Arbitrary Number Of Nodes Research Articles

Geom-DeepONet: A point-cloud-based deep operator network for field predictions on 3D parameterized geometries

Modern digital engineering design process commonly involves expensive repeated simulations on varying three-dimensional (3D) geometries. The efficient prediction capability of neural networks (NNs) makes them a suitable surrogate to provide design insights. Nevertheless, few available NNs can handle solution prediction on varying 3D shapes. We present a novel deep operator network (DeepONet) variant called Geom-DeepONet, which encodes parameterized 3D geometries and predicts full-field solutions on an arbitrary number of nodes. To the best of the authors’ knowledge, this is the first attempt in the literature and is our primary novelty. In addition to expressing shapes using mesh coordinates, the signed distance function for each node is evaluated and used to augment the inputs to the trunk network of the Geom-DeepONet, thereby capturing both explicit and implicit representations of the 3D shapes. The powerful geometric encoding capability of a sinusoidal representation network (SIREN) is also exploited by replacing the classical feedforward neural networks in the trunk with SIREN. Additional data fusion between the branch and trunk networks is introduced by an element-wise product. A numerical benchmark was conducted to compare Geom-DeepONet to PointNet and vanilla DeepONet, where results show that our architecture trains fast with a small memory footprint and yields the most accurate results among the three. Results show a much lower generalization error of our architecture on unseen dissimilar designs than vanilla DeepONet. Training the model on 2500 cuboid designs is done within 2 h on a single A100 GPU while generating the training dataset through finite element simulations took about 27 h. Once trained, the model can predict vector fields and a single prediction can be over 105 times faster than its corresponding implicit finite element simulation if the mesh is large. The ability of the proposed model to perform efficient and accurate field predictions on variable 3D geometries, especially those discretized by different nodes and elements, makes it a valuable tool for preliminary performance evaluation and design optimizations and is the most significant contribution of the current work.

ATWin: An Improved and Detailed Startup Model of TTP/C

TTP/C (Time-Triggered Protocol Class C) is a mainstream communication protocol commonly utilized in cyber–physical systems within the aerospace and automotive industry. Unfortunately, when it comes to the startup model, there are three issues in the standard of TTP/C (namely AS6003). Firstly, AS6003 only mentions a high-level specification, which leads to a gap between the standard and its implementation. Secondly, the standard startup model in AS6003 aggressively handles the multi-clique problem by dropping the first valid frame unconditionally without a contention-detecting mechanism, resulting in additional time consumption in some types of contention scenarios. At last, there is lack of the formal verification for the validity of the standard startup model with an arbitrary number of nodes and the formal derivation of its upper bound of startup time. To address these limitations, we propose a detailed and improved startup model named ATWin based on AS6003. It not only bridges the gap between the top-level standard and its implementation by supplementing the undefined details, but it also enhances the efficiency of the startup time by adding a contention-detecting strategy to the standard startup model. The ATWin model is developed as an open-source implementation for TTP/C’s startup. We also formally demonstrate the validity of ATWin and deduce its upper bound of startup time with an arbitrary number of nodes in this paper.

On Transient Analysis of Delta _N-Markov Chains

Consider a cyber-physical system which has the purpose of maintaining the security of some physical asset. A particularly relevant scenario is one in which the system must perform its functions while at the same time enduring malicious attacks for an extended amount of time without energy renewal. We will study a theoretical model analogous to this cyber-physical system with an arbitrary number of nodes. The nodes in this system are able to communicate with one another and have the task of maintaining the security of the system. Initially all nodes comprising this system are in working order, however, due to attacks they can eventually become corrupted and then work against the security of the system. Of particular interest is the calculation of a number of metrics related to reliability of the system including the reliability function and the mean-time to failure. A particular case of this model has been examined by many researchers in the past, mostly using numerical methods. The contribution of this paper is the presentation of explicit expressions for the transient-state transition probabilities, reliability function, and the mean-time to failure along with rigorous proofs for the validity of these expressions. A result such as this is stronger than previous results via numerical methods and is an extension of previous analytical results where additional constraints on the model were imposed.

FLCD: A Flexible Low Complexity Design of Coded Distributed Computing

We propose a flexible low complexity design (FLCD) of coded distributed computing (CDC) with empirical evaluation on Amazon Elastic Compute Cloud (Amazon EC2). CDC can expedite MapReduce like computation by trading increased map computations to reduce communication load and shuffle time. A main novelty of FLCD is to utilize the design freedom in defining map and reduce functions to develop asymptotic homogeneous systems to support varying intermediate values (IV) sizes under a general MapReduce framework. Compared to existing designs with constant IV sizes, FLCD offers greater flexibility in adapting to network parameters and significantly reduces the implementation complexity by requiring fewer input files and shuffle groups. The FLCD scheme is the first proposed low-complexity CDC design that can operate on a network with an arbitrary number of nodes and computation load. We perform empirical evaluations of the FLCD by executing the TeraSort algorithm on an Amazon EC2 cluster. This is the first time that theoretical predictions of the CDC shuffle time are validated by empirical evaluations. The evaluations demonstrate a 2.0 to 4.24 speedup compared to conventional uncoded MapReduce, a 12% to 52% reduction in total time, and a wider range of operating network parameters compared to existing CDC schemes.

Structural characterization of oscillations in brain networks with rate dynamics

Among the versatile forms of dynamical patterns of activity exhibited by the brain, oscillations are one of the most salient and extensively studied, yet are still far from being well understood. In this paper, we provide various structural characterizations of the existence of oscillatory behavior in neural networks using a classical neural mass model of mesoscale brain activity called linear-threshold dynamics. Exploiting the switched-affine nature of this dynamics, we obtain various necessary and/or sufficient conditions on the network structure and its external input for the existence of oscillations in (i) two-dimensional excitatory–inhibitory networks (E-I pairs), (ii) networks with one inhibitory but arbitrary number of excitatory nodes, (iii) purely inhibitory networks with an arbitrary number of nodes, and (iv) networks of E-I pairs. Throughout our treatment, and given the arbitrary dimensionality of the considered dynamics, we rely on the lack of stable equilibria as a system-based proxy for the existence of oscillations, and provide extensive numerical results to support its tight relationship with the more standard, signal-based definition of oscillations in computational neuroscience.

Accurate thermomechanical analysis of sandwich beams with nonhomogeneous core by quadrature element method

Although theoretical analysis of sandwich beam and panel with homogeneous face sheets and functionally graded (FG) core is available, however, accurate modeling and predicting the through-thickness distribution of the shear stress (strain) is still a challenging task. In this paper, an accurate thermomechanical bending analysis of sandwich beams is presented. Elasticity theory is directly employed for the entire sandwich panel to capture the through-thickness distribution of the shear stress (strain) accurately. Explicit formulation of quadrature element method (QEM) with an arbitrary number of nodes and nodes of any type is developed to ease the programming and convergence study. The influence of power-law index, porosity and temperature changes on the deflection, through-thickness distributions of stresses and shear strain is studied. The results may be useful for developing new panel theories and numerical methods.

Higher-order motif analysis in hypergraphs

A deluge of new data on real-world networks suggests that interactions among system units are not limited to pairs, but often involve a higher number of nodes. To properly encode higher-order interactions, richer mathematical frameworks such as hypergraphs are needed, where hyperedges describe interactions among an arbitrary number of nodes. Here we systematically investigate higher-order motifs, defined as small connected subgraphs in which vertices may be linked by interactions of any order, and propose an efficient algorithm to extract complete higher-order motif profiles from empirical data. We identify different families of hypergraphs, characterized by distinct higher-order connectivity patterns at the local scale. We also propose a set of measures to study the nested structure of hyperedges and provide evidences of structural reinforcement, a mechanism that associates higher strengths of higher-order interactions for the nodes that interact more at the pairwise level. Our work highlights the informative power of higher-order motifs, providing a principled way to extract higher-order fingerprints in hypergraphs at the network microscale.

Analysis of an optimal policy in dynamic bipartite matching models

A dynamic bipartite matching model is given by a bipartite matching graph which determines the possible matchings between the various types of supply and demand items. Both supply and demand items arrive to the system according to a stochastic process. Matched pairs leave the system and the others wait in the queues, which induces a holding cost. We model this problem as a Markov Decision Process and study the discounted cost and the average cost problem. We assume that the cost function is linear on the queue sizes. We show that for the N-shaped matching graph, an optimal matching control prioritizes the matchings in the pendant edges and is of threshold type for the diagonal edge. In addition, for the average cost problem, we compute the optimal threshold value. We then show how the obtained results can be used to characterize the structure of an optimal matching control for a quasi-complete graph with an arbitrary number of nodes. For arbitrary bipartite graphs, we show that, when the cost of the pendant edges is larger than in the neighbors, an optimal matching policy prioritizes the items in the pendant edges. We also study the W-shaped matching graph and, when the cost of the pendant edges is larger than the cost of the middle edge, we conjecture that an optimal matching policy is also of threshold type with priority to the pendant edges; however, when the cost of the middle edge is larger, we present simulations that show that it is not optimal to prioritize items in the pendant edges.

A rotation-free quadrature element formulation for free vibration analysis of thin sectorial plates with arbitrary boundary supports

Due to corner stress singularities, free vibration analysis of thin sectorial plates with arbitrary boundary supports including a free vertex is a rather challenging problem. In this paper, a novel rotation-free quadrature element formulation based on Kirchhoff plate theory is presented to solve the problem. Different from all existing quadrature thin plate element formulations, rotational degrees of freedom are not used. Instead, a boundary point is modeled by two nodes separated by a very small distance and thus the C1 continuity is easily enforced. Explicit formulations with arbitrary number of nodes and nodes of any type are worked out to ease the p-refinement. Numerical results demonstrate that the proposed formulation is simple, straightforward and has excellent performance for solving thin sectorial plate with arbitrary combinations of boundary supports. Some tabulated data are believed new which may serve as a reference.

The aging effect in evolving scientific citation networks

The study of citation networks is of interest to the scientific community. However, the underlying mechanism driving individual citation behavior remains imperfectly understood, despite the recent proliferation of quantitative research methods. Traditional network models normally use graph theory to consider articles as nodes and citations as pairwise relationships between them. In this paper, we propose an alternative evolutionary model based on hypergraph theory in which one hyperedge can have an arbitrary number of nodes, combined with an aging effect to reflect the temporal dynamics of scientific citation behavior. Both theoretical approximate solution and simulation analysis of the model are developed and validated using two benchmark datasets from different disciplines, i.e. publications of the American Physical Society (APS) and the Digital Bibliography & Library Project (DBLP). Further analysis indicates that the attraction of early publications will decay exponentially. Moreover, the experimental results show that the aging effect indeed has a significant influence on the description of collective citation patterns. Shedding light on the complex dynamics driving these mechanisms facilitates the understanding of the laws governing scientific evolution and the quantitative evaluation of scientific outputs.

Adaptive analysis using scaled boundary finite element method in 3D

In this paper, an adaptive refinement technique using the scaled boundary finite element method (SBFEM) is proposed. The salient feature of this technique is that it is not required to regenerate the mesh for the whole model during the iterations. To this end, a local mesh refinement strategy is implemented based on a polytree algorithm in three dimensions, which can be applied to polyhedral elements with arbitrary number of nodes, edges and faces. These elements constructed by the SBFEM can be used in analysis with their boundaries discretized only, which reduce the difficulty to connect elements with different sizes. An explicit residual based error indicator is developed using the discontinuity of the stress field to guide the adaptive mesh refinement. The accuracy and efficiency of the proposed method are demonstrated using five numerical examples, including complex geometry and stress singularity.

Generation and application of river network analogues for use in ecology and evolution.

Several key processes in freshwater ecology are governed by the connectivity inherent to dendritic river networks. These have extensively been analyzed from a geomorphological and hydrological viewpoint, yet structures classically used in ecological modeling have been poorly representative of the structure of real river basins, often failing to capture well‐known scaling features of natural rivers. Pioneering work identified optimal channel networks (OCNs) as spanning trees reproducing all scaling features characteristic of natural stream networks worldwide. While OCNs have been used to create landscapes for studies on metapopulations, biodiversity, and epidemiology, their generation has not been generally accessible.Given the increasing interest in dendritic riverine networks by ecologists and evolutionary biologists, we here present a method to generate OCNs and, to facilitate its application, we provide the R‐package OCNet. Owing to the stochastic process generating OCNs, multiple network replicas spanning the same surface can be built; this allows performing computational experiments whose results are irrespective of the particular shape of a single river network. The OCN construct also enables the generation of elevational gradients derived from the optimal network configuration, which can constitute three‐dimensional landscapes for spatial studies in both terrestrial and freshwater realms. Moreover, the package provides functions that aggregate OCNs into an arbitrary number of nodes, calculate several descriptors of river networks, and draw relevant network features.We describe the main functionalities of the package and its integration with other R‐packages commonly used in spatial ecology. Moreover, we exemplify the generation of OCNs and discuss an application to a metapopulation model for an invasive riverine species.In conclusion, OCNet provides a powerful tool to generate realistic river network analogues for various applications. It thereby allows the design of spatially realistic studies in increasingly impacted ecosystems and enhances our knowledge on spatial processes in freshwater ecology in general.

A Non-Matching Nodes Interface Model with Radial Interpolation Function for Simulating 2D Soil–Structure Interface Behaviors

In this paper, the meshless method is extended to simulate the interaction between soil and structure through 2D finite element (FE) model. The background mesh line shared by each surface of interface is introduced for Gauss points’ generation and interpolation. Thus, instead of a series of interface elements, the whole soil–structure interface can be presented by an arbitrary number of nodes with flexible distribution on the contacting surfaces. The radial basis function (RBF) is introduced as the interpolation function to obtain the displacement of each Gauss points by surrounding the nodes along the surfaces. The research of shape parameters and the rate of convergence are also conducted. With non-matching nodes interface, the soil and structure zone can be modeled independently and connected with the proposed non-matching nodes interface flexibly and effectively. Furthermore, the proposed method can easily enable cross-scale modeling, which has high utility for enabling refined analysis without excessively increasing the computational costs. In addition, under the standard finite element framework, nonlinear constitutive models can be employed to capture the complex behaviors at the interface. Several simulations are presented to demonstrate the high flexibility, extensive applicability and precision of the proposed non-matching nodes interface based on meshless method.

Statistical Characteristics of Stationary Flow of Substance in a Network Channel Containing Arbitrary Number of Arms.

We study flow of substance in a channel of network which consists of nodes of network and edges which connect these nodes and form ways for motion of substance. The channel can have arbitrary number of arms and each arm can contain arbitrary number of nodes. The flow of substance is modeled by a system of ordinary differential equations. We discuss first a model for a channel which arms contain infinite number of nodes each. For stationary regime of motion of substance in such a channel we obtain probability distributions connected to distribution of substance in any of channel’s arms and in entire channel. Obtained distributions are not discussed by other authors and can be connected to Waring distribution. Next, we discuss a model for flow of substance in a channel which arms contain finite number of nodes each. We obtain probability distributions connected to distribution of substance in the nodes of the channel for stationary regime of flow of substance. These distributions are also new and we calculate corresponding information measure and Shannon information measure for studied kind of flow of substance.

A general integration scheme in quadrature element method

For the first time, a general integration scheme is proposed which can be employed in the development of quadrature elements with nodes of any type. With the proposed scheme, explicit formulations of quadrature elements with an arbitrary number of nodes can be derived indirectly via the differential quadrature law. Similar to the conventional finite element method, either reduced or full integration can be adopted in the explicit formulation by using the proposed scheme.

Multiscale analysis of heterogeneous materials in boundary representation

AbstractThis paper deals with a numerical method for modeling heterogeneous materials with nonlinear behavior. Many novel high‐performance materials consist of different components. In the frame of nonlinear behavior the resulting macroscopic material properties cannot be determined without great experimental effort. In order to simulate the nonlinear material behavior, a nested finite element method (FE2) is used. An accompanying homogenization is performed for each load step. The material behavior is determined from the represented volume element (RVE) on the heterogeneous micro structure. The present approach is dealing with a discretization method of the heterogeneous structure. It based on the geometrical data of the interface boundary of the different constituents. A quad‐tree algorithm, in combination with a trimming algorithm is used for the mesh generation. Based on the geometrical data it yields an initial mesh for the analysis. Within the algorithm a staircase approximation of voids or inclusions is circumvented. However, the resulting mesh yields polygonal elements with an arbitrary number of nodes on the element boundary. To this end a novel polygonal element formulation is provided. It is based on the scaled boundary finite element method (SBFEM). The basic idea is to scale the boundary representation in relation to a scaling center. In contrast to SBFEM the present method makes us of an approximation of the displacement response in scaling direction. This enables the analysis of geometrical and material‐related nonlinear problems in solid mechanics. The interpolation at the boundary in circumferential direction is independent of the interpolation in scaling direction. This allows for novel refinement strategies, where e.g. p‐refinement is only applied for the interior element domain. The internal degrees of freedom are eliminated by static condensation. It leads to an element formulation with an arbitrary number of nodes at the element boundary. Thus, the present element is perfectly suited for a quad‐tree meshing algorithm of the RVE. Its hierarchical, tree‐like data structure makes it very useful for adaptive mesh refinements of complex geometries and regions with localized gradients. The classical hanging‐nodes problem for standard elements is omitted by the present element formulation. Some numerical examples show the capability of the formulation with respect to the numerical homogenization of heterogeneous materials.

Parallel and Serial Graph Coloring Implementations with Tabu Search Method

One of the well-known property of graph is graph coloring. Any two vertices of a graph are different colors such that they are adjacent to each other. The objective of this paper is to analyse the behavioral performance of Tabu Search method through serial and parallel implementations. We explore both parallel and serial Tabu search algorithm for graph coloring with arbitrary number of nodes.

A computational framework for brittle crack-propagation based on efficient virtual element method

An efficient low order virtual element method (VEM) for crack-propagation in elastic solids at small strains is outlined within this work. The recently developed VEM is a competitive discretization scheme for meshes with highly irregular shaped elements and arbitrary number of nodes. The formulation in this contribution is based on minimization of an energy expression with stabilization techniques for brittle fracture in 2D problems. Novel aspect here is the development of robust cutting techniques through elements for crack propagation in two-dimensional solids using VEM. The performance of the formulation is underlined by means of representative examples.

An efficient technique for simultaneous local and overall buckling analysis of stiffened panels

The overall buckling and local buckling of stiffened panels are two possible failure modes and thus should be concerned by engineers in the preliminary design of lightweight structures. In this paper, an efficient technique is proposed to solve the local and overall buckling problem of stiffened panels simultaneously. A weak form quadrature plate element with stiffeners located anywhere in the plates other than along the nodal lines of the plate element is formulated. Explicit formulations with an arbitrary number of nodes are given. Improvement of solution accuracy can be easily done by increasing the number of element nodes if necessary. A convergence study is performed. Several numerical examples are given. Results are compared with either existing analytic solutions or finite element data for verification. It is shown that high accuracy can be achieved with a small number of nodes. In addition, the proposed method can allow a quick analysis of simultaneous overall and local buckling behavior of stiffened panels and thus may be suitable for optimization routines in preliminary design of stiffened panels.

Establishing quantum steerability on cavity arrays coupled by optical fibers with open boundary conditions

We study quantum steerability on one-dimensional cavity array systems with open boundary conditions, where each cavity is doped with a two-level atom and coupled with its neighbor nodes by optical fibers. In the far off-resonant condition, we obtain explicit expressions for the dynamical evolution of the array system with arbitrary number of nodes. By investigating the steerable weight for two-node subsystems, we show that remote quantum steerability can be established through both single-array and double independent arrays. Moreover, comparisons between quantum steerability and quantum entanglement in this model are also examined.