Asymmetric Tree Research Articles

Closeness Centrality of Asymmetric Trees and Triangular Numbers

The combinatorial problem in this paper is motivated by a variant of the famous traveling salesman problem where the salesman must return to the starting point after each delivery. The total length of a delivery route is related to a metric known as closeness centrality. The closeness centrality of a vertex v in a graph G was defined in 1950 by Bavelas to be CC(v)=|V(G)|−1SD(v), where SD(v) is the sum of the distances from v to each of the other vertices (which is one-half of the total distance in the delivery route). We provide a real-world example involving the Metro Atlanta Rapid Transit Authority rail network and identify stations whose SD values are nearly identical, meaning they have a similar proximity to other stations in the network. We then consider theoretical aspects involving asymmetric trees. For integer values of k, we considered the asymmetric tree with paths of lengths k,2k,…,nk that are incident to a center vertex. We investigated trees with different values of k, and for k=1 and k=2, we established necessary and sufficient conditions for the existence of two vertices with identical SD values, which has a surprising connection to the triangular numbers. Additionally, we investigated asymmetric trees with paths incident to two vertices and found a sufficient condition for vertices to have equal SD values. This leads to new combinatorial proofs of identities arising from Pascal’s triangle.

Differential warming at crown scale impacts walnut primary growth onset and secondary growth rate.

Trees are exposed to significant spatio-temporal thermal variations, which can induce intracrown discrepancies in the onset and dynamics of primary and secondary growth. In recent decades, an increase in late winter and early spring temperatures has been observed, potentially accelerating bud break, cambial activation and their potential coordination. Intracrown temperature heterogeneities could lead to asymmetric tree shapes unless there is a compensatory mechanism at the crown level. An original warming experiment was conducted on young Juglans regia trees in a greenhouse. From February to August, the average temperature difference during the day between warmed and control parts was 4°C. The warming treatment advanced the date of budbreak significantly, by up to 14 days. Warming did not alter secondary growth resumption but increased growth rates, leading to higher xylem cell production (twice as many) and to an increase in radial increment (+80% compared to control). Meristems resumptions were asynchronous without coordination in response to temperature. Buds on warmed branches began to swell two weeks prior to cambial division, which was one week earlier than on control branches. A difference in carbon and water remobilisation at the end of bud ecodormancy was noted under warming. Overall, our results argue for a lack of compensatory mechanisms at the crown scale, which may lead to significant changes in tree architecture in response to intra-crown temperature heterogeneities.

Monte Carlo tree search for dynamic shortest‐path interdiction

AbstractWe present a reinforcement learning‐based heuristic for a two‐player interdiction game called the dynamic shortest path interdiction problem (DSPI). The DSPI involves an evader and an interdictor who take turns in the problem, with the interdictor selecting a set of arcs to attack and the evader choosing an arc to traverse at each step of the game. Our model employs the Monte Carlo tree search framework to learn a policy for the players using randomized roll‐outs. This policy is stored as an asymmetric game tree and can be further refined as the game unfolds. We leverage alpha–beta pruning and existing bounding schemes in the literature to prune suboptimal branches. Our numerical experiments demonstrate that the prescribed approach yields near‐optimal solutions in many cases and allows for flexibility in balancing solution quality and computational effort.

Three-Way Alignment Improves Multiple Sequence Alignment of Highly Diverged Sequences

The standard approach for constructing a phylogenetic tree from a set of sequences consists of two key stages. First, a multiple sequence alignment (MSA) of the sequences is computed. The aligned data are then used to reconstruct the phylogenetic tree. The accuracy of the resulting tree heavily relies on the quality of the MSA. The quality of the popularly used progressive sequence alignment depends on a guide tree, which determines the order of aligning sequences. Most MSA methods use pairwise comparisons to generate a distance matrix and reconstruct the guide tree. However, when dealing with highly diverged sequences, constructing a good guide tree is challenging. In this work, we propose an alternative approach using three-way dynamic programming alignment to generate the distance matrix and the guide tree. This three-way alignment incorporates information from additional sequences to compute evolutionary distances more accurately. Using simulated datasets on two symmetric and asymmetric trees, we compared MAFFT with its default guide tree with MAFFT with a guide tree produced using the three-way alignment. We found that (1) the three-way alignment can reconstruct better guide trees than those from the most accurate options of MAFFT, and (2) the better guide tree, on average, leads to more accurate phylogenetic reconstruction. However, the improvement over the L-INS-i option of MAFFT is small, attesting to the excellence of the alignment quality of MAFFT. Surprisingly, the two criteria for choosing the best MSA (phylogenetic accuracy and sum-of-pair score) conflict with each other.

A new method of calculating crown projection area and its comparative accuracy with conventional calculations for asymmetric tree crowns

A new method of calculating crown projection area and its comparative accuracy with conventional calculations for asymmetric tree crowns

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 < βm, while the opposite effect is observed when β > 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.

Lightning Discharge as a Self-Organizing Transport Network. Part 1. The Concept of an Asymmetric Discharge Tree

Lightning is a self-developing transport system of plasma channels demonstrating the ability to self-regulation due to self-consistent maintenance of zero total charge of the entire branched discharge network. The lightning structural evolution is accompanied by significant morphological changes: new plasma channels appear, and some of old ones disappear. The accomplished work was in general aimed at studying intracloud lightning and cloud-to-ground discharges up to the moment the latter come in contact with the ground. It has been shown, as part of the study, that the ability of lightning, as an open system, to maintain its structural “homeostasis” is closely linked with macroscale asymmetry: the lightning morphological and transport properties are caused by loss of electric discharge tree structural symmetry when the discharge polarity changes for the opposite. Indeed, the asymmetry of electric field threshold strength levels needed to support the growth of positive and negative streamers leads to pronounced macroscale effects in the physics of lightning. Ground discharges of negative polarity consist most often of a series of strokes passing through the same channel, while positive flashes are as a rule limited to a single stroke. Negative and positive lightning leaders have significant morphological differences: the growth of positive leaders is accompanied by development of negative recoil leaders, whereas no one has observed positive recoil leaders, if they exist at all. The results of the study are presented in two parts. This article contains an introductory part that sets out the narration general context, and, by analogy with the hierarchical Horton-Strahler scheme used for river systems, analyzes the asymmetry of the spatial distribution of capacitance in different parts of the lightning discharge tree. The concept of a point of zero induced charge or a reversing point is discussed.

A multiscale framework for defining homeostasis in distal vascular trees: applications to the pulmonary circulation.

Pulmonary arteries constitute a low-pressure network of vessels, often characterized as a bifurcating tree with heterogeneous vessel mechanics. Understanding the vascular complexity and establishing homeostasis is important to study diseases such as pulmonary arterial hypertension (PAH). The onset and early progression of PAH can be traced to changes in the morphometry and structure of the distal vasculature. Coupling hemodynamics with vessel wall growth and remodeling (G&R) is crucial for understanding pathology at distal vasculature. Accordingly, the goal of this study is to provide a multiscale modeling framework that embeds the essential features of arterial wall constituents coupled with the hemodynamics within an arterial network characterized by an extension of Murray's law. This framework will be used to establish the homeostatic baseline characteristics of a pulmonary arterial tree, including important parameters such as vessel radius, wall thickness and shear stress. To define the vascular homeostasis and hemodynamics in the tree, we consider two timescales: a cardiac cycle and a longer period of vascular adaptations. An iterative homeostatic optimization, which integrates a metabolic cost function minimization, the stress equilibrium, and hemodynamics, is performed at the slow timescale. In the fast timescale, the pulsatile blood flow dynamics is described by a Womersley's deformable wall analytical solution. Illustrative examples for symmetric and asymmetric trees are presented that provide baseline characteristics for the normal pulmonary arterial vasculature. The results are compared with diverse literature data on morphometry, structure, and mechanics of pulmonary arteries. The developed framework demonstrates a potential for advanced parametric studies and future G&R and hemodynamics modeling of PAH.

Improved Learning-Based Design Space Exploration for Approximate Instance Generation

Design methodologies for approximation of medium to large-scale accelerators have largely relied on search-based design space exploration. Due to the enormously sized solution space, Artificial Intelligence (AI) based heuristic search has remained one of the most common techniques to explore cost and performance trade-offs. As a sub-class of AI techniques, Monte Carlo Tree Search (MCTS) has recently shown great potential as an intelligent stochastic search algorithm to solve computational problems with large branching factors. MCTS employs reinforced learning that combines past statistics and stochastic processes to traverse new paths in the search tree. Inspired by the success of MCTS in the games domain (AlphaGo), it has been recently applied to explore the solution space of approximate circuits. In this paper, a modified MCTS-based intelligent search technique is proposed that can handle huge search space for approximation of fairly large benchmark circuits. The proposed learning-based heuristic for MCTS directs the search towards deeper nodes in the search tree resulting in a rather asymmetric tree to efficiently utilize the search budget on the exploration of more promising nodes in the design space. The modified MCTS algorithm is based on reinforced learning where an agent uses past information to improve the overall gain. Experimental results confirm that the proposed heuristics can reach out to deeper nodes in the search tree which account for larger area savings in the context of approximate computing. The modified search algorithm enables 34.23% more area savings than the original search algorithm.

Firewall Anomaly Detection Based on Double Decision Tree

To solve the problems regarding how to detect anomalous rules with an asymmetric structure, which leads to the firewall not being able to control the packets in and out according to the administrator’s idea, and how to carry out an incremental detection efficiently when the new rules are added, anomaly detection algorithms based on an asymmetric double decision tree were considered. We considered the packet filter, the most common and used type of First Matching Rule, for the practical decision space of each rule and the whole policy. We adopted, based on the asymmetric double decision tree detection model, the policy equivalent decision tree and the policy decision tree of anomalies. Therefore, we can separate the policy’s effective decision space and the anomalous decision space. Using the separated decision trees can realize the optimization of the original policy and the faster incremental detection when adding new rules and generating a detailed report. The simulation results demonstrate that the proposed algorithms are superior to the other decision tree algorithms in detection speed and can achieve incremental detection. The results demonstrate that our approach can save about 33% of the time for complete detection compared with the other approaches, and the time of incremental anomaly detection compared to complete detection is about 90% of the time saved in a complex policy.

Simulation-driven 3D forest growth forecasting based on airborne topographic LiDAR data and shading

Reliable forest growth forecasting requires detailed tree data for forest simulation, while manual on-site collection of relevant data is work-intensive and unfeasible in larger forests. This paper proposes a complete methodology for fully automated forest growth simulation that relies primarily on airborne topographic Light Detection And Ranging (LiDAR) point clouds of individual trees. The proposed method estimates tree parameters and performs growth of individual trees based on an individual-based forest growth simulator, named BWINPro. In addition, competition and detailed asymmetric tree crown growth are modeled regarding the shading of tree crowns, which is estimated from the surrounding environment and neighbor trees. The result of the proposed approach is a new point cloud for subsequent analyses. The proposed method was validated by comparing canopy height models derived from the point clouds of the simulated trees with canopy height models derived from more recent ground truth point clouds. The results demonstrate the efficacy of the proposed method which achieves a 9.4% higher accuracy than the averaged linear regression model and, in the case of datasets with more distinct self-standing trees, where a tree crown boundary plays major role, a 4.1% higher accuracy than the directly fitted linear regression model.

Rigorous mathematical optimization of synthetic hepatic vascular trees.

In this paper, we introduce a new framework for generating synthetic vascular trees, based on rigorous model-based mathematical optimization. Our main contribution is the reformulation of finding the optimal global tree geometry into a nonlinear optimization problem (NLP). This rigorous mathematical formulation accommodates efficient solution algorithms such as the interior point method and allows us to easily change boundary conditions and constraints applied to the tree. Moreover, it creates trifurcations in addition to bifurcations. A second contribution is the addition of an optimization stage for the tree topology. Here, we combine constrained constructive optimization (CCO) with a heuristic approach to search among possible tree topologies. We combine the NLP formulation and the topology optimization into a single algorithmic approach. Finally, we attempt the validation of our new model-based optimization framework using a detailed corrosion cast of a human liver, which allows a quantitative comparison of the synthetic tree structure with the tree structure determined experimentally down to the fifth generation. The results show that our new framework is capable of generating asymmetric synthetic trees that match the available physiological corrosion cast data better than trees generated by the standard CCO approach.

Assessment of Heterogeneity in Lung Structure and Function During Mechanical Ventilation: A Review of Methodologies.

The mammalian lung is characterized by heterogeneity in both its structure and function, by incorporating an asymmetric branching airway tree optimized for maintenance of efficient ventilation, perfusion, and gas exchange. Despite potential benefits of naturally occurring heterogeneity in the lungs, there may also be detrimental effects arising from pathologic processes, which may result in deficiencies in gas transport and exchange. Regardless of etiology, pathologic heterogeneity results in the maldistribution of regional ventilation and perfusion, impairments in gas exchange, and increased work of breathing. In extreme situations, heterogeneity may result in respiratory failure, necessitating support with a mechanical ventilator. This review will present a summary of measurement techniques for assessing and quantifying heterogeneity in respiratory system structure and function during mechanical ventilation. These methods have been grouped according to four broad categories: (1) inverse modeling of heterogeneous mechanical function; (2) capnography and washout techniques to measure heterogeneity of gas transport; (3) measurements of heterogeneous deformation on the surface of the lung; and finally (4) imaging techniques used to observe spatially-distributed ventilation or regional deformation. Each technique varies with regard to spatial and temporal resolution, degrees of invasiveness, risks posed to patients, as well as suitability for clinical implementation. Nonetheless, each technique provides a unique perspective on the manifestations and consequences of mechanical heterogeneity in the diseased lung.

A novel approach to quantify ventilation heterogeneity in occluded bronchial tree based on lung admittance

Obstructions in airways result in significant alterations in ventilation distribution and consequently reduce the ventilation to perfusion ratio, affecting gas exchange. This study presents a lumped parameter-based model to quantify the spatial ventilation distribution using constructal theory. An extension of the existing theory is made for the conductive bronchial tree and is represented in matrix frame incorporated with airway admittances. The proposed lung admittance model has a greater advantage over the existing methodologies based on lung impedance, as it can be applicable for both fully and partially blocked regions. We proved the well-posedness of the problem, and the generated matrix is highly sparse in nature. A modified block decomposition method is implemented for symmetric and asymmetric trees of various obstructions 0:20:100% to reduce the memory size. The asymmetry is considered in every left branch of the bronchial tree recursively, following the mathematical relations: Li, 2j=ΓLi, 2j+1 and Di, 2j=ΓDi, 2j+1, where L and D are the length, diameter of the jth branch at ith generation, respectively, for Γ∈0.9:0.01:1.0. It is observed that relative flow rate (Qi,jQi,jhealthy) decreases exponentially with the generation index. In tidal breathing, the regional ventilation pattern is found to vary spatially instead of spatio-temporally. The comparison of our result with the clinical data is found to be accurate when 40% or more obstruction is considered in the proximal region (observed in asthma). Moreover, this predicts an increment of lung impedance by 6%, which can be used for further improvement of clinical observations.

A vectorial tree distance measure

A vectorial distance measure for trees is presented. Given two trees, we define a Tree-Alignment (T-Alignment). We T-align the trees from their centers outwards, starting from the root-branches, to make the next level as similar as possible. The algorithm is recursive; condition on the T-alignment of the root-branches we T-align the sub-branches, thereafter each T-alignment is conditioned on the previous one. We define a minimal T-alignment under a lexicographic order which follows the intuition that the differences between the two trees constitutes a vector. Given such a minimal T-alignment, the difference in the number of branches calculated at any level defines the entry of the distance vector at that level. We compare our algorithm to other well-known tree distance measures in the task of clustering sets of phylogenetic trees. We use the TreeSimGM simulator for generating stochastic phylogenetic trees. The vectorial tree distance (VTD) can successfully separate symmetric from asymmetric trees, and hierarchical from non-hierarchical trees. We also test the algorithm as a classifier of phylogenetic trees extracted from two members of the fungi kingdom, mushrooms and mildews, thus showimg that the algorithm can separate real world phylogenetic trees. The Matlab code can be accessed via: https://gitlab.com/avner.priel/vectorial-tree-distance.

Bifurcation analysis of mixed-mode oscillations and Farey trees in an extended Bonhoeffer–van der Pol oscillator

The two-variable Bonhoeffer–van der Pol oscillator, which is equivalent to the FitzHugh–Nagumo model, can be represented by a natural circuit, i.e., a circuit consisting only of simple two-terminal elements. An extended Bonhoeffer–van der Pol (BVP) oscillator is a circuit extended to a three-variable system from a two-variable BVP oscillator; this is obtained by adding an inductor–resistor branch to the original BVP oscillator. The extended BVP oscillator is known to generate mixed-mode oscillations. In this study, we classify the bifurcations of the simple sequences and their daughters, which constitute asymmetric Farey trees. Because the extended BVP oscillator is an extremely simple circuit, the parents–daughter processes can be quite precisely explained. We confirm that simple sequences 1s (s≥0) are born via saddle–node bifurcations and can be basic parents, which correspond to each stable fixed point of a Poincaré return map, where 1s represents one large excursion followed by a number s of small peaks. The two basic parents 1s and 1s+1 generate daughters [1s+1,1s×n] sequentially for the successive values of n via mixed-mode oscillation-incrementing bifurcations. The terms [1s+1,1s×n] indicate that 1s+1 is followed by 1sn-times. The daughters are born in a similar fashion to period-adding bifurcations generated by the circle map, and the parents–daughter processes satisfy Farey arithmetic and are terminated by a saddle–node bifurcation through which 1s appears. We create multiple two-parameter bifurcation diagrams and confirm that these phenomena are stably observed in these diagrams over broad ranges, i.e., complex bifurcations, such as codimension-two bifurcations or cusps, do not appear in the diagrams. Furthermore, the theoretical results are confirmed using laboratory measurements and experiments.

ECCENTRIC DISTANCE SUM OF SUBSTITUTION TREE NETWORKS

In this paper, we study the eccentric distance sum of substitution tree networks. Calculation of eccentric distance sum naturally involves calculation of average geodesic distance and it is much more complicated. We obtain the asymptotic formulas of average geodesic distance and eccentric distance sum of both symmetric and asymmetric substitution tree networks. Our result on average geodesic distance generalizes the result of [T. Li, K. Jiang and L. Xi, Average distance of self-similar fractal trees, Fractals 26(1) (2018) 1850016.] from symmetric case to asymmetric case. To derive formulas, we investigate the corresponding integrals on self-similar measure and use the self-similarity of distance and measure. For simplicity, we introduce some systematic symbolic assignments and make some assumptions on the graph. We verify that our formulas are correct using the numerical calculation results.

Leader selection for coherence in symmetric and asymmetric trees

This paper studies consensus dynamics in symmetric and asymmetric trees with leader selection under additive noise environment, which is characterized as leader–follower coherence determined by the spectrum. In order to compare the effect of the leader’s positions on the coherence, we choose a tree-like network model and employ three different ways to assign the leaders. Based on the tree construction, we obtain exact solutions for the leader–follower coherence depending on the number of leaders and network parameters. We then show that the consensus in symmetric and asymmetric trees becomes better with an increasing number of leaders. When the number of leaders and network parameters satisfy certain conditions, the leader’s positions and topological structures have a profound impact on the coherence.

Mixed-mode oscillations from a constrained extended Bonhoeffer-van der Pol oscillator with a diode.

An extended Bonhoeffer-van der Pol (BVP) oscillator is a circuit that is naturally extended to a three-variable system from a two-variable BVP oscillator. A BVP oscillator is known to exhibit a canard explosion, and the extended BVP oscillator generates mixed-mode oscillations (MMOs). In this work, we considered a case study where the nonlinear conductor in the extended BVP oscillator includes an idealized diode. The idealized case corresponds to a degenerate case where one of the parameters tends to infinity, and circuit dynamics are represented using a constrained equation, and at the expense of the model's naturalness, i.e., in a case in which the solutions of the dynamics are defined only forward in time, the Poincaré return maps are constructed as one-dimensional (1D). Using these 1D return maps, we explain various phenomena, such as simple MMOs and MMO-incrementing bifurcations. In this oscillator, there exists a small amplitude oscillation, which emerges as a consequence of supercritical Hopf bifurcation, and there exists large relaxation oscillation which appears via canard explosion by changing the bifurcation parameter. Between these small and large amplitude oscillations, the MMO bifurcations exhibit asymmetric Farey trees. Furthermore, these theoretical results were verified using laboratory measurements and experiments.

Probabilistic Contextual and Structural Dependencies Learning in Grammar-Based Genetic Programming.

Genetic Programming is a method to automatically create computer programs based on the principles of evolution. The problem of deceptiveness caused by complex dependencies among components of programs is challenging. It is important because it can misguide Genetic Programming to create suboptimal programs. Besides, a minor modification in the programs may lead to a notable change in the program behaviours and affect the final outputs. This article presents Grammar-Based Genetic Programming with Bayesian Classifiers (GBGPBC) in which the probabilistic dependencies among components of programs are captured using a set of Bayesian network classifiers. Our system was evaluated using a set of benchmark problems (the deceptive maximum problems, the royal tree problems, and the bipolar asymmetric royal tree problems). It was shown to be often more robust and more efficient in searching the best programs than other related Genetic Programming approaches in terms of the total number of fitness evaluation. We studied what factors affect the performance of GBGPBC and discovered that robust variants of GBGPBC were consistently weakly correlated with some complexity measures. Furthermore, our approach has been applied to learn a ranking program on a set of customers in direct marketing. Our suggested solutions help companies to earn significantly more when compared with other solutions produced by several well-known machine learning algorithms, such as neural networks, logistic regression, and Bayesian networks.