Tree-shaped Network Research Articles

Solution Algorithms for the Capacitated Location Tree Problem with Interconnections

This paper addresses the Capacitated Location Tree Problem with Interconnections, a new combinatorial optimization problem with applications in network design. In this problem, the required facilities picked from a set of potential facilities must be opened to serve customers using a tree-shaped network. Costs and capacities are associated with the opening of facilities and the establishment of network links. Customers have a given demand that must be satisfied while respecting the facilities and link capacities. The problem aims to minimize the total cost of designing a distribution network while considering facility opening costs, demand satisfaction, capacity constraints, and the creation of interconnections to enhance network resilience. A valid mixed-integer programming was proposed and an exact solution method based on the formulation was used to solve small- and medium-sized instances. To solve larger instances two metaheuristic approaches were used. A specific decoder procedure for the metaheuristic solution approaches was also proposed and used to help find solutions, especially for large instances. Computational experiments and results using the three solution approaches are also presented. Finally, a case study on the design of electrical transportation systems was presented and solved.

Evolution of dispersal in river networks.

Evolution of dispersal is a fascinating topic at the intersection of ecology and evolutionary dynamics that has generated many challenging problems in the analysis of reaction-diffusion equations. Early results indicated that lower random diffusion rates are generally beneficial. However, in riverine environments with downstream drift, high diffusion may be optimal, depending on downstream boundary conditions. Most of these results were obtained from modeling a single river reach, yet many rivers form intricate tree-shaped networks. We study the evolution of dispersal on a metric graph representing the simplest such possible network: two upstream segments joining to form one downstream segment. We first show that the shape of the positive steady state of a single population depends crucially on the geometry of the network, here considered as the relative length of the three segments. We then study the evolution of dispersal by considering the possibility of "invasion" of a second type (invader) at the steady state of the first type (resident). We show that the geometry of the network determines whether higher or intermediate dispersal is favored.

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

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

Network nonlocality sharing in a two-forked tree-shaped network

Network nonlocality sharing in a two-forked tree-shaped network

Conditional Information Gain Trellis

Conditional computing processes an input using only part of the neural network’s computational units. Learning to execute parts of a deep convolutional network by routing individual samples has several advantages: This can facilitate the interpretability of the model, reduce the model complexity, and reduce the computational burden during training and inference. Furthermore, if similar classes are routed to the same path, that part of the network learns to discriminate between finer differences and better classification accuracies can be attained with fewer parameters. Recently, several papers have exploited this idea to select a particular child of a node in a tree-shaped network or to skip parts of a network. In this work, we follow a Trellis-based approach for generating specific execution paths in a deep convolutional neural network. We have designed routing mechanisms that use differentiable information gain-based cost functions to determine which subset of features in a convolutional layer will be executed. We call our method Conditional Information Gain Trellis (CIGT). We show that our conditional execution mechanism achieves comparable or better model performance compared to unconditional baselines, using only a fraction of the computational resources. We provide our code and model checkpoints used in the paper at: https://github.com/ufukcbicici/cigt/tree/prl/prl_scripts.

Persistency of quantum non-multi-local correlations in noisy acyclic networks

The topic of network quantum nonlocal correlations arises from the large-scale quantum communications. It has been demonstrated that non-m-local correlations (m is the number of sources) in some special kinds of networks will decay under the influence of noises from imperfect devices as these networks extend, including linear and star networks. Furthermore, we observe that under the same noisy level, persistency of non-multi-local correlations in aforementioned different kinds of networks appears obvious discrepancy. Therefore, it becomes a natural and challenging task to check the persistency of non-multi-locality in more complex acyclic network, since star and linear networks can be regarded as acyclic networks. It is worth noting that an acyclic network is one indeterminate forked tree-shaped networks. So the study is focused on the tree-shaped network. We first devote to discussing the determinate forked case. We obtain inequality persistency criteria of determinate k-forked tree-shaped network non-(s n (k))-local correlations (s n (k) is the number of total sources). We show that the larger the fork number k is larger, the better the non-multi-locality of this network persists. In the indeterminate forked case, the inequality persistency criteria are also established. We observe that the larger the number of parties in the last layer of an acyclic network, the better the non-multi-locality of this network is persisted. This theoretical research may guide us how to build quantum networks with the stronger correlation in practical communications.

Tree-shaped multiobjective evolutionary CNN for hyperspectral image classification

Convolutional neural networks (CNNs) have achieved significant performances in hyperspectral image (HSI) classification in recent years. However, designing a high-performance CNN depends on human expertise heavily, which usually takes considerable time and labor. With regard to reducing the burden of designing the networks, neural architecture search (NAS) has attracted increasing attention. A typical NAS approach aims to optimize the network architectures in a predefined search space with a suitable search algorithm automatically. However, the existing NAS work does not fully consider the spatial resolution and the spectral noise interference of HSIs. Furthermore, most NAS approaches use sequential blocks or cells to construct the networks, which are unsuitable for extracting multiscale features of HSIs and result in degraded performance. Considering the above challenges, we propose a tree-shaped multiobjective evolutionary CNN (TMOE-CNN) for HSI classification. An expanded search space is designed, which includes the image patch size and the channel number of the input image patches. A multibranch supernetwork structure is proposed, which resembles a tree as the fundamental architecture for the network block. The image patch size and the denoising strength of the input image patches can be established adaptively throughout the evolutionary search process. The tree-shaped networks can fuse multiscale features to enhance the capacity of the network for feature extraction. Additionally, we consider both the classification accuracy and the floating-point computational complexity in the environmental selection. It is helpful to find the networks with simple structure and low complexity while ensuring classification accuracy. Experiments on different HSI datasets show that TMOE-CNN can search CNNs with high accuracies and simple structures automatically.

Observer based control for a tree-shaped network of Timoshenko beams using Lyapunov’s method

Observer based control for a tree-shaped network of Timoshenko beams using Lyapunov’s method

Quantum steering in two-forked tree-shaped networks

Abstract Network quantum steering (NQS) arises from network models required with classification of trusted and untrusted parties. The network local hidden state (NLHS) models have first been proposed to define the NQS in a linear network with end points being trusted. In the paper, we devote to establishing the NLHS model to define the NQS in a kind of more complex and applied-extensively networks, namely, the two-forked tree-shaped network. Here we assume that the parties at the last layer are trusted while the remaining parties are untrusted in this network. According to the NLHS model, we observe that network nonlocality implies network steerability. Furthermore, we pay more attentions to discovering the relationship between the network quantum unsteerability and separability/unsteerability of bipartite sources in this two-forked tree-shaped network. Moreover, we generalize two kinds of bipartite steering inequality criteria as the NQS criteria. They are built based on statistical quantities, which can be directly evaluated in experiments.

Uncertainty in vulnerability of metro transit networks: A global perspective

This study measures the “uncertainty in vulnerability” of 50 metro transit networks in the most populated cities across the globe under benign and malicious attack scenarios. Uncertainty in vulnerability delineates the gap between the performance loss trajectory formed by link percolation under benign and malicious attacks. Three observations are discerned. First, vulnerability and uncertainty in vulnerability are a function of both size and physics of the network explained by connectivity measures. A 1% increase in the ratio of links to nodes increases the vulnerability by 0.50% and increases the uncertainty in vulnerability by 2.24%. A 1% increase in the ratio of the number of links to the maximum possible number of links decreases vulnerability by 0.03% and the uncertainty in vulnerability by 0.12%. Second, the topology of metro transit networks with <100 nodes follows one of the three analogous forms of tree-shaped networks, networks with one undirected cycle, or single depot networks, while the topology of metro transit networks with ≥100 nodes is closer to grid and matching pairs. Third, metro transit networks (i) are less likely to resume the operation under malicious attacks, (ii) are more likely to resume the operation under benign attacks, and (iii) are susceptible to both severe and non-severe degradations under random attacks. Overall, it is shown that the most vulnerable transit networks experience the maximal uncertainty in vulnerability and own a topology analogous to a single depot. New York, Delhi, and London metro transit networks have the most vulnerable topology. Ahmedabad, Mumbai, and Sydney metro transit networks have the least vulnerable topology.

On the Controllability of Entropy Solutions of Scalar Conservation Laws at a Junction via Lyapunov Methods

In this note, we prove a controllability result for entropy solutions of scalar conservation laws on a star-shaped graph. Using a Lyapunov-type approach, we show that, under a monotonicity assumption on the flux, if u and v are two entropy solutions corresponding to different initial data and same in-flux boundary data (at the exterior nodes of the star-shaped graph), then u ≡ v for a sufficiently large time. In order words, we can drive u to the target profile v in a sufficiently large control time by inputting the trace of v at the exterior nodes as in-flux boundary data for u. This result can also be shown to hold on tree-shaped networks by an inductive argument. We illustrate the result with some numerical simulations.

Invasion of a porous domain by a fluid network, a constructal perspective

This paper presents a methodology to predict the growth of fluid networks within a porous domain. Tree-shaped networks are generated for minimum volume and constant volumetric flow rate, maximum flow rate at constant volume and minimum walls-fluid contact surface at constant volumetric flow rate. The constructal methodology relies on the development of an algorithm inspired by the Constrained Constructive Optimization technique combined to the Hess-Murray's law. It is shown that the fluid network reconfigures itself entirely while growing, but its average bifurcation angle remains constant regardless the number of outlets connected. Furthermore, our results show that the fluid networks tend to invade the entire space regardless the shape of the domain.

A Safety Level Evaluation Model based on Network Analysis: Enhancing Accessibility & Evacuation Safety in Ho Chi Minh City’s Alleyways

ABSTRACT In this study, an evaluation model is developed to analyze the safety level of a street network in terms of accessibility for emergency services and evacuation risk for residents, especially for cities experiencing rapid urbanization and densification. The evaluation model is created based on the network geometry and street width using the Network Voronoi algorithm, and four evaluation variables are developed, namely the accessibility risk, unreachability risk, edge responsibility, and flow capacity. Next, the model is applied to an alleyway neighborhood in Ho Chi Minh City, characterized by a labyrinthine mesh and tree-shaped network, and narrow street widths. Finally, improvement interventions, such as adding new links and widening alleys, are implemented in three case studies, and the results are compared in terms of cost, social impact, and safety improvement. The results show that the most efficient improvement strategy is to target the weakest point in the network, except for the flow capacity, which, however, can detect intersections at risk on evacuation routes, which cannot be derived from the network topology. The developed evaluation model is not only useful to analyze the current risk level in the network but is also a powerful tool to evaluate future infrastructure improvement projects.

Quantum Nonlocality in Any Forked Tree-Shaped Network.

In the last decade, much attention has been focused on examining the nonlocality of various quantum networks, which are fundamental for long-distance quantum communications. In this paper, we consider the nonlocality of any forked tree-shaped network, where each node, respectively, shares arbitrary number of bipartite sources with other nodes in the next “layer”. The Bell-type inequalities for such quantum networks are obtained, which are, respectively, satisfied by all -local correlations and all local correlations, where denotes the total number of nodes in the network. The maximal quantum violations of these inequalities and the robustness to noise in these networks are also discussed. Our network can be seen as a generalization of some known quantum networks.

Input-output $ L^2 $-well-posedness, regularity and Lyapunov stability of string equations on networks

&lt;p style='text-indent:20px;'&gt;We consider the general networks of elastic strings with Neumann boundary feedbacks and collocated observations in this paper. By selecting an appropriate multiplier, we show that this system is input-output &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ L^2 $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;-well-posed. Moreover, we verify its regularity by calculating the input-output transfer function of system. In the end, by choosing an appropriate multiplier, we give a method to construct a Lyapunov functional and prove the exponential decay of tree-shaped networks with one fixed root under velocity feedbacks acted on all leaf vertices.&lt;/p&gt;

Hierarchical Modeling of the Liver Vascular System.

The liver plays a key role in the metabolic homeostasis of the whole organism. To carry out its functions, it is endowed with a peculiar circulatory system, made of three main dendritic flow structures and lobules. Understanding the vascular anatomy of the liver is clinically relevant since various liver pathologies are related to vascular disorders. Here, we develop a novel liver circulation model with a deterministic architecture based on the constructal law of design over the entire scale range (from macrocirculation to microcirculation). In this framework, the liver vascular structure is a combination of superimposed tree-shaped networks and porous system, where the main geometrical features of the dendritic fluid networks and the permeability of the porous medium, are defined from the constructal viewpoint. With this model, we are able to emulate physiological scenarios and to predict changes in blood pressure and flow rates throughout the hepatic vasculature due to resection or thrombosis in certain portions of the organ, simulated as deliberate blockages in the blood supply to these sections. This work sheds light on the critical impact of the vascular network on mechanics-related processes occurring in hepatic diseases, healing and regeneration that involve blood flow redistribution and are at the core of liver resilience.

Optimization of Pipe Network Simulation Algorithm for Tree-Shaped Water Injection System in Large-Scale Oilfield

As intelligence technology develops, there is a higher requirement for computing speed and accuracy of water injection system simulation. In this paper, aiming at the tree-shaped water injection pipe network system of large-scale oilfields, based on the energy equation for calculating the pressure drop [Formula: see text] of pipe section, a mathematical model of the pipeline unit and the node unit is established, and finally, a mathematical model of pipe network for the entire water injection system is established; then, the improved iterative algorithm is used to solve the simulation model of water injection system. In this way, we determine the boundary calculation conditions, take the water injection station as reference node, and use the maximum pressure of water injection well as the initial value of the reference node for calculation, which reduces the number of iterations in model calculation; by comparing the simulation results of different iteration steps, 0.01 is selected as the iteration step size due to its higher calculation accuracy; and the calculation process has also been optimized. The process of solving the characteristic matrix [Formula: see text] is combined with the process of calculating the pressure drop [Formula: see text] of pipe section, and placed outside the algorithm loop, thereby shortening the calculation time of a single cycle and reducing the calculation amount of the algorithm. The application cases show that the proposed optimization algorithm for water injection system pipe network simulation can be used as an effective method to improve the solution speed and calculation accuracy of the simulation algorithm of tree-shaped water injection system in large-scale oilfields.

Simulation of imbibition in porous media with a tree-shaped fracture following the level-set method

Imbibition is an important mechanism for enhancing oil recovery in low-permeability reservoirs, such as shale and tight sandstone, and a tree-shaped network has been successfully used to characterize fracturing fracture. Therefore, understanding the imbibition mechanism in porous media with a tree-shaped fracture (TFPM) is important for developing low-permeability reservoirs. In this study, a simulation model for imbibition in TFPM was established based on the level-set method, and the model was verified by comparing it with an analytical solution. The influences of the fracture width, bifurcation angle, tortuosity, and water flow rate on imbibition in TFPM were then discussed. Based on the results, the following points have been established: (1) During the early stage, the imbibition in TFPM included countercurrent and a combined imbibition, and only countercurrent imbibition occurred during the later stage. (2) At a constant fracture width ratio, increasing the primary fracture width could reduce the residual oil in the TFPM, thereby improving the oil recovery factor. (3) At a fracture bifurcation angle ranging from 0° to 45°, the oil recovery factor increased as the bifurcation angle increased. (4) At a fracture tortuosity of 1.0 to 1.24, changes in tortuosity had little effect on the oil recovery factor during the early stage of imbibition, while it significantly affected the distribution of the residual oil. (5) At a water flow rate of 5 mm/s, the simulated oil recovery factor in the TFPM was highest. This investigation can provide a reference for the development of low-permeability reservoirs.

Rapid fabrication of gelatin-based scaffolds with prevascularized channels for organ regeneration

One of the biggest hindrances in tissue engineering in recent decades has been the complexity of the prevascularized channels of the engineered scaffold, which was still lower than that of human tissues. Another relative difficulty was the lack of precision molding capability, which restricted the clinical applications of the huge engineered scaffold. In this study, a promising approach was proposed to prepare hydrogel scaffold with prevascularized channels by liquid bath printing, in which chitosan/β-sodium glycerophosphate served as the ink hydrogel, and gelation/nanoscale bacterial cellulose acted as the supporting hydrogel. Here, the ink hydrogel was printed by a versatile nozzle and embedded in the supporting hydrogel. The ink hydrogel transformed into liquid effluent at low temperature after the cross-linking of gelatin by microbial transglutaminase (mTG). No residual template was seen on the channel surface after template removal. This preparation had a high degree of freedom in the geometry of the channel, which was demonstrated by making various prevascularized channels including circular, branched, and tree-shaped networks. The molding accuracy of the channel was assessed by studying the roundness of the cross section of the molded hollow channel, and the effect of the mechanical properties by adding bacterial cellulose to the supporting hydrogel was analyzed. Human umbilical vein endothelial cells were injected into the aforementioned channels which formed a confluent and homogeneous distribution on the surface of the channels. Altogether, these results showed that this approach can construct hydrogel scaffolds with complex and accurate molding prevascularized channels, and hs great potential to resolve the urgent vascularization issue of bulk tissue-engineering scaffold.

Networks of geometrically exact beams: Well-posedness and stabilization

&lt;p style='text-indent:20px;'&gt;In this work, we are interested in tree-shaped networks of freely vibrating beams which are geometrically exact (GEB) – in the sense that large motions (deflections, rotations) are accounted for in addition to shearing – and linked by rigid joints. For the intrinsic GEB formulation, namely that in terms of velocities and internal forces/moments, we derive transmission conditions and show that the network is locally in time well-posed in the classical sense. Applying velocity feedback controls at the external nodes of a star-shaped network, we show by means of a quadratic Lyapunov functional and the theory developed by Bastin &amp;amp; Coron in [&lt;xref ref-type="bibr" rid="b2"&gt;2&lt;/xref&gt;] that the zero steady state of this network is exponentially stable for the &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ H^1 $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; and &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ H^2 $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; norms. The major obstacles to overcome in the intrinsic formulation of the GEB network, are that the governing equations are semilinar, containing a quadratic nonlinearity, and that linear lower order terms cannot be neglected.&lt;/p&gt;