for internode length, respectively. In a broader application to 603 trees from tropical, temperate and urban forests, we demonstrate that the derived morphological and topological traits support testing of structure‐related metabolic scaling theories. Testing branches over 10 cm in diameter across 18 657 branching nodes shows that Treegraph‐derived branch‐level scaling exponents deviate from WBE predictions, exhibiting area‐preserving behaviour while displaying asymmetry in length and diameter of daughter branches. Available as open‐source Python software, Treegraph provides fine‐level branching network information, promoting improved insights into tree structure and function. This data‐driven approach reduces the need for empirical heuristic parameters, which has the potential for advancing large‐scale ecological studies on tree architecture.

Fractal analysis of dimensionless permeability and Kozeny–Carman constant of spherical granular porous media with randomly distributed tree-like branching networks

The seepage of porous media has garnered significant interest due to its ubiquitous presence in nature, but most of the research is based on the model of a single dendritic branching network. In this study, we derive a fractal model of the dimensionless permeability and the Kozeny–Carman (KC) constant of porous media consisting of spherical particles and randomly distributed tree-like branching networks based on fractal theory. In addition, three different types of corrugated pipes are considered. Then, the relationships between the KC constant, dimensionless permeability, and other structural parameters were discussed in detail. It is worth noting that the KC constant of the porous media composed of three types of pipes decreases sharply first and then increases with the increase in the internal diameter ratio, while the dimensionless permeability has the opposite trend and conforms to the physical law. In addition, empirical constants are not included in the analytical formulas of the present model, and the physical mechanism of fluid flow in spherical granular porous media with randomly distributed tree-like branching networks is clearly revealed.

Scaling laws for optimized power-law fluid flow in self-similar tree-like branching networks

The power-law fluid flow in tree-like self-similar branching networks is prevalent throughout the natural world and also finds numerous applications in technology such as oil recovery and microfluidic devices. We investigate analysis of optimal power-law fluid flow conditions and the optimal structures within tree-like branching networks, focusing on maximizing flow conductance under the constraint of the network tube’s volume and the surface area. The study considered fully developed laminar power-law fluid flow regimes without considering any losses in the network system. A key observation was the sensitivity of the dimensionless effective flow conductance to the network’s geometrical parameters. We found that the maximum flow conductance occurs when a dimensionless radius ratio β∗ satisfies the equation β∗=N−1/3 and β∗=N−(n+1)/(3n+2) under constrained tube-volume and surface-area, respectively. Here, N represents the bifurcation number of branches splitting at each junction, and n is the fluid power-law index. We further find that this optimal condition occurs when pressure drops are equipartition across each branching level. We validated our results with various experimental results and theories under limiting conditions. Further, Hess–Murray’s law is justified and extended for the shear-thinning and shear-thickening fluid flows for an arbitrary number of branches N. Further, in this study, we also derive the relationships between the geometrical and flow characteristics of the parent and daughter tubes as well as the generalized scaling laws at the optimal conditions for the other essential parameters such as tube-wall stresses, length ratios, mean velocities, tube-volume, and surface-area of the tube distributing within the networks. We find that the fluid power-law index n does not influence the constrained tube-volume scaling at the optimal conditions; however, the scaling laws vary with n under the constrained tube’s surface area. These findings offer valuable design principles for developing efficient transport and flow systems.

Preparation and moisture transport behavior of multilevel branching network nanofiber membrane: Based on the Lattice Boltzmann method and inspired by plant transpiration

Ensuring the efficiency and safety of firefighters relies heavily on optimizing the moisture permeability of their suits. Inspired by the intricate multi-level network structure of plant transpiration, this study utilized electrospinning technology to prepare biomimetic vascular, veined multilevel branched network quick-drying nanofiber membranes. Combining X-ray microtomography (XMT) and the lattice Boltzmann method (LBM), this study conducted a 3D reconstruction of the microstructure of quick-drying nanofiber materials, establishing a characterization method for moisture permeability behavior from a micro to mesoscale perspective and conducted numerical simulations. The results indicate that in the nanofiber membrane, the fiber diameter and pore size between fibers gradually decrease from the inlet to the outlet in the forward flow direction (from PET side to PAN side). At the same displacement pressure difference, the average and maximum flow rates of forward percolation were significantly greater than reverse percolation (from PAN side to PET side); in the initial stage of forward percolation (x < 11), the flow rate first increased and then gradually decreased, with the rate of increase (k = 0.712623) significantly higher than the rate of decrease (k'=0.001102), while in reverse percolation, the flow rate continuously increased throughout the process; These phenomena are primarily due to different startup pressure gradients. Furthermore, the analysis of moisture transport performance indicates that the fiber membrane exhibits highly efficient unidirectional moisture transport capability. This study expands the understanding of the moisture permeability mechanism of nanofibers, which is significant for enhancing the protective performance and comfort of quick-drying firefighter fabrics.

The length and spacing of river tributaries

River networks are composed of a mainstem and tributaries. These tributaries dissect landscapes, regulate water and habitat availability, and transport sediment and nutrients. Despite the importance of tributaries, we currently lack theory and data describing whether and how tributary length and spacing varies within watersheds, thereby limiting our ability to accurately describe river network geometry. We address this knowledge gap by analyzing 4,696 tributaries across six landscapes with varying climate, tectonic setting, and lithology. Our results show that both tributary length and spacing systematically increase with downstream distance along the mainstem river, following a power-law scaling. This power-law scaling can be modulated by basin shape, with tributaries becoming shorter and, in some cases, more closely spaced as basin elongate. Furthermore, the power-law scaling may break down in cases where river networks have been disturbed by pervasive faulting, raising the possibility that the scaling we observe is not unique to all branching networks, and instead may be universal across undisturbed fluvial networks. These findings can be used to improve predictions of river network geometry and potentially to distinguish fluvial river networks from other branching networks.

An analytical model for permeability of fractal tree-like branched networks composed of converging–diverging capillaries

Seepage processes in tree-fractal networks have attracted extensive research, but the results of most of these studies presuppose a constant pore cross section. This research investigates fluid flow in a fractal tree-like branching network composed of five different types of circular cross section pipes and establishes the effective permeability of the network. Furthermore, the effective permeability of the fractal tree-like network is compared with that of a typical parallel channel network, and the effect of structural parameters on the seepage process of the tree-like branching network is systematically investigated. The effective permeability of all pipelines increased sharply with an increase in the internal diameter ratio at first and then decreased. Furthermore, a considerable advantage was seen in the permeability of the fractal tree network over the traditional parallel channel network, with the benefit becoming more noticeable as branching levels increased. The clear physics of the model offers a useful framework for studying seepage processes.

Unraveling the molecular mechanisms governing axillary meristem initiation in plants.

Axillary meristems (AMs) located in the leaf axils determine the number of shoots or tillers eventually formed, thus contributing significantly to the plant architecture and crop yields. The study of AM initiation is unavoidable and beneficial for crop productivity. Shoot branching is an undoubted determinant of plant architecture and thus greatly impacts crop yield due to the panicle-bearing traits of tillers. The emergence of the AM is essential for the incipient bud formation, and then the bud is dormant or outgrowth immediately to form a branch or tiller. While numerous reviews have focused on plant branching and tillering development networks, fewer specifically address AM initiation and its regulatory mechanisms. This review synthesizes the significant advancements in the genetic and hormonal factors governing AM initiation, with a primary focus on studies conducted in Arabidopsis (Arabidopsis thaliana L.) and rice (Oryza sativa L.). In particular, by elaborating on critical genes like LATERAL SUPPRESSOR (LAS), which specifically regulates AM initiation and the networks in which they are involved, we attempt to unify the cascades through which they are positioned. We concentrate on clarifying the precise mutual regulation between shoot apical meristem (SAM) and AM-related factors. Additionally, we examine challenges in elucidating AM formation mechanisms alongside opportunities provided by emerging omics approaches to identify AM-specific genes. By expanding our comprehension of the genetic and hormonal regulation of AM development, we can develop strategies to optimize crop production and address global food challenges effectively.

Heuristic optimal transport in branching networks

Optimal transport aims to learn a mapping of sources to targets by minimizing the cost, which is typically defined as a function of distance. The solution to this problem consists of straight line segments optimally connecting sources to targets, and it does not exhibit branching. These optimal solutions are in stark contrast with both natural, and man-made transportation networks, where branching structures are prevalent. Here, we discuss a fast heuristic branching method for optimal transport in networks. We also provide several numerical applications to synthetic examples, a simplified cardiovascular network, and the “Santa Claus” distribution network which includes 141[Formula: see text]182 cities around the world, with known location and population.

Bioinspired Synaptic Branched Network within Quasi-Solid Polymer Electrolyte for High-Performance Microsupercapacitors.

The branched network-driven ion solvating quasi-solid polymer electrolytes (QSPEs) are prepared via one-step photochemical reaction. A poly(ethylene glycol diacrylate) (PEGDA) is combined with an ion-conducting solvate ionic liquid (SIL), where tetraglyme (TEGDME), which acts like interneuron in the human brain and creates branching network points, is mixed with EMIM-NTf2 and Li-NTf2. The QSPE exhibits a unique gyrified morphology, inspired by the cortical surface of human brain, and features well-refined nano-scale ion channels. This human-mimicking method offers excellent ion transport capabilities through a synaptic branched network with high ionic conductivity (σDC ≈ 1.8 mS cm-1 at 298 K), high dielectric constant (εs ≈ 125 at 298 K), and strong ion solvation ability, in addition to superior mechanical flexibility. Furthermore, the interdigitated microsupercapacitors (MSCs) based on the QSPE present excellent electrochemical performance of high energy (E = 5.37 µWh cm-2) and power density (P = 2.2 mW cm-2), long-term cycle stability (≈94% retention after 48 000 cycles), and mechanical stability (>94% retention after continuous bending and compressing deformation). Moreover, these MSC devices have flame-retarding properties and operate effectively in air and water across a wide temperature range (275 to 370 K), offering a promising foundation for high-performance, stable next-generation all-solid-state energy storage devices.

Flow and heat transfer performance of asymmetric fractal tree network in fractal porous media

This study aims to investigate the fluid transport and heat transfer characteristics in fractal porous media, introduce asymmetric factors to derive a generalized optimization principle for asymmetric branching flow and heat transfer, and obtain the optimal radius ratio for the superior flow resistance/heat resistance model; and the accurate models of permeability and thermal conductivity of asymmetric tree-fractal networks are developed and validated against the traditional Murray's law and symmetric tree-fractal network models. The results show that (a) the symmetric case can be regarded as a special case of the asymmetric fractal network model, and Murray's law is correct only for the symmetric bifurcation (flow percentage Ψi = 0.5), and the errors predicted by Murray's law for the asymmetric case with a flow percentage of 10% (Ψi = 0.1, n = 1) are 23.5% and 33.1% with respect to the optimal radius ratio of flow and heat transfer, respectively. (b) The symmetric case has the largest flow resistance and the smallest thermal resistance. The asymmetric length factor and radius ratio have significant effects on the dimensionless flow resistance/thermal resistance of the asymmetric fractal network, and there is a critical radius ratio (βm = 0.84), where a larger asymmetric length factor is detrimental to the flow of the tree-like branching network when β &amp;lt; βm, while the opposite effect is observed when β &amp;gt; βm. (c) The asymmetric radius factor affects the optimal radius ratio for thermal conductivity, but does not change the maximum value of thermal conductivity. (d) The pressure gradient and heat transfer coefficient in the fractal microchannel are related to the variation of the volume flow rate and the increase in the heat flux will weaken heat transfer.

Bioengineered Tubular Biliary Organoids.

Liver organoids have emerged as promising in vitro models for toxicology, drug discovery, and disease modeling. However, conventional 3D epithelial organoid culture systems suffer from significant drawbacks, including limited culture duration, a nonphysiological 3D cystic anatomy with an inaccessible apical surface, and lack of in vivo-like cellular organization. To address these limitations, herein a hydrogel-based organoid-on-a-chip model for the development functional tubular biliary organoids is reported. The resulting constructs demonstrate long-term stability for a minimum duration of 45 d, while retaining their biliary organoid identity and exhibiting key cholangiocyte characteristics including transport activities, formation of primary cilia, and protective glycocalyx. Additionally, tubular organoids are susceptible to physical and chemical injury, which cannot be applied in such resolution to classical organoids. To enhance tissue-level complexity, in vitro formation of a perfusable branching network is induced using a predetermined geometry that faithfully mimics the intricate structure of the intrahepatic biliary tree. Finally, cellular complexity is augmented through co-culturing with vascular endothelial cells and fibroblasts. The models described in this study offer valuable opportunities for investigating biliary morphogenesis and elucidating associated pathophysiological mechanisms.