Leaf Nodes Research Articles

Adaptive physics-informed neural operator for coarse-grained non-equilibrium flows

This work proposes a new machine learning (ML)-based paradigm aiming to enhance the computational efficiency of non-equilibrium reacting flow simulations while ensuring compliance with the underlying physics. The framework combines dimensionality reduction and neural operators through a hierarchical and adaptive deep learning strategy to learn the solution of multi-scale coarse-grained governing equations for chemical kinetics. The proposed surrogate’s architecture is structured as a tree, with leaf nodes representing separate neural operator blocks where physics is embedded in the form of multiple soft and hard constraints. The hierarchical attribute has two advantages: (i) It allows the simplification of the training phase via transfer learning, starting from the slowest temporal scales; (ii) It accelerates the prediction step by enabling adaptivity as the surrogate’s evaluation is limited to the necessary leaf nodes based on the local degree of non-equilibrium of the gas. The model is applied to the study of chemical kinetics relevant for application to hypersonic flight, and it is tested here on pure oxygen gas mixtures. In 0-textrm{D} scenarios, the proposed ML framework can adaptively predict the dynamics of almost thirty species with a maximum relative error of 4.5% for a wide range of initial conditions. Furthermore, when employed in 1-textrm{D} shock simulations, the approach shows accuracy ranging from 1% to 4.5% and a speedup of one order of magnitude compared to conventional implicit schemes employed in an operator-splitting integration framework. Given the results presented in the paper, this work lays the foundation for constructing an efficient ML-based surrogate coupled with reactive Navier-Stokes solvers for accurately characterizing non-equilibrium phenomena in multi-dimensional computational fluid dynamics simulations.

Local Gaussian Process Extrapolation for BART Models with Applications to Causal Inference

Bayesian additive regression trees (BART) is a semi-parametric regression model offering state-of-the-art performance on out-of-sample prediction. Despite this success, standard implementations of BART typically suffer from inaccurate prediction and overly narrow prediction intervals at points outside the range of the training data. This article proposes a novel extrapolation strategy that grafts Gaussian processes to the leaf nodes in BART for predicting points outside the range of the observed data. The new method is compared to standard BART implementations and recent frequentist resampling-based methods for predictive inference. We apply the new approach to a challenging problem from causal inference, wherein for some regions of predictor space, only treated or untreated units are observed (but not both). In simulation studies, the new approach boasts superior performance compared to popular alternatives, such as Jackknife+. Supplementary materials for this article are available online.

Prediction Model of Borehole Spontaneous Combustion Based on Machine Learning and Its Application

In order to quickly and accurately predict borehole spontaneous combustion danger and avoid borehole spontaneous combustion fires, a borehole spontaneous combustion prediction model combining the Hunger Games search optimization algorithm (HGS) and Random Forest (RF) algorithm was introduced. The number of trees and the minimum number of leaf nodes in RF were optimized by HGS. Based on the data obtained from the temperature rise experiment of spontaneous combustion characteristics in a Shandong mine laboratory, O2, CO, C2H4, CO/∆O2 and C2H4/C2H6 were selected as the input indexes for the prediction of borehole spontaneous combustion, and the spontaneous combustion temperature was selected as the output indexes to train the built model. The prediction performance and accuracy of the model were evaluated using four indexes: the mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE) and coefficient of determination (R2). At the same time, the prediction results of the HGS-RF model were compared with those of the RF model, Sparrow search algorithm (SSA) optimization RF model, particle swarm optimization RF model (PSO) optimization RF model and quantum particle swarm optimization RF model (QPSO) optimization. The results showed that the MAE of the RF, SSA-RF, PSO-RF, QPSO-RF and HGS-RF model samples were 17.541, 15.7752, 12.5903, 6.8594 and 6.6921, respectively. MAPE was 13.81%, 10.9766%, 9.6802%, 4.5731% and 5.1536%, respectively. RMSE values were 21.5646, 15.2017, 17.0091, 11.9879 and 12.1691, respectively. The R2 values were 0.9043, 0.9315, 0.9266, 0.9668, and 0.9717, respectively. At the same time, the reliability of the HGS-RF model was supplemented by taking the test data of the Zhengjia1204 coal mining face as an example. Finally, the model was applied to the prediction of borehole spontaneous combustion in the Jinniu Coal Mine, Shanxi Province. The prediction results show that the HGS-RF model can predict the spontaneous combustion temperature of different boreholes quickly and accurately. The results show that the HGS-RF model is more universal and stable than other models, indicating that the HGS-RF model is more suitable for the prediction of borehole spontaneous combustion.

Injury severity prediction of cyclist crashes using random forests and random parameters logit models

Cycling provides numerous benefits to individuals and to society but the burden of road traffic injuries and fatalities is disproportionately sustained by cyclists. Without awareness of the contributory factors of cyclist death and injury, the capability to implement context-specific and appropriate measures is severely limited. In this paper, we investigated the effects of the characteristics related to the road, the environment, the vehicle involved, the driver, and the cyclist on severity of crashes involving cyclists analysing 72,363 crashes that occurred in Great Britain in the period 2016–2018. Both a machine learning method, as the Random Forest (RF), and an econometric model, as the Random Parameters Logit Model (RPLM), were implemented.Three different RF algorithms were performed, namely the traditional RF, the Weighted Subspace RF, and the Random Survival Forest. The latter demonstrated superior predictive performances both in terms of F-measure and G-mean. The main result of the Random Survival Forest is the variable importance that provides a ranked list of the predictors associated with the fatal and severe cyclist crashes. For fatal classification, 19 variables showed a normalized importance higher than 5% with the second involved vehicle manoeuvring and the gender of the driver of the second vehicle having the greatest predictive ability. For serious injury classification, 13 variables showed a normalized importance higher than 5% with the bike leaving the carriageway having the greatest normalized importance. Furthermore, each path from the root node to the leaf nodes has been retraced the way back generating 361 if-then rules with fatal crash as consequent and 349 if-then rules with serious injury crash as consequent. The RPLM showed significant unobserved heterogeneity in the data finding four normal distributed indicator variables with random parameters: cyclist age ≥ 75 (fatal prediction), cyclist gender male (fatal and serious prediction), and driver aged 55–64 (serious prediction). The model’s McFadden Pseudo R2 is equal to 0.21, indicating a very good fit. Furthermore, to understand the magnitude of the effects and the contribution of each variable to injury severity probabilities the pseudo-elasticity was assessed, gaining valuable insights into the relative importance and influence of the variables.The RF and the RPLM resulted complementary in identifying several roadways, environmental, vehicle, driver, and cyclist-related factors associated with higher crash severity. Based on the identified contributory factors, safety countermeasures useful to develop strategies for making bike a safer and more friendly form of transport were recommended.

BIP-Tree: Tree Variant With Behavioral Intention Perception for Heterogeneous Trajectory Prediction

An insightful understanding and relational reasoning of motion behavior are typical components for trajectory prediction to achieve safe planning when navigating in complex scenarios. Due to the differences in behavioral responses of heterogeneous agents and the existence of chain effect in message passing, an effective prediction method is desired to better acquire potential behavioral intention and model motion behavior. In this paper, we construct a trajectory prediction method to represent and encode the behavioral interactions among heterogeneous agents, called as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Tree variant with Behavioral Intention Perception (BIP-Tree)</i> . Specifically, a dual-behavior interaction module is presented to deeply understand behavioral intention by simultaneously considering the behavioral perception and behavioral response in spatial interaction. The behavioral perception means that individual acquires behavioral features from interactive objects located in its perception range, while the behavioral response means that each agent makes distinctive reactions to different categories of agents (for example, due to different collision risks caused by pedestrian and vehicle, a pedestrian will respond differently to the interactive agents at the same distance). Meanwhile, we also introduce one new tree variant in message passing stage to enhance the acquisition of potential motion feature, denoting traffic agents as nodes and the interactions among them as tree trunks. The interaction message can be delivered along tree trunks from leaf nodes to root node, to further achieves the chain effect of high-order interactions beyond adjacent entities. Our method is evaluated on several public datasets, such as Apolloscape, nuScenes, Argoverse, SDD, INTERACTION, inD, and Waymo. The extensive experimental results demonstrate that our method can predict more plausible and realistic trajectories with multi-modality. Among them, the best performance is achieved on three datasets. More remarkably, compared with state-of-the-arts, our method achieves significant performance and decreases by at least <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$13.04\%$</tex-math> </inline-formula> on average ADE and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$19.42\%$</tex-math> </inline-formula> on average FDE on inD dataset with four intersections. The dataset and code are available at: htpps://github.com/VTP-TL/BIP-Tree.

An intracellular transporter OsNRAMP7 is required for distribution and accumulation of iron into rice grains

Iron (Fe) is an essential micronutrient for plant growth and human health. Plants have evolved an efficient transport system for absorbing and redistributing Fe from the soil to other organs; however, the molecular mechanisms underlying Fe loading into grains are poorly understood. Our study shows that OsNRAMP7, a member of the natural resistance-associated macrophage protein (NRAMP) family, is a rice Fe transporter that localizes to the Golgi and trans-Golgi network (TGN). OsNRAMP7 was highly expressed in leaf blade, node I, pollen, and vascular tissues of almost tissues at the rice flowering stage. OsNRAMP7 knockdown by RNA interference (RNAi) increased Fe accumulation in the flag leaf blade, but decreased the Fe concentration in node I and rice grains. In addition, the knockdown of OsNRAMP7 also reduced grain fertility, pollen viability, and grain Fe concentration in the paddy fields; OsNRAMP7 overexpression significantly promoted Fe accumulation in the grains. Thus, our results suggest that OsNRAMP7 is required for the distribution and accumulation of Fe in rice grains and its overexpression could be a novel strategy for Fe biofortification in staple food crops.

Coupled maize model: A 4D maize growth model based on growing degree days

Crop canopy parameters are critical for environmental remote sensing, describing crop phenotypes, and ensuring food security. Evaluating the effect of temperature on crop growth is crucial for estimating crop canopy parameters. However, existing crop growth and plant functional-structural models cannot simultaneously model temperature responses, perform accurate dynamic simulations, and provide multi-scale computer visualizations. This limitation has hindered the application of structural models of maize plants for use in 3D radiative transfer models, crop structure evaluations, and crop phenotype descriptions. We improve the leaf/organ-level thermal-driven crop growth model (MAIZSIM) and the plant functional-structural algorithm. To address these limitations, we propose the coupled maize model, a four-dimensional (4D) growth model based on growing degree days. This model can simulate and visualize the structural parameters of the maize canopy at the organ, plant, seasonal, and population levels. The model outputs three-dimensional (3D) predictions of the maize structure (file format.obj), enabling editing and 3D visualizations. We use maize datasets from multiple phenological periods to test the proposed model’s accuracy and stability in simulating the canopy parameters at multiple levels. The results show that the normalized root mean square errors (NRMSEs) between the simulated and measured maize leaf size, area, leaf node height, and vein curve derived from the coupled maize model are below 0.1, demonstrating the model's high accuracy.

Identification of Influential Nodes in Social Network: Graph Approach

The identification of nodes that are actually influencing other nodes is one of the core and fundamental research problems in the social network data sciences. There are multiple proven techniques available globally that depict the influence of the root node on the remaining nodes in the given network. Although methods and methodology is already proven and multiple experiments have been carried out in this area, the current research work is an extension of the influential node identification problem with the perspective of graph traversal. To prove the methodology and new approach a tree and AUC (area under the curve) - based analysis method has been proposed, TArank in which the information collected from the breadth-first search tree is used to identify influential nodes. From the obtained results and analysis, the effectiveness of TARank in the identification of influential nodes has been validated. The concentration of data at a particular segment of the plot is observed. Additionally, the tree view of the analysis predicts the root and leaf node thus helping in the identification of the most influential nodes in the online social media network. Keywords: Influential Node, PCC, TARank, Degree Centrality, PCC

A Model Based on the Random Forest Algorithm That Predicts the Total Oil–Water Two-Phase Flow Rate in Horizontal Shale Oil Wells

Due to variables like wellbore deviation variation and flow rate, the local flow velocity in the output wellbore of horizontal shale oil wells varied significantly at various points in the wellbore cross-section, making it challenging to calculate the total single-layer production with accuracy. The oil–water two-phase flow rate calculation techniques for horizontal wells developed based on particular flow patterns and array spinners had excellent applicability in their respective niches but suffered from poor generalizability and demanding experience levels for logging interpreters. In this study, we employed five spinners in a triangular walled array instrument to create the multi-decision tree after figuring out how many leaf nodes there were and examining the defining characteristics of the observed values gathered under various experimental setups. The construction of the entire oil–water two-phase flow prediction model was made possible when the random forest regression approach was used with it. The total oil–water flow rate at each perforated layer was predicted using the model in sample wells, and the mean square error with the third party’s interpretation conclusion was 1.42, indicating that the model had an excellent application effect. The approach, which offered a new interpretation method for calculating the oil–water two-phase flow rate of horizontal wells based on multi-location local flow rate, required less interpretation knowledge from the interpreter and had a stronger generalization capacity.

DTEC: Decision tree-based evidential clustering for interpretable partition of uncertain data

Recently, the evidential clustering has been developed as a promising clustering framework for uncertain data, which generalizes those hard, fuzzy, possibilistic and rough clustering. However, the resulting cluster assignments are less interpretable in terms of human cognition, which limits its applications in those security, privacy or ethic related fields. In this study, the unsupervised decision tree model is introduced into the evidential clustering framework to improve the interpretability of the evidential partition. A Decision Tree-based Evidential Clustering (DTEC) algorithm is developed to build an unsupervised evidential decision tree, which uses the paths from the root node to leaf nodes to achieve the interpretability of each cluster. The proposed algorithm is composed of three procedures, i.e., cutting-point selection, node evidential splitting, and cluster adjustment, in which the first two procedures are carried out iteratively to build a preliminary unsupervised decision tree and the last procedure is designed to adjust the preliminary decision tree if the number of clusters is available. Both synthetic and real datasets are used to evaluate the performance of the proposed algorithm, and the experimental results demonstrate the good performance of the proposal compared with some representative fuzzy, evidential or decision tree-based clustering algorithms.

Extracting Decision Tree From Trained Deep Reinforcement Learning in Traffic Signal Control

Deep reinforcement learning (DRL) has achieved impressive success in traffic signal control systems (TSCS). However, since a key component of many DRL models is the complex deep neural networks (DNNs), it hinders humans or experts from understanding and explaining the learned policy. Recently, many works have focused on developing interpretable techniques to compress or distill complex DNNs into smaller, faster, or more understandable models. The decision trees (DTs) are viewed as the de facto technique for interpretable and transparent machine learning, and can provide an easy-understanding decision path from the root to the leaf node. In this work, we utilize modified DTs to extract models with simpler hierarchical structures from premium policy achieved by DRL methods. First, we use a DRL algorithm to learn a premium policy for traffic signal control. Then, we collect a dataset with the learned premium policy by interacting with the environment. Finally, we extract the DTs with the collected dataset of state-actions pairs. We evaluate our method on a Simulation of Urban Mobility simulator in a simulation way. Simulation results show that the extracted DTs can generate human-understandable decision processes and provide explicit knowledge from the DNNs reference of the DRL.

Lithological Classification by Hyperspectral Images Based on a Two-Layer XGBoost Model, Combined with a Greedy Algorithm

Lithology classification is important in mineral resource exploration, engineering geological exploration, and disaster monitoring. Traditional laboratory methods for the qualitative analysis of rocks are limited by sampling conditions and analytical techniques, resulting in high costs, low efficiency, and the inability to quickly obtain large-scale geological information. Hyperspectral remote sensing technology can classify and identify lithology using the spectral characteristics of rock, and is characterized by fast detection, large coverage area, and environmental friendliness, which provide the application potential for lithological mapping at a large regional scale. In this study, ZY1-02D hyperspectral images were used as data sources to construct a new two-layer extreme gradient boosting (XGBoost) lithology classification model based on the XGBoost decision tree and an improved greedy search algorithm. A total of 153 spectral bands of the preprocessed hyperspectral images were input into the first layer of the XGBoost model. Based on the tree traversal structural characteristics of the leaf nodes in the XGBoost model, three built-in XGBoost importance indexes were split and combined. The improved greedy search algorithm was used to extract the spectral band variables, which were imported into the second layer of the XGBoost model, and the bat algorithm was used to optimize the modeling parameters of XGBoost. The extraction model of rock classification information was constructed, and the classification map of regional surface rock types was drawn. Field verification was performed for the two-layer XGBoost rock classification model, and its accuracy and reliability were evaluated based on four indexes, namely, accuracy, precision, recall, and F1 score. The results showed that the two-layer XGBoost model had a good lithological classification effect, robustness, and adaptability to small sample datasets. Compared with the traditional machine learning model, the two-layer XGBoost model shows superior performance. The accuracy, precision, recall, and F1 score of the verification set were 0.8343, 0.8406, 0.8350, and 0.8157, respectively. The variable extraction ability of the constructed two-layer XGBoost model was significantly improved. Compared with traditional feature selection methods, the GREED-GFC method, when applied to the two-layer XGBoost model, contributes to more stable rock classification performance and higher lithology prediction accuracy, and the smallest number of extracted features. The lithological distribution information identified by the model was in good agreement with the lithology information verified in the field.

Automatic Identification of Corrosion in Marine Vessels Using Decision-Tree Imaging Hierarchies

We propose an unsupervised method for eigen tree hierarchies and quantisation group association for segmentation of corrosion in marine vessel hull inspection via camera images. Our unsupervised approach produces image segments that are examined to decide on defect recognition. The method generates a binary decision tree, which, by means of bottom-up pruning, is revised, and dominant leaf nodes predict the areas of interest. Our method is compared with other techniques, and the results indicate that it achieves better performance for true- vs. false-positive area against ideal (ground truth) coverage.

Tree-based data filtering for online user-generated reviews

Analysis of online user-generated reviews has attracted extensive attention with broad applications in recent years. However, the high-volume and low-value density of online reviews bring challenges to a timely and effective data utilization. To address that challenge, this work proposes an unsupervised review filtering method based on the inherent tree-structured hierarchies among review data that reflect the general-to-specific characteristics of various quality aspects discussed in reviews. In particular, the reviews with aspects distributed near the leaf nodes of the tree are capable of providing more specific and detailed information about the examined product, which is more likely to be reserved after the tree-based filtering. To enable an effective extraction of aspect hierarchies from a broad variety of review corpora, a Bayesian nonparametric hierarchical topic model has been constructed and incorporated with an enhanced Pólya urn scheme. The approximate inference of model parameters is obtained by an efficient collapsed Gibbs sampling procedure. The proposed method can enhance the layered effect of individual reviews according to their general-to-specific characteristics and reserve an information-rich subset filtered from the raw review corpus. The merits of the proposed method have been elaborated by case studies on two real-world data sets and an extensive simulation study.

Path planning and collision avoidance based on the RRT*FN framework for a robotic manipulator in various scenarios

AbstractIn this article, we present a new path planning algorithm based on the rapidly exploring random tree-fixed node (RRT*FN) algorithm for manipulators. It addresses the problem that RRT*FN complex environment processing is not fast enough to meet real-time requirements, and RRT*FN is basically impossible to search for an effective manipulator path in a narrow-channel environment. In the new path planning algorithm, a heuristic sampling method is adopted and the leaf nodes outside the ellipsoids are preferentially deleted to address the node removal problem, resulting in better search paths and faster search speeds. When the nodes are expanded, new nodes are generated due to goal gravity and random point gravity, with the weight values dynamically adjusted via dichotomy, and the new nodes are expanded to the goal point twice to more rapidly obtain a tree extension direction that is closer to the goal point. For boundary points, the issues of narrow channels and stepped obstacles can be effectively solved by extending the local environment sampling boundaries. To optimize the paths, the redundant intermediate nodes are simplified based on the triangle inequality. Simulation analyses show that the proposed planner can adapt to a variety of scenarios in real time while satisfying optimal path conditions.

BP-Tree: Overcoming the Point-Range Operation Tradeoff for In-Memory B-Trees

B-trees are the go-to data structure for in-memory indexes in databases and storage systems. B-trees support both point operations (i.e., inserts and finds) and range operations (i.e., iterators and maps). However, there is an inherent tradeoff between point and range operations since the optimal node size for point operations is much smaller than the optimal node size for range operations. Existing implementations use a relatively small node size to achieve fast point operations at the cost of range operation throughput. We present the BP-tree , a variant of the B-tree, that overcomes the decades-old point-range operation tradeoff in traditional B-trees. In the BP-tree, the leaf nodes are much larger in size than the internal nodes to support faster range scans. To avoid any slowdown in point operations due to large leaf nodes, we introduce a new insert-optimized array called the buffered partitioned array (BPA) to efficiently organize data in leaf nodes. The BPA supports fast insertions by delaying ordering the keys in the array. This results in much faster range operations and faster point operations at the same time in the BP-tree. Our experiments show that on 48 hyperthreads, on workloads generated from the Yahoo! Cloud Serving Benchmark (YCSB), the BP-tree supports similar or faster point operation throughput (between .94×-1.2× faster) compared to Masstree and OpenBw-tree, two state-of-the-art in-memory key-value (KV) stores. On a YCSB workload with short scans, the BP-tree is about 7.4× faster than Masstree and 1.6× faster than OpenBw-tree. Furthermore, we extend the YCSB to add large range workloads, commonly found in database applications, and show that the BP-tree is 30× faster than Masstree and 2.5× faster than OpenBw-tree. We also provide a reference implementation for a concurrent B + -tree and find that the BP-tree supports faster (between 1.03×-1.2× faster) point operations when compared to the best-case configuration for B + -trees for point operations while supporting similar performance (about .95× as fast) on short range operations and faster (about 1.3× faster) long range operations.

Probabilistic Attribute Tree Structured Convolutional Neural Networks for Facial Expression Recognition in the Wild

Very recent work has demonstrated tremendous improvements in facial expression recognition (FER) using laboratory-controlled datasets. However, recognizing facial expressions under in-the-wild conditions still remains a challenge, especially on unseen subjects due to high inter-subject variations. In this paper, we propose a novel Probabilistic Attribute Tree Convolutional Neural Network (PAT-CNN) to explicitly deal with large intra-class variations caused by identity-related attributes, e.g., age, race, and gender. Specifically, a PAT module with an associated PAT loss is proposed to learn features in a hierarchical tree structure organized according to identity-related attributes, where the final features are less affected by the attributes. Then, expression-related features are extracted from leaf nodes. Samples are probabilistically assigned to tree nodes at different levels such that expression-related features can be learned from all samples weighted by probabilities. Furthermore, the proposed PAT-CNN can be learned from limited attribute-annotated samples to make the best use of available data. Experimental results on four spontaneous facial expression datasets, i.e., RAF-DB, SFEW, ExpW, and FER-2013, have demonstrated that the proposed PAT-CNN achieves the best performance when compared to state-of-the-art methods by explicitly modeling attributes. Impressively, a single model PAT-CNN achieves the best performance on the SFEW test dataset when compared to the state-of-the-art methods using an ensemble of hundreds of CNNs.

PM2VE: Power Metering Model for Virtualization Environments in Cloud Data Centers

Virtualization technologies provide solutions for cloud computing. Virtual resource scheduling is a crucial task in data centers, and the power consumption of virtual resources is a critical foundation of virtualization scheduling. Containers are the smallest unit of virtual resource scheduling and migration. Although many practical models for estimating the power consumption of virtual machines (VMs) have been proposed, few power estimation models of containers have been put forth. In this paper, we propose a fast-training piecewise regression model based on a decision tree for VM power metering and estimate the power of containers configured on the VM by treating the container as a group of processes on the VM. We select appropriate features from the collected metrics of VMs/containers to help our model fit the nonlinear relationship between power and features well. Besides, we optimize the leaf nodes of the regression tree, realizing the effective power metering of virtualization environments. We evaluate the proposed model on 13 tasks in PARSEC and compare it with several commonly used models in data centers. The experimental results prove the effectiveness of the proposed model, and the estimated power of containers is in line with expectations.

INDUCTION OF TOMATO POLYPHENOL OXIDASES IN RESPONSE TO COMMON CUTWORM (Spodoptera litura) AND JACK BEARDSLEY MEALYBUG (Pseudococcus jackbeardsleyi) INFESTATIONS

Our objectives were to evaluate the induction of polyphenol oxidases (PPOs) and expression patterns of PPO A, B, D, E, and F genes upon infestations by common cutworm (Spodoptera litura) and Jack Beardsley mealybug (Pseudococcus jackbeardsleyi). After common cutworm infestation at leaf node 4, PPO activities increased 10.2-fold locally, leading to systemic increase in PPO activities at upper leaf nodes 1-2 (3.0-fold) and lower leaf node 6 (1.7-fold). While infestation at leaf node 6 locally induced PPO activities 14.5-fold, and systemically induced PPO activities 3.0-fold at leaf node 4. By contrast, no significant induction of PPO was observed at any leaf nodes when either leaf node 4 or 6 was infested by mealybug. When common cutworm fed on PPO B::GUS fusion tomatoes, induced PPO B expression was observed locally particularly in mature leaves at veins, petioles, and abscission zones. However, PPO D::GUS fusion tomatoes showed locally induced expression especially in older leaves at veins and petioles. Systemically induced expression was also observed. Mealybug feeding also locally induced PPO B and PPO D expression in vascular tissues but at lower levels.

From trees to barcodes and back again II: Combinatorial and probabilistic aspects of a topological inverse problem

In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered connection between the symmetric group and barcodes in general position, based on the simple observation that death order is a permutation of birth order. We show how to lift this combinatorial characterization of barcodes to an analogous combinatorialization of merge trees. As result of this study, we provide the first clear combinatorial distinction between the space of phylogenetic trees (as defined by Billera, Holmes and Vogtmann) and the space of merge trees: generic phylogenetic trees on n+1 leaf nodes fall into (2n−1)!! distinct equivalence classes, but the analogous number for merge trees is equal to the number of maximal chains in the lattice of partitions, i.e., (n+1)!n!2−n. The second aspect of our study is the derivation of precise formulas for the distribution of tree realization numbers (the number of merge trees realizing a given barcode) when we assume that barcodes are sampled using a uniform distribution on the symmetric group. We are able to characterize some of the higher moments of this distribution, thanks in part to a reformulation of our distribution in terms of Dirichlet convolution. This characterization provides a type of null hypothesis, apparently different from the distributions observed in real neuron data, which opens the door to doing more precise statistics and science.