Random Branching Research Articles

Modelling branch surface area of Fagus sylvatica L.

ABSTRACT Allometric models describe properties of trees that are difficult to measure. Here, we provide a set of allometric models for estimating branch properties for European beech (Fagus sylvatica L.). Branches affect rainfall and snow interception, provide habitat for other organisms and contribute to the economic and aesthetic value of trees. Using randomized branch sampling (RBS) of 27 beech trees in Austria we developed models for branch surface area, branch number, branch base diameter and branch length, depending on stem diameter, tree height and crown ratio. For individual branches, branch diameter was the best predictor of branch surface area while including branch length or position along the stem did not improve the models. For the entire tree, stem diameter was the most important predictor. Branch surface area (and in consequence also branch volume) assessed by RBS was greater than the branch surface area estimated as a cylinder from measurements of branch length and branch base diameter. Since the branch allometry of beech differs considerably from a previous study on branches of Picea abies, we conclude that assumptions and models derived from other tree species can lead to considerable biased results in assessing the functions of tree branches.

Tuning poly(isatin biphenyl) anion exchange membranes by copolymerization and branching

The cardo structure and long side chain of poly(isatin biphenyl) are conducive to the motion and aggregation of cations over mainchain type membranes, therefore it is used as the pristine membrane. It is well known that random copolymerization and branching can effectively modify the configuration and properties of polymers. Herein, we use random copolymerization and branching to improve the behaviors of poly(isatin biphenyl) anion exchange membranes (AEMs). High-curvature random copolymers (QPIDBP-n) and high free volume branched polymers (b-QPIBP-x) are synthesized via polycondensation. The random copolymerization results in the formation of a twisted chain structure, while the introduction of branching agent leads to the formation of orderly stacking of chains. Both of these approaches have been demonstrated to boost the microphase-separated morphology of the pristine polymer. A series of QPIDBP-n and b-QPIBP-x are tested and an optimal ratio is explored. QPIDBP-40 and b-QPIBP-5 exhibit high overall performance. Among the as-prepared membranes, b-QPIBP-5 exhibits the highest conductivity (80 °C, 160.7 mS cm−1) with a swelling ratio of 20.7 %. The residual conductivity of b-QPIBP-5 is 93.1 % after the 1200 h alkali stability test. The cell assembled by b-QPIBP-5 achieves a peak power density of 680 mW cm−2. Moreover, the b-QPIBP-5 based cell holds 88.6 % voltage after the in-situ stability test for 50 h.

In Vitro Biocompatibility and Endothelial Permeability of Branched Polyglycidols Generated by Ring-Opening Polymerization of Glycidol with B(C6F5)3 under Dry and Wet Conditions.

Polyglycidol or polyglycerol (PG), a polyether widely used in biomedical applications, has not been extensively studied in its branched cyclic form (bcPG), despite extensive research on hyperbranched PG (HPG). This study explores the biomedical promise of bcPG, particularly its ability to cross the blood-brain barrier (BBB). We evaluate in vitro biocompatibility, endothelial permeability, and formation of branched linear PG (blPG) as topological impurities in the presence of water. Small angle X-ray scattering in solution revealed a fractal dimension of approximately two for bcPG and the mixture bc+blPG, suggesting random branching. Comparisons of cytotoxicity and endothelial permeability between bcPG, bc+blPG, and HPG in a BBB model using hCMEC/D3 cells showed different biocompatibility profiles and higher endothelial permeability for HPG. bcPG showed a tendency to accumulate around cell nuclei, in contrast to the behavior of HPG. This study contributes to the understanding of the influence of polymer topology on biological behavior.

Prediction of Student Performance Using Random Forest Combined With Naïve Bayes

Abstract Random forest is a powerful ensemble learning technique celebrated for its heightened predictive performance and robustness in handling complex datasets; nevertheless, it is criticized for its computational expense, particularly with a large number of trees in the ensemble. Moreover, the model’s interpretability diminishes as the ensemble’s complexity increases, presenting challenges in understanding the decision-making process. Although various pruning techniques have been proposed by researchers to tackle these issues, achieving a consensus on the optimal strategy across diverse datasets remains elusive. In response to these challenges, this paper introduces an innovative machine learning algorithm that integrates random forest with Naïve Bayes to predict student performance. The proposed method employs the Naïve Bayes formula to evaluate random forest branches, classifying data by prioritizing branches based on importance and assigning each example to a single branch for classification. The algorithm is utilized on two sets of student data and is evaluated against seven alternative machine-learning algorithms. The results confirm its strong performance, characterized by a minimal number of branches.

Leveraging Hyperspectral Images for Accurate Insect Classification with a Novel Two-Branch Self-Correlation Approach

Insect recognition, crucial for agriculture and ecology studies, benefits from advancements in RGB image-based deep learning, yet still confronts accuracy challenges. To address this gap, the HI30 dataset is introduced, comprising 2115 hyperspectral images across 30 insect categories, which offers richer information than RGB data for enhancing classification accuracy. To effectively harness this dataset, this study presents the Two-Branch Self-Correlation Network (TBSCN), a novel approach that combines spectrum correlation and random patch correlation branches to exploit both spectral and spatial information. The effectiveness of the HI30 and TBSCN is demonstrated through comprehensive testing. Notably, while ImageNet-pre-trained networks adapted to hyperspectral data achieved an 81.32% accuracy, models developed from scratch with the HI30 dataset saw a substantial 9% increase in performance. Furthermore, applying TBSCN to hyperspectral data raised the accuracy to 93.96%. Extensive testing confirms the superiority of hyperspectral data and validates TBSCN’s efficacy and robustness, significantly advancing insect classification and demonstrating these tools’ potential to enhance precision and reliability.

Effects of Space Dimensionality within Scaffold for Bone Regeneration with Large and Oriented Blood Vessels.

The internal structure of the scaffolds is a key factor for bone regeneration. In this study, we focused on the space dimensionality within the scaffold that may control cell migration and evaluated the effects on the size and orientation of blood vessels and the amount of bone formation in the scaffold. The carbonate apatite scaffolds with intrascaffold space allowing one-dimensional (1D), two-dimensional (2D), or three-dimensional (3D) cell migration were fabricated by 3D printing. These scaffolds had the same space size, i.e., distances between the struts (~300 µm). The scaffolds were implanted into the medial condyle of rabbit femurs for four weeks. Both the size and orientation degree of the blood vessels formed in the scaffolds allowing 1D cell migration were 2.5- to 4.0-fold greater than those of the blood vessels formed in the scaffolds allowing 2D and 3D cell migration. Furthermore, the amount of bone formed in the scaffolds allowing 1D cell migration was 1.4-fold larger than that formed in the scaffolds allowing 2D and 3D cell migration. These are probably because the 1D space limited the direction of cell migration and prevented the branching of blood vessels, whereas 2D and 3D spaces provided the opportunity for random cell migration and blood vessel branching. Thus, scaffolds with 1D space are advantageous for inducing large and oriented blood vessels, resulting in a larger amount of bone formation.

A new method for fault identification of T-connection transmission line based on multi-scale traveling wave reactive power and random forest.

Though the traditional fault diagnosis method of T-connected transmission lines can identify the faults inside and outside the area, it can not identify the specific branches. To improve the accuracy and reliability of fault diagnosis of T-connection transmission lines, a new method is proposed to identify specific faulty branches of T-connection transmission lines based on multi-scale traveling wave reactive power and random forest. Based on the S-transform, the mean and sum ratios of the corresponding short-time series traveling wave reactive powers of each two traveling wave protection units at multiple frequencies are calculated respectively to form the fault feature vector sample set of the T-connection transmission line. A random forest fault branch identification model is established, and it is trained and tested by the fault feature sample set of T-connection transmission line to identify the fault branch. The simulation results show that the proposed algorithm can identify the branch where the fault is located inside and outside the protection zone of T-connection transmission line quickly and accurately under various working conditions. This method also shows good performance to identify faults even under the situation of CT saturation, noise influence and data loss.

Scaling properties of RNA as a randomly branching polymer.

Formation of base pairs between the nucleotides of a ribonucleic acid (RNA) sequence gives rise to a complex and often highly branched RNA structure. While numerous studies have demonstrated the functional importance of the high degree of RNA branching-for instance, for its spatial compactness or interaction with other biological macromolecules-RNA branching topology remains largely unexplored. Here, we use the theory of randomly branching polymers to explore the scaling properties of RNAs by mapping their secondary structures onto planar tree graphs. Focusing on random RNA sequences of varying lengths, we determine the two scaling exponents related to their topology of branching. Our results indicate that ensembles of RNA secondary structures are characterized by annealed random branching and scale similarly to self-avoiding trees in three dimensions. We further show that the obtained scaling exponents are robust upon changes in nucleotide composition, tree topology, and folding energy parameters. Finally, in order to apply the theory of branching polymers to biological RNAs, whose length cannot be arbitrarily varied, we demonstrate how both scaling exponents can be obtained from distributions of the related topological quantities of individual RNA molecules with fixed length. In this way, we establish a framework to study the branching properties of RNA and compare them to other known classes of branched polymers. By understanding the scaling properties of RNA related to its branching structure, we aim to improve our understanding of the underlying principles and open up the possibility to design RNA sequences with desired topological properties.

Loop-erased random walk branch of uniform spanning tree in topological polygons

We consider uniform spanning tree (UST) in topological polygons with 2N marked points on the boundary with alternating boundary conditions. In an earlier work by Liu-Peltola-Wu, the authors derive the scaling limit of the Peano curve in the UST. They are variants of SLE8. In this article, we derive the scaling limit of the loop-erased random walk branch (LERW) in the UST. They are variants of SLE2. The conclusion is a generalization of an earlier work by Han-Liu-Wu where the authors derive the scaling limit of the LERW branch of UST when N=2. When N=2, the limiting law is SLE2(−1,−1;−1,−1). However, the limiting law is no longer in the family of SLE2(ρ) process as long as N≥3.

Prediction of internal and external flow with sparse convolution neural network: A computationally effective reduced-order model

This paper presents a novel reduced-order model for internal and external flow field estimations based on a sparse convolution neural network. Since traditional convolution neural network requires “rectangular” matrixes as input, the convolutional operation is computationally inefficient when applied to these problems with input matrix having sparse information. In our approach, we innovatively introduce a sparse convolution neural network (SCNN) to collect spatial information on geometries that are inherently sparse, e.g., the flow in thin pipelines in a much larger domain or the pipelines with random branches. Different from the traditional convolution neural network (CNN) model, the SCNN only collects features from areas with flow information for both the input matrix and each convolutional layer, which not only reduces the consumption of computational resources but also significantly increases network attention to flow area. The model learns the mapping relationship between geometries and the physical field of fluid flow, and the spatial positions of geometry are represented using the nearest wall signed distance function. The proposed SCNN model has the promising adaptability to arbitrary geometry and less computational resource cost compared to the traditional CNN model: the mean error of the SCNN is less than 5.4% (while the CNN is 7.1%) for the internal flow and less than 6.5% (while the CNN is 8.1%) for the external flow. Moreover, the SCNN has 72% less GPU resource usage and 52% less random access memory cost than the CNN for internal flow. For the first time, our framework introduces the sparse convolution network to flow field prediction, and the SCNN shows outstanding performance on prediction accuracy and computational resource saving for the flow problems with a sparse input information.

Random Branching and Cross‐linking of Polymer Chains, Analytical Functions for the Bivariate Molecular Weight Distributions

AbstractCross‐linking and branching of primary polymer molecules are investigated using the Galton–Watson (GW) process. Starting with the probability generating function (pgf) of the primary molecular weight distribution (MWD), analytical expressions are derived for the bivariate pgfs g(nbr, s) of branched polymers which depend also on the number of branch points nbr. The bivariate MWDs n(nbr, i) (i: number of molecular units) are then derived as Taylor expansions in s. All three cases of random branching: X‐shaped (cross‐linking), T‐shaped (only one end takes part in the branching process), and H‐shaped (both ends can take part in the branching process) are treated. An extension of the formalism does not require the construction of the pgf and allows the direct use of the MWD of the primary chains. However, using pgfs allows to go past the gel point and to determine the MWD and content of the sol. Explicit expressions are given for special distributions: the mono modal, the most probable, the Schulz‐Zimm, the Poisson, and the Catalan distribution for the cases of X‐shaped and T‐shaped branching.

Probabilistic Load Flow for Wind Integrated Power System Considering Node Power Uncertainties and Random Branch Outages

This paper proposes an analytical probabilistic load flow (PLF) approach that considers conventional generator outages, load variability, and random branch outages. The branch outages are modeled as 0-1 distributions of fictitious power injections at the appropriate nodes. The distribution of state variables and line power flows is then obtained using a combined Cumulant and Gram-Charlier series expansion approach. The proposed PLF performs contingency sequencing with fuzzy logic to eliminate random line checking and avoid masking mistakes faced by performance index-based algorithms. The Jacobian inverse calculation in the traditional Cumulant method is eliminated to conserve storage space and speed up the computation using the Gauss-Jordan method. The correlations among loads and wind power generations has been modeled using the Nataf transformation process. Results of 24-bus and 259-bus equivalent systems of the Indian southern and western power grids are analyzed and validated with those obtained using the Monte Carlo simulation method. The suggested method's efficacy is justified by its accuracy and low computational burden.

Effects of network connectivity on viscoelastic relaxation in transient networks using experimental approach

The effect of network connectivity on viscoelastic relaxation in transient networks with well-defined structures (Tetra-PEG slime) was experimentally evaluated and compared to bond dissociation kinetics. To control the connectivity and discuss the pure effect precisely, we mixed the precursors in off-stoichiometric ratio. With decreasing network connectivity, the viscoelastic relaxation time accelerated and became shorter than the bond dissociation time. With increasing polymer concentration, the connectivity at which the viscoelastic relaxation time matched the dissociation time shifted to the high-connectivity region. The dependence of viscoelastic relaxation on connectivity can be adequately explained within the framework of the lifetime of a backbone. The backbone has numerous breakage points in low-connectivity region nearby the gelation point, resulting in a shorter lifetime than the dissociation time. However, the Rubinstein-Semenov model based on backbone relaxation does not predict the concentration dependence, suggesting that the formation of the network in the dilute/semi-dilute region deviates from a random branching process. These findings provide a crucial foundation for the molecular comprehension of transient network materials.

Revisiting the structure of copolymer via anionic hybrid copolymerization of methyl methacrylate and ε-caprolactone

Anionic hybrid copolymerization of vinyl and cyclic monomers provides a powerful strategy to synthesize heteropolymers. Yet, there are some open questions regarding its mechanism and the structure of the resulted polymer. We reported that the copolymer (Poly(MMA- co -CL)) of methyl methacrylate (MMA) and ε-caprolactone (CL) via such copolymerization was random. However, a recent study proposed that the copolymer might be simple graft one with poly(methyl methacrylate) (PMMA) as the main chain and poly(ε-caprolactone) (PCL) as the graft chain. In this study, we synthesized a model graft copolymer (PMMA- g -PCL) by using a combination of reversible complexation-mediated polymerization and ring-opening polymerization, and made comparison with Poly(MMA- co -CL) in their properties and hydrolysis. Differential scanning calorimeter (DSC) measurements show that the graft copolymer PMMA- g -PCL possesses two glass transitions and a melt peak. In contrast, Poly(MMA- co -CL) exhibits only one glass transition without a melt peak because it is amorphous, clearly indicating that it is random. Proton nuclear magnetic resonance ( 1 H NMR) measurements reveal that the hydrolysis of PMMA- g -PCL yields only PMMA oligomers. However, the hydrolyzed products of Poly(MMA- co -CL) consist of MMA and CL units. The facts further indicate that the copolymer Poly(MMA- co -CL) is random. Considering that the transesterification reactions are unavoidable in the anionic hybrid copolymerization, the copolymer should consist of random main chain and random branches. • The present study demonstrates that anionic hybrid copolymerization of MMA and CL generally yields random copolymer but not graft copolymer. • Transesterification is not the essential step in the anionic hybrid copolymerization, but it can cause branching of the copolymer. • The hybrid copolymer of MMA and CL consists random main chain and random branches.

Solution sampling with random table constraints

Constraint programming provides generic techniques to efficiently solve combinatorial problems. In this paper, we tackle the natural question of using constraint solvers to sample combinatorial problems in a generic way. We propose an algorithm, inspired from Meel’s ApproxMC algorithm on SAT, to add hashing constraints to a CP model in order to split the search space into small cells. By uniformly sampling the solutions in one cell, we can generate random solutions without revamping the model of the problem. We ensure the randomness by introducing a new family of hashing constraints: randomly generated tables, which keeps the cost of the hashing process tractable. We implemented this solving method using the constraint solver Choco-solver. The quality of the randomness and the running time of our approach are experimentally compared to a random branching strategy. We show that our approach improves the randomness while being in the same order of magnitude in terms of running time. We also use our algorithm with an other, more powerful, set of hashing constraints: linear modular equalities. We experimentally show that the resulting sampling is uniform, at the cost of a longer running time.

Concentration inequalities from monotone couplings for graphs, walks, trees and branching processes

Generalized gamma distributions arise as limits in many settings involving random graphs, walks, trees, and branching processes. Peköz et al. (2016) exploited characterizing distributional fixed point equations to obtain uniform error bounds for generalized gamma approximations using Stein’s method. Here we show how monotone couplings arising with these fixed point equations can be used to obtain sharper tail bounds that, in many cases, outperform competing moment-based bounds and the uniform bounds obtainable with Stein’s method. Applications are given to concentration inequalities for preferential attachment random graphs, branching processes, random walk local time statistics and the size of random subtrees of uniformly random binary rooted plane trees.

Symmetric branching random walks in random media: comparing theoretical and numerical results

We consider a continuous-time branching random walk on a multidimensional lattice in a random branching medium. It is theoretically known that, in such branching random walks, large rare fluctuations of the medium may lead to anomalous properties of a particle field, e.g., such as intermittency. However, the time intervals on which this intermittency phenomenon can be observed are very difficult to estimate in practice. In this paper, branching media containing only a finite and non-finite number of branching sources are considered. The evolution of the mean number of particles with a random point perturbation and one initial ancestor particle at a lattice point is described by an appropriate Cauchy problem for the evolutionary operator. We review some previous results about the long-time behavior of the medium-averaged moments for the particle population at every lattice point as well as the total one over the lattice and present an algorithm for the simulation of branching random walks under various assumptions about the medium, including the medium randomness. The effects arising in random non-homogeneous and homogeneous media are then compared and illustrated by simulations based on the potential with Weibull-type upper tail. A wide range of models under different assumptions on a branching medium, a configuration of branching sources, and a lattice dimension were considered during the comparison. The simulation results indicate that intermittency can be observed in random media even over finite time intervals.

Random forest based power sustainability and cost optimization in smart grid

Abstract Presently power control and management play a vigorous role in information technology and power management. Instead of non-renewable power manufacturing, renewable power manufacturing is preferred by every organization for controlling resource consumption, price reduction and efficient power management. Smart grid efficiently satisfies these requirements with the integration of machine learning algorithms. Machine learning algorithms are used in a smart grid for power requirement prediction, power distribution, failure identification etc. The proposed Random Forest-based smart grid system classifies the power grid into different zones like high and low power utilization. The power zones are divided into number of sub-zones and map to random forest branches. The sub-zone and branch mapping process used to identify the quantity of power utilized and the non-utilized in a zone. The non-utilized power quantity and location of power availabilities are identified and distributed the required quantity of power to the requester in a minimal response time and price. The priority power scheduling algorithm collect request from consumer and send the request to producer based on priority. The producer analysed the requester existing power utilization quantity and availability of power for scheduling the power distribution to the requester based on priority. The proposed Random Forest based sustainability and price optimization technique in smart grid experimental results are compared to existing machine learning techniques like SVM, KNN and NB. The proposed random forest-based identification technique identifies the exact location of the power availability, which takes minimal processing time and quick responses to the requestor. Additionally, the smart meter based smart grid technique identifies the faults in short time duration than the conventional energy management technique is also proven in the experimental results.

Improved ResNet Based Apple Leaf Diseases Identification

Apple leaf diseases occur frequently and have a wide variety, which seriously affects the yield and quality of apples. The real-time and accurate identification of apple leaf diseases is the premise to control the common leaf diseases of apple trees during the whole growth cycle, to improve apple quality, and to ensure high-quality apple output. To improve the accuracy of the apple leaf disease identification model, two improved schemes integrated ResNet18 network is proposed for the classification of apple leaf diseases. According to our experiments, the classification accuracies of the ResNet with CBAM module (ResNet-CBAM) and ResNet18 with random clipping branches (ResNet18-RC) are 95.2% and 97.2% respectively, which all slightly improved the performance of ResNet18. The improved ResNet18 networks boost the accuracy of apple leaf disease classification and can provide a theoretical basis for the prevention and control of apple leaf disease.

The growth simulation of pine-needle like structure with diffusion-limited aggregation and oriented attachment.

A growth model combined with diffusion-limited aggregation (DLA) and oriented attachment (OA) is developed for deducing quantitative understanding of the growth process of pine-needle like structures. We define the completely random parameters for describing the realistic Brownian motion in DLA. The results indicate that the cluster by DLA changes from random branches to regular needles by the introduction of OA. And the cluster of DLA and OA has a fractal dimensionality of about 1.0 during the whole growth process. The maximum length of needels (Lmax) depends on the number of particles (Np). They satisfy the relation Lmax = aNpb (a and b are constant) over the whole range. The model has also been used to describe the formation of needles on a line, plane and sphere. The growth of needles has obvious steric hindrance from the outer needles. In particular, only one needle grows in the later period in the plane.