Topology Change and the Propagation of Massless Fields
英文论文写作中一些可能用到的词汇
英⽂论⽂写作中⼀些可能⽤到的词汇英⽂论⽂写作过程中总是被⾃⼰可怜的词汇量击败, 所以我打算在这⾥记录⼀些在阅读论⽂过程中见到的⼀些⾃⼰不曾见过的词句或⽤法。
这些词句查词典都很容易查到，但是只有带⼊论⽂原⽂中才能体会内涵。
毕竟原⽂和译⽂中间总是存在⼀条看不见的思想鸿沟。
形容词1. vanilla: adj. 普通的, 寻常的, 毫⽆特⾊的. ordinary; not special in any way.2. crucial: adj. ⾄关重要的, 关键性的.3. parsimonious：adj. 悭吝的, 吝啬的, ⼩⽓的.e.g. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity.4. diverse: adj. 不同的, 相异的, 多种多样的, 形形⾊⾊的.5. intriguing: adj. ⾮常有趣的, 引⼈⼊胜的; 神秘的. *intrigue: v. 激起…的兴趣, 引发…的好奇⼼; 秘密策划(加害他⼈), 密谋.e.g. The results of this paper carry several intriguing implications.6. intimate: adj. 亲密的; 密切的. v.透露; (间接)表⽰, 暗⽰.e.g. The above problems are intimately linked to machine learning on graphs.7. akin: adj. 类似的, 同族的, 相似的.e.g. Akin to GNN, in LOCAL a graph plays a double role: ...8. abundant: adj. ⼤量的, 丰盛的, 充裕的.9. prone: adj. 有做(坏事)的倾向; 易于遭受…的; 俯卧的.e.g. It is thus prone to oversmoothing when convolutions are applied repeatedly.10.concrete: adj. 混凝⼟制的; 确实的, 具体的(⽽⾮想象或猜测的); 有形的; 实在的.e.g. ... as a concrete example ...e.g. More concretely, HGCN applies the Euclidean non-linear activation in...11. plausible: adj. 有道理的; 可信的; 巧⾔令⾊的, 花⾔巧语的.e.g. ... this interpretation may be a plausible explanation of the success of the recently introduced methods.12. ubiquitous: adj. 似乎⽆所不在的;⼗分普遍的.e.g. While these higher-order interac- tions are ubiquitous, an evaluation of the basic properties and organizational principles in such systems is missing.13. disparate: adj. 由不同的⼈(或事物)组成的;迥然不同的;⽆法⽐较的.e.g. These seemingly disparate types of data have something in common: ...14. profound: adj. 巨⼤的; 深切的, 深远的; 知识渊博的; 理解深刻的;深邃的, 艰深的; ⽞奥的.e.g. This has profound consequences for network models of relational data — a cornerstone in the interdisciplinary study of complex systems.15. blurry: adj. 模糊不清的.e.g. When applying these estimators to solve (2), the line between the critic and the encoders $g_1, g_2$ can be blurry.16. amenable: adj. 顺从的; 顺服的; 可⽤某种⽅式处理的.e.g. Ou et al. utilize sparse generalized SVD to generate a graph embedding, HOPE, from a similarity matrix amenableto de- composition into two sparse proximity matrices.17. elaborate: adj. 复杂的;详尽的;精⼼制作的 v.详尽阐述;详细描述;详细制订;精⼼制作e.g. Topic Modeling for Graphs also requires elaborate effort, as graphs are relational while documents are indepen- dent samples.18. pivotal: adj. 关键性的；核⼼的e.g. To ensure the stabilities of complex systems is of pivotal significance toward reliable and better service providing.19. eminent: adj. 卓越的，著名的，显赫的;⾮凡的;杰出的e.g. To circumvent those defects, theoretical studies eminently represented by percolation theories appeared.20. indispensable: adj. 不可或缺的;必不可少的 n. 不可缺少的⼈或物e.g. However, little attention is paid to multipartite networks, which are an indispensable part of complex networks.21. post-hoc: adj. 事后的e.g. Post-hoc explainability typically considers the question “Why the GNN predictor made certain prediction?”.22. prevalent: adj. 流⾏的;盛⾏的;普遍存在的e.g. A prevalent solution is building an explainer model to conduct feature attribution23. salient: adj. 最重要的;显著的;突出的. n. 凸⾓;[建]突出部;<军>进攻或防卫阵地的突出部分e.g. It decomposes the prediction into the contributions of the input features, which redistributes the probability of features according to their importance and sample the salient features as an explanatory subgraph.24. rigorous: adj. 严格缜密的;严格的;谨慎的;细致的;彻底的;严厉的e.g. To inspect the OOD effect rigorously, we take a causal look at the evaluation process with a Structural Causal Model.25. substantial: adj. ⼤量的;价值巨⼤的;重⼤的;⼤⽽坚固的;结实的;牢固的. substantially: adv. ⾮常;⼤⼤地;基本上;⼤体上;总的来说26. cogent: adj. 有说服⼒的;令⼈信服的e.g. The explanatory subgraph $G_s$ emphasizes tokens like “weak” and relations like “n’t→funny”, which is cogent according to human knowledge.27. succinct: adj. 简练的;简洁的 succinctly: adv. 简⽽⾔之，简明扼要地28. concrete: adj. 混凝⼟制的;确实的，具体的(⽽⾮想象或猜测的);有形的;实在的 concretely: adv. 具体地;具体;具体的;有形地29. predominant：adj. 主要的;主导的;显著的;明显的;盛⾏的;占优势的动词1. mitigate: v. 减轻, 缓和. (反 enforce)e.g. In this work, we focus on mitigating this problem for a certain class of symbolic data.2. corroborate: v. [VN] [often passive] (formal) 证实, 确证.e.g. This is corroborated by our experiments on real-world graph.3. endeavor: n./v. 努⼒, 尽⼒, 企图, 试图.e.g. It encourages us to continue the endeavor in applying principles mathematics and theory in successful deployment of deep learning.4. augment: v. 增加, 提⾼, 扩⼤. n. 增加, 补充物.e.g. We also augment the graph with geographic information (longitude, latitude and altitude), and GDP of the country where the airport belongs to.5. constitute: v. (被认为或看做)是, 被算作; 组成, 构成; (合法或正式地)成⽴, 设⽴.6. abide: v. 接受, 遵照(规则, 决定, 劝告); 逗留, 停留.e.g. Training a graph classifier entails identifying what constitutes a class, i.e., finding properties shared by graphs in one class but not the other, and then deciding whether new graphs abide to said learned properties.7. entail: v. 牵涉; 需要; 使必要. to involve sth that cannot be avoided.e.g. Due to the recursive definition of the Chebyshev polynomials, the computation of the filter $g_α(\Delta)f$ entails applying the Laplacian $r$ times, resulting cal operator affecting only 1-hop neighbors of a vertex and in $O(rn)$ operations.8. encompass: v. 包含, 包括, 涉及(⼤量事物); 包围, 围绕, 围住.e.g. This model is chosen as it is sufficiently general to encompass several state-of-the-art networks.e.g. The k-cycle detection problem entails determining if G contains a k-cycle.9. reveal: v. 揭⽰, 显⽰, 透露, 显出, 露出, 展⽰.10. bestow: v. 将(…)给予, 授予, 献给.e.g. Aiming to bestow GCNs with theoretical guarantees, one promising research direction is to study graph scattering transforms (GSTs).11. alleviate: v. 减轻, 缓和, 缓解.12. investigate: v. 侦查(某事), 调查(某⼈), 研究, 调查.e.g. The sensitivity of pGST to random and localized noise is also investigated.13. fuse: v. (使)融合, 熔接, 结合; (使)熔化, (使保险丝熔断⽽)停⽌⼯作.e.g. We then fuse the topological embeddings with the initial node features into the initial query representations using a query network$f_q$ implemented as a two-layer feed-forward neural network.14. magnify: v. 放⼤, 扩⼤; 增强; 夸⼤(重要性或严重性); 夸张.e.g. ..., adding more layers also leads to more parameters which magnify the potential of overfitting.15. circumvent: v. 设法回避, 规避; 绕过, 绕⾏.e.g. To circumvent the issue and fulfill both goals simultaneously, we can add a negative term...16. excel: v. 擅长, 善于; 突出; 胜过平时.e.g. Nevertheless, these methods have been repeatedly shown to excel in practice.17. exploit: v. 利⽤(…为⾃⼰谋利); 剥削, 压榨; 运⽤, 利⽤; 发挥.e.g. In time series and high-dimensional modeling, approaches that use next step prediction exploit the local smoothness of the signal.18. regulate: v. (⽤规则条例)约束, 控制, 管理; 调节, 控制(速度、压⼒、温度等).e.g. ... where $b >0$ is a parameter regulating the probability of this event.19. necessitate: v. 使成为必要.e.g. Combinatorial models reproduce many-body interactions, which appear in many systems and necessitate higher-order models that capture information beyond pairwise interactions.20. portray:描绘, 描画, 描写; 将…描写成; 给⼈以某种印象; 表现; 扮演(某⾓⾊).e.g. Considering pairwise interactions, a standard network model would portray the link topology of the underlying system as shown in Fig. 2b.21. warrant: v. 使有必要; 使正当; 使恰当. n. 执⾏令; 授权令; (接受款项、服务等的)凭单, 许可证; (做某事的)正当理由, 依据.e.g. Besides statistical methods that can be used to detect correlations that warrant higher-order models, ... (除了可以⽤来检测⽀持⾼阶模型的相关性的统计⽅法外, ...)22. justify: v. 证明…正确(或正当、有理); 对…作出解释; 为…辩解(或辩护); 调整使全⾏排满; 使每⾏排齐.e.g. ..., they also come with the assumption of transitive, Markovian paths, which is not justified in many real systems.23. hinder:v. 阻碍; 妨碍; 阻挡. (反 foster: v. 促进; 助长; 培养; ⿎励; 代养, 抚育, 照料(他⼈⼦⼥⼀段时间))e.g. The eigenvalues and eigenvectors of these matrix operators capture how the topology of a system influences the efficiency of diffusion and propagation processes, whether it enforces or mitigates the stability of dynamical systems, or if it hinders or fosters collective dynamics.24. instantiate:v. 例⽰；⽤具体例⼦说明.e.g. To learn the representation we instantiate (2) and split each input MNIST image into two parts ...25. favor:v. 赞同;喜爱, 偏爱; 有利于, 便于. n. 喜爱, 宠爱, 好感, 赞同; 偏袒, 偏爱; 善⾏, 恩惠.26. attenuate: v. 使减弱; 使降低效⼒.e.g. It therefore seems that the bounds we consider favor hard-to-invert encoders, which heavily attenuate part of the noise, over well conditioned encoders.27. elucidate:v. 阐明; 解释; 说明.e.g. Secondly, it elucidates the importance of appropriately choosing the negative samples, which is indeed a critical component in deep metric learning based on triplet losses.28. violate: v. 违反, 违犯, 违背(法律、协议等); 侵犯(隐私等); 使⼈不得安宁; 搅扰; 亵渎, 污损(神圣之地).e.g. Negative samples are obtained by patches from different images as well as patches from the same image, violating the independence assumption.29. compel:v. 强迫, 迫使; 使必须; 引起(反应).30. gauge: v. 判定, 判断(尤指⼈的感情或态度); (⽤仪器)测量, 估计, 估算. n. 测量仪器(或仪表);计量器;宽度;厚度;(枪管的)⼝径e.g. Yet this hyperparameter-tuned approach raises a cubic worst-case space complexity and compels the user to traverse several feature sets and gauge the one that attains the best performance in the downstream task.31. depict: v. 描绘, 描画; 描写, 描述; 刻画.e.g. As they depict different aspects of a node, it would take elaborate designs of graph convolutions such that each set of features would act as a complement to the other.32. sketch: n. 素描;速写;草图;幽默短剧;⼩品;简报;概述 v. 画素描;画速写;概述;简述e.g. Next we sketch how to apply these insights to learning topic models.33. underscore：v. 在…下⾯划线;强调;着重说明 n.下划线e.g. Moreover, the walk-topic distributions generated by Graph Anchor LDA are indeed sharper than those by ordinary LDA, underscoring the need for selecting anchors.34. disclose: v. 揭露;透露;泄露;使显露;使暴露e.g. Another drawback lies in their unexplainable nature, i.e., they cannot disclose the sciences beneath network dynamics.35. coincide: v. 同时发⽣;相同;相符;极为类似;相接;相交;同位;位置重合;重叠e.g. The simulation results coincide quite well with the theoretical results.36. inspect: v. 检查;查看;审视;视察 to look closely at sth/sb, especially to check that everything is as it should be名词1. capacity: n. 容量, 容积, 容纳能⼒; 领悟(或理解、办事)能⼒; 职位, 职责.e.g. This paper studies theoretically the computational capacity limits of graph neural networks (GNN) falling within the message-passing framework of Gilmer et al. (2017).2. implication: n. 可能的影响(或作⽤、结果); 含意, 暗指; (被)牵连, 牵涉.e.g. Section 4 analyses the implications of restricting the depth $d$ and width $w$ of GNN that do not use a readout function.3. trade-off:(在需要⽽⼜相互对⽴的两者间的)权衡, 协调.e.g. This reveals a direct trade-off between the depth and width of a graph neural network.4. cornerstone:n. 基⽯; 最重要部分; 基础; 柱⽯.5. umbrella: n. 伞; 综合体; 总体, 整体; 保护, 庇护(体系).e.g. Community detection is an umbrella term for a large number of algorithms that group nodes into distinct modules to simplify and highlight essential structures in the network topology.6. folklore:n. 民间传统, 民俗; 民间传说.e.g. It is folklore knowledge that maximizing MI does not necessarily lead to useful representations.7. impediment:n. 妨碍,阻碍,障碍; ⼝吃.e.g. While a recent approach overcomes this impediment, it results in poor quality in prediction tasks due to its linear nature.8. obstacle:n. 障碍;阻碍; 绊脚⽯; 障碍物; 障碍栅栏.e.g. However, several major obstacles stand in our path towards leveraging topic modeling of structural patterns to enhance GCNs.9. vicinity:n. 周围地区; 邻近地区; 附近.e.g. The traits with which they engage are those that are performed in their vicinity.10. demerit: n. 过失,缺点,短处; (学校给学⽣记的)过失分e.g. However, their principal demerit is that their implementations are time-consuming when the studied network is large in size. Another介/副/连词1. notwithstanding:prep. 虽然;尽管 adv. 尽管如此.e.g. Notwithstanding this fundamental problem, the negative sampling strategy is often treated as a design choice.2. albeit: conj. 尽管;虽然e.g. Such methods rely on an implicit, albeit rigid, notion of node neighborhood; yet this one-size-fits-all approach cannot grapple with the diversity of real-world networks and applications.3. Hitherto:adv. 迄今;直到某时e.g. Hitherto, tremendous endeavors have been made by researchers to gauge the robustness of complex networks in face of perturbations.短语1.in a nutshell: 概括地说, 简⾔之, ⼀⾔以蔽之.e.g. In a nutshell, GNN are shown to be universal if four strong conditions are met: ...2. counter-intuitively: 反直觉地.3. on-the-fly:动态的(地), 运⾏中的(地).4. shed light on/into:揭⽰, 揭露; 阐明; 解释; 将…弄明⽩; 照亮.e.g. These contemporary works shed light into the stability and generalization capabilities of GCNs.e.g. Discovering roles and communities in networks can shed light on numerous graph mining tasks such as ...5. boil down to: 重点是; 将…归结为.e.g. These aforementioned works usually boil down to a general classification task, where the model is learnt on a training set and selected by checking a validation set.6. for the sake of:为了.e.g. The local structures anchored around each node as well as the attributes of nodes therein are jointly encoded with graph convolution for the sake of high-level feature extraction.7. dates back to:追溯到.e.g. The usual problem setup dates back at least to Becker and Hinton (1992).8. carry out:实施, 执⾏, 实⾏.e.g. We carry out extensive ablation studies and sensi- tivity analysis to show the effectiveness of the proposed functional time encoding and TGAT-layer.9. lay beyond the reach of:...能⼒达不到e.g. They provide us with information on higher-order dependencies between the components of a system, which lay beyond the reach of models that exclusively capture pairwise links.10. account for: ( 数量或⽐例上)占; 导致, 解释(某种事实或情况); 解释, 说明(某事); (某⼈)对(⾏动、政策等)负有责任; 将(钱款)列⼊(预算).e.g. Multilayer models account for the fact that many real complex systems exhibit multiple types of interactions.11. along with: 除某物以外; 随同…⼀起, 跟…⼀起.e.g. Along with giving us the ability to reason about topological features including community structures or node centralities, network science enables us to understand how the topology of a system influences dynamical processes, and thus its function.12. dates back to:可追溯到.e.g. The usual problem setup dates back at least to Becker and Hinton (1992) and can conceptually be described as follows: ...13. to this end:为此⽬的;为此计;为了达到这个⽬标.e.g. To this end, we consider a simple setup of learning a representation of the top half of MNIST handwritten digit images.14. Unless stated otherwise:除⾮另有说明.e.g. Unless stated otherwise, we use a bilinear critic $f(x, y) = x^TWy$, set the batch size to $128$ and the learning rate to $10^{−4}$.15. As a reference point:作为参照.e.g. As a reference point, the linear classification accuracy from pixels drops to about 84% due to the added noise.16. through the lens of:透过镜头. (以...视⾓)e.g. There are (at least) two immediate benefits of viewing recent representation learning methods based on MI estimators through the lens of metric learning.17. in accordance with:符合；依照；和…⼀致.e.g. The metric learning view seems hence in better accordance with the observations from Section 3.2 than the MI view.It can be shown that the anchors selected by our Graph Anchor LDA are not only indicative of “topics” but are also in accordance with the actual graph structures.18. be akin to:近似, 类似, 类似于.e.g. Thus, our learning model is akin to complex contagion dynamics.19. to name a few:仅举⼏例;举⼏个来说.e.g. Multitasking, multidisciplinary work and multi-authored works, to name a few, are ingrained in the fabric of science culture and certainly multi-multi is expected in order to succeed and move up the scientific ranks.20. a handful of:⼀把;⼀⼩撮;少数e.g. A handful of empirical work has investigated the robustness of complex networks at the community level.21. wreak havoc: 破坏;肆虐;严重破坏;造成破坏;浩劫e.g. Failures on one network could elicit failures on its coupled networks, i.e., networks with which the focal network interacts, and eventually those failures would wreak havoc on the entire network.22. apart from: 除了e.g. We further posit that apart from node $a$ node $b$ has $k$ neighboring nodes.。
水下滑翔机组网的动态MAC机制
水下滑翔机组网的动态MAC机制金志刚;吴婷;苏毅珊;羊秋玲【摘要】水下滑翔机的运动导致滑翔机位置和相对距离的变化,引起了滑翔机间的信号传输时间改变,进而导致水下滑翔机间通信可靠性的下降.传统水下媒体接入控制(MAC)协议面向静态拓扑网络,不适用于动态变化的网络拓扑.该文提出一种水下滑翔机组网的动态MAC机制.新机制利用水下滑翔机运动模型进行位置预测,根据预测结果和相邻滑翔机间的位置共享动态计算时隙长度,并进行分配和预约收发,水下滑翔机在收发过程中以团队协作方式避免冲突.实验结果表明,该机制的数据包投递率与运动预测MAC(P-MAC)和预约MAC(R-MAC)协议相比分别提高了12％和25％,更适用于由水下滑翔机组成的动态网络.%The movement of the underwater gliders leads to the change in the position and relative distance among the gliders, which causes a change in the propagation delay of packets between gliders, and then it leads to a decrease in the reliability of communication between underwater gliders. The traditional underwater Media Access Control (MAC) protocols are for static topology networks and do not apply to dynamically varying network topology. Thus, a new MAC mechanism for the underwater glider networks is proposed. It predicts location based on underwater glider motion model. It calculates time slots dynamically according to the predicted results and the shared position information of underwater gliders. Then, it allocates time slots and reserves to the send and the receive. Underwater gliders avoid collisions with teamwork in the process of sending and receiving. Simulation results show that in this mechanism, the packet received rate increases by 12％and 25％ comparing to the Prediction based MAC (P-MAC) protocol and Reservation based MAC (R-MAC) protocol, respectively. The result indicates that the new mechanism is more suitable for the dynamic network composed of underwater gliders.【期刊名称】《电子与信息学报》【年(卷),期】2018(040)005【总页数】7页(P1108-1114)【关键词】水下滑翔机组网;动态媒体接入控制机制;团队协作【作者】金志刚;吴婷;苏毅珊;羊秋玲【作者单位】天津大学电气自动化与信息工程学院天津 300072;天津大学电气自动化与信息工程学院天津 300072;天津大学电气自动化与信息工程学院天津300072;海南大学信息学院海口 570208【正文语种】中文【中图分类】TP393水声无线传感网络(Underwater Acoustic Wireless Sensor Networks, UAWSNs)[1]在海洋资源勘探、海洋环境监控等方面中发挥重要作用。
计算机网络与互联网(英语)chap8
Disadvantages
Requires more cable length than a linear topology.
If the hub or concentrator fails, nodes attached are disabled.
The number of connections passing between two locations can exceed the total number of computers being connected
Direct Point to Point Calculating Required Lines
Classification Terminology
Network technologies classified into three broad categories
Local Area Network (LAN) Metropolitan Area Network (MAN) Wide Area Network (WAN)
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Simulating Fully 3D Hydraulic Fracturing
Simulating Fully 3D Hydraulic FracturingB.J. Carter†, J. Desroches‡, A.R. Ingraffea†, and P.A. Wawrzynek††Cornell University, Ithaca, NY‡Schlumberger Well Services, Houston, TX1.0 IntroductionHydraulic fracturing, the process of initiation and propagation of a crack by pumping fluid at relatively high flow rates and pressures, is one of several techniques for creating cracks in rock. Fractures in the earth's crust are desired for a variety of reasons, including enhanced oil and gas recovery, re-injection of drilling or other environmentally sensitive wastes, measurement of in situ stresses, geothermal energy recovery, and enhanced well water production. These fractures can range in size from a few meters to hundreds of meters, and their cost is often a significant portion of the total development cost. In locations where the in situ stress field, including the directions, is known and the wellbore is aligned with one of the far-field principal stresses, the hydraulic fracture geometry can be predicted and controlled with reasonable accuracy. For those wellbores that are not aligned with such a direction (deviated wells), the hydraulic fracture geometry is usually more complex and more difficult to model, especially close to the wellbore where the local stress field is significantly different from the far-field stresses. Field data from hydraulic fracturing operations exist primarily in the form of pressure response curves. It is difficult to define the actual hydraulic fracture geometry from this data alone, however. Therefore, numerical simulations are used to evaluate and predict the location, direction and extent of these hydraulic fractures.Simulations range from two to fully three dimensional depending on the degree of complexity of the wellbore and fracture geometries, the capability of the available simulator, and the required accuracy of the predictions. Numerous 2D, pseudo-3D, and planar 3D hydraulic fracturing simulators exist, and these simulators work very well in many cases where the geometry of the fracture is easily defined and constrained to a single plane. However, there are instances where a fully 3D simulator is necessary for more accurate modeling. For example, fractures from deviated wellbores are generally non-planar with arbitrary crack front shapes. Most hydrofracturing simulators simply ignore the near-wellbore effects of deviated wells and assume a planar starting crack that has extended beyond this region. The problem with this approach is that most of the difficulties and failures in hydraulic fracturing of deviated wellbores can be attributed to restricted flow in the near-wellbore region. Restricted flow usually is due to fracture reorientation and interaction with other fractures. Hydraulic fracturing of deviated wells, where the fractures reorient as they propagate, clearly requires fully 3D simulation capabilities and accurate modeling of the near-wellbore geometry.Efficient numerical simulation of fully 3D hydraulic fracturing requires at least two key components. The first is a capability for representing and visualizing the complex wellbore and fracture geometries. The second is a method for solving the highly non-linear coupling between the equations for the fluid flow in the fracture and the deformation and propagation of the fracture. The first component can be partitioned into several sub-components, including geometrical and topological solid modeling tools, routines to model geometry and topology changes for fracture propagation, automated meshing and remeshing capabilities, visualization ofresponse information, and analysis control information (i.e. input for a stress analysis program). The second component consists of a stress analysis procedure, fluid flow simulation capabilities, and a method for coupling the structural response with the fluid flow, including rules for determining hydraulic fracture propagation direction and extent. The authors have developed a simulator that includes all of these components for modeling multiple, non-planar, fully 3D, hydraulic fracture propagation. This simulator treats hydraulic fracturing as a quasi-static process, and the solution consists of a series of “snapshots in time” of the fracture geometry, fluid pressures, and crack opening displacements.A brief history of hydraulic fracturing and the development of hydrofracturing simulators are discussed in the next section. Then the key components of the new simulator are described in some detail, including the software framework for model representation, the coupled elasticity and lubrication theory, the finite element implementation of this theory, and the iterative solution procedure. The simulator has been verified for a radial (penny-shape) and a slot-like (part-through) fracture by comparing results to those from a robust and accurate 2D simulator, Loramec (Desroches and Thiercelin, 1993). Further simulations that compare well with experimental results show the ability of the system to model more realistic hydraulic fracture geometries. This chapter concentrates on the development of the simulator rather than actual simulations, however. Detailed simulations of hydraulic fracturing from cased, perforated, deviated wellbores is possible now, but is computationally intensive and is left as the subject of future publications.2.0 BackgroundThe process of hydraulic fracturing is not new. Nature has produced many such fractures in the earth's crust (see for example Bahat, 1991). The first recorded application of hydraulic fracturing for enhancing oil recovery that the authors are aware of was in 1947 in Kansas (see Howard and Fast, 1970). The "Hydrafrac" concept was formalized first by Clark (1949), although others had recognized previously that "pressure parting" could occur during acid treatment and water injection, a phenomenon considered to be closely related to the "Hydrafrac" concept (Howard and Fast, 1970). The Hugotan field in western Kansas was the site of the first hydraulic fracturing operation, and by the mid-1960's, hydraulic fracturing had become the dominant method of stimulation in this and many other fields (Howard and Fast, 1970).During this early period of hydraulic fracturing, two simple models were proposed to try to predict the shape and size of a hydraulic fracture based on the rock and fluid properties, the pumping parameters, and the in situ stresses (Khristianovic and Zheltov, 1955; Geertsma and de Klerk, 1969; Perkins and Kern, 1961; Nordgren, 1972). The models are known as the KGD and PKN models, and their description can be found in the above references and in many other summaries or texts (eg. Geertsma, 1989; Mendelsohn, 1984a,b). Perkins and Kern (1961) and Geertsma and de Klerk (1969) also derived a model for radial hydraulic fracturing. The radial, KGD, and PKN models are essentially two dimensional plane strain formulations with fluid flow only along the length (or radius) of the fracture. The fracture width and shape are related to the fluid pressure distribution in the fracture; the KGD model has a constant height and constantwidth through the height, while the PKN model has a constant height and an elliptical vertical cross-section.The 2D models are not able to simulate both vertical and lateral propagation. Therefore, pseudo-3D models were formulated by removing the assumption of constant and uniform height (Settari and Cleary, 1986; Morales, 1989). The height in the pseudo-3D models is a function of position along the fracture as well as time. The major assumption is that the fracture length is much greater than the height, and an important difference between the pseudo-3D and the 2D models is the addition of a vertical fluid flow component. The pseudo-3D models have been used to model fractures through multiple rock layers with differing stresses and properties. These models are simple, fast, and relatively effective. Warpinski et al. (1994) recently provided brief descriptions and a comparison of predictions for a number of simulators, including 2D and pseudo-3D models.Pseudo-3D models cannot handle fractures of arbitrary shape and orientation, however; fully 3D models are required for this purpose. The literature contains numerous references to fully 3D simulators; the majority of these are limited to planar fracture surfaces, however. These are called planar-3D simulators in this chapter to differentiate them from true fully 3D simulators which can model out-of-plane fracture growth. Planar-3D simulators have been developed by Clifton and Abou-Sayed (1979), Barree (1983), Touboul et al. (1986), Morita et al.(1988), Advani et al. (1990), and Gu and Leung (1993). Out of plane 3D hydraulic fracture growth has been modeled by Lam et al. (1986), Vandamme and Jeffrey (1986), and Sousa et al. (1993). To the authors’ knowledge, only Carter et al.(1994), using the predecessor of the simulatordescribed herein, have modeled 3D fracture in the near-wellbore region of a cased, perforated, and deviated wellbore.The increasing use of deviated wellbores implies that fully 3D hydraulic fracture simulators are vital to the petroleum industry. Hydrofracturing is often less effective for deviated wellbores as compared to traditional vertical wells. Some of the problems have been attributed to a poor understanding of the mechanics of fracture initiation and propagation from a deviated wellbore. The complex state of stress which is generated around an inclined wellbore (Yew and Li, 1988; Ong and Roegiers, 1995) means that the fracture propagates with a complex geometry (Behrmann and Elbel, 1990; Hallam and Last, 1991; Weijers and de Pater, 1992; Abass et al., 1996). The complex stress state and fracture geometry can limit the fracture width at the wellbore and hinder the injection of proppant into the fracture leading to premature screenout (Hallam and Last, 1991; Soliman et al., 1996). Nevertheless, the advantages of drilling inclined wellbores are significant. For example, the ability to drill several wells from a single location minimizes production infrastructure and impact on the environment. Therefore, the ability to model hydraulic fracturing from deviated wells is of ever increasing importance.In addition to inadequate modeling of the fracture geometry, many of the current hydraulic fracturing simulators do not predict the correct wellbore fluid pressure or fracture geometry even for planar fractures. The proposed reasons for this are numerous (Medlin and Fitch, 1983; Warpinski, 1985; Shlyapobersky et al., 1988; Jeffrey, 1989; Palmer and Veatch, 1990; Johnson and Cleary, 1991; Gardner, 1992; Papanastasiou and Thiercelin, 1993; de Pater et al., 1993 and van den Hoek et al., 1993). The simulator developed here addresses this problem by properlymodeling the near crack tip behavior (SCR, 1993). Furthermore, the simulator is ideal for modeling non-planar hydraulic fracturing, and is able to model multiple branching, intersecting, and merging fractures as will be shown in the following section.3.0 Model RepresentationThe first key component of an efficient, fully 3D, hydraulic fracture simulator is the geometric representation of the model. Representation implies computer storage and visualization of the model topology and geometry. This portion of the hydraulic fracture simulator is actually a general purpose, fully 3D, fracture analysis code, called FRANC3D, under development at Cornell University since 1987 (Martha, 1989; Wawrzynek, 1991; Potyondy, 1993). FRANC3D is capable of modeling multiple, arbitrary, non-planar, 3D cracks in complex structures, and has pre- and post-processing capabilities for both finite and boundary elements. It relies on a boundary surface representation of the model and a radial edge data structure for storing and accessing topological and geometrical information. It has the ability to do fully automatic or fully user-controlled crack growth simulations, including post-processing of the response information, modifying the geometry, remeshing, and updating the boundary conditions for each stage of crack growth. The complex geometry associated with perforated, cased, and deviated wellbores with multiple non-planar evolving 3D cracks requires a sophisticated, but easy to use simulation capability. FRANC3D has these capabilities, and some of its individual components are described briefly in the following sections.3.1 Representational Model of Fracture PropagationCrack growth simulation in FRANC3D is an incremental process, where a sequence of operations is repeated for a progression of models (Figure 1). Each step in the process relies on previously computed results and represents one crack configuration. There are four primary collections of data, or databases, required for each step. The first is the representational database, denoted R i(where the subscript identifies the step). The representational database contains a description of the solid model geometry, including the cracks, the boundary conditions, and the material properties. The representational database is transformed by a discretization (or meshing, M) process to a stress analysis database A i. The analysis database contains a complete, but approximate description of the body, suitable for input to a solution procedure (S), usually a finite or boundary element stress analysis program.The solution procedure is used to transform the analysis database to an equilibrium database E i which consists of field variables, such as displacements and stresses, that define the equilibrium solution for the analysis model A i. The equilibrium model should contain field variables and material state information for all locations in the body, and in the context of a crack growth simulation, should also contain values for stress-intensity factors, or other fracture parameters F i for all crack fronts. The equilibrium database is used in conjunction with the current representational database to update (U(C)) the representational model R i+1including the increment of crack growth as governed by the fracture parameters F i and the crack growth function C. This process is performed repeatedly (Figure 1) until a suitable termination condition is reached.FRANC3D encompasses all components of this conceptual model except for the stress analysis procedure (Figure 2). The individual components consist of unique databases and functions that operate on the databases, some of which are described in more detail in the following sections.3.2 Solid Modeling For Crack Growth SimulationsSimulation of crack growth is more complicated than many other applications of computational mechanics because the geometry and topology of the structure evolve during the simulation. For this reason, a geometric description of the body that is independent of any mesh needs to be maintained and updated as part of the simulation process. The geometry database should contain an explicit description of the solid model including the crack. The three most widely used solid modeling techniques, boundary representation (B-rep), constructive solid geometry (CSG), and parametric analytical patches (PAP) (Hoffmann, 1989; Mäntylä, 1988; Mortenson; 1985), are capable of representing uncracked geometries. A B-rep modeler stores surfaces and surface geometries explicitly. If explicit topological adjacency information (as defined in the next section) is available as well, two topologically distinct surfaces can share a common geometric description. Cracks, for instance, consist of two surfaces that have the same geometric description; for this reason, among others, a boundary representation was found to be the most suitable of the three modeling techniques for modeling cracks.3.3 Computational Topology as a Framework for Crack Growth SimulationExplicit topological information is an essential feature of the representational database for crack growth simulations. The topology of an object is the information about relationships, proximity, and order among features of the geometry—incomplete geometric information. These are the properties of the actual geometry that are invariant with respect to geometric transformations; the geometry can change, but the topology remains the same (Figure 3). A topology framework serves as an organizational tool for the data that represents an object and the algorithms that operate on the data.There are several reasons for using a topological representation for crack growth simulation: 1) topological information, unlike geometrical information, can be stored exactly with no approximations or ambiguity; 2) there are formal and rigorous procedures for storing and manipulating topology data (Mäntylä, 1988; Hoffmann, 1989; Weiler, 1986); 3) any topological configuration can represent an infinite number of geometrical configurations; and 4) topology generally changes much less frequently than the geometry during crack propagation. Investigations into the use of data structures for storing information needed for crack propagation simulations (Wawrzynek and Ingraffea 1987a,b) showed that topological databases were a convenient and powerful organizing agent, and efficient topological adjacency queries make this data structure ideally suited for interactive modeling.Explicit topological information is used as a framework for the representational database R i and aids in implementation of the meshing function M and the updating function U(C). In particular, by using a topological database in conjunction with a B-rep modeler, topological entities can serve as the principal elements of the database with geometrical descriptions and allother attributes (such as boundary conditions and material properties) accessed through the topological entities.Several topological data structures have been proposed for manifold objects: the winged-edge (Baumgart, 1975), the modified winged-edge, the face-edge, the vertex-edge (Weiler, 1985), and the half-edge (Mäntylä, 1988) data structures. However, these data structures cannot be used for modeling fully 3D hydraulic fracturing because features like bi-material interfaces create non-manifold topologies. Weiler (1986) presented another edge-based data structure for storing non-manifold objects, called the radial-edge, and outlined the corresponding generalized non-manifold Euler operators. The basic topological entities used for modeling are vertices, edges, faces, and regions. An internal crack, for example, consists of vertices, edges, and faces with a null volume region between the crack surfaces. The edge entity is the object through which topological relationships are maintained and queried (Figure 4). As the name implies, the edge uses are ordered radially about the edge; each face has two face uses and each face use has a corresponding edge use on the given edge. The radial ordering allows for efficient storage, querying and manipulation of the model topology. As shown in Figure 5, this data structure, in addition to bi-material interfaces, is clearly able to represent model topologies consisting of branching or intersecting cracks; both are important features when modeling hydraulic fracturing in a layered rock mass from a cased and deviated wellbore.A crack is defined within this representational database by both geometry and topology. It consists of multiple surfaces in order to represent the evolving geometry as well as the possibility of intersecting, branching, and merging cracks. Crack surfaces are arranged in pairs (main andmate surface, see Figure 5), and each surface is composed of faces, edges and vertices. The edges and vertices are further classified based on their location on the crack surface. For instance, crack front edges represent the leading edge of the crack within the solid. Note that crack growth involves modifying the model topology and geometry to represent newly created fracture surfaces.3.4 Meshing, Crack Growth and Model Update FunctionsThe combination of the boundary representation solid model and the radial edge topological database comprises the representational model R i. Complex 3D models of deviated, perforated, and cased wellbores including multiple non-planar fractures can be built fairly quickly and easily using this representational model. The other components of the abstract model, such as the discretization (meshing), crack growth and model updating, post-processing, and visualization also take advantage of the topological database. The meshing capabilities (Potyondy et al., 1995) and the crack growth and model update functions (Martha et al., 1993; Carter et al., 1997) in FRANC3D have been described elsewhere. For completeness however, a brief description of both functions is needed here as they relate to modeling hydraulic fracturing.FRANC3D maintains a consistent geometric representation of the model at each step of propagation. During fracture propagation, the previous crack surface geometry remains the same; new fracture surface is simply added to the model to represent the crack growth (Figure 6). There are some exceptions when it is necessary to rebuild the entire fracture geometry, but this is beyond the scope of the present discussion. Therefore, the mesh that is attached to the existinggeometric crack surfaces is unaffected by fracture growth because the existing geometry does not change. In truth, the mesh is removed from the geometric crack surface during propagation, but an identical mesh can be regenerated on that surface. A new mesh is attached to the new crack surface. Thus, the process of modeling crack propagation involves neither a "fixed" nor a "moving" mesh as described in other hydraulic fracturing literature. The mesh on the existing crack surface can remain fixed or it can be modified, but a new mesh must be added to the new crack surface. Mapping of information from the previous step of propagation to the current step is discussed later.4.0 The Physics and Mechanics of Hydraulic FracturingThe second important component of a robust and accurate, fully 3D, hydraulic fracture simulator is the ability to properly model the fluid flow coupled with the fracture deformation and propagation. The following discussion is restricted to the framework of linear elasticity and lubrication theory.4.1 Elastic Stress AnalysisBES is a linear elastic, 3D, boundary element program (Lutz, 1991). It is based on a direct formulation and uses special hypersingular integration techniques and non-conforming elements on and around the crack surfaces. It is capable of handling multiple loading cases, specifically generating basic solutions (displacements and tractions) for unit tractions at points on the cracksurface. Unit tractions are applied to each node on the discretized crack surface. The traction is distributed according to the shape functions of the incident elements, starting at unity at the given node and vanishing to zero at all adjacent nodes. The displacements at all nodes in the structure are evaluated for each unit traction loading case, providing a matrix of solutions whose generic element K ij is the displacement at node i due to a unit traction at node j.The set of basic solutions is combined to build a single influence matrix which then is used along with the equilibrium fluid pressures to determine the overall structural response due to both the far field boundary conditions and the fluid pressure in the crack. The displacements in the structure can be computed by multiplying each of the basic solutions, obtained for a unit traction at a node, by the fluid pressure at that node. This means that the stress analysis, which is the most time consuming process of the entire simulation, can be performed once for a specific model or crack geometry. Various fluid properties and flow parameters then can be used in the hydraulic fracture simulator based on this single stress analysis.4.2 Fluid FlowA peculiarity of hydraulic fracturing consists of the strong nonlinear coupling between fluid flow and solid deformation, particularly in the vicinity of the fracture front. Proper coupling, as derived by the Geomechanics Group at Schlumberger Cambridge Research (SCR, 1993, 1994), yields an analytical model for pressure and width near the crack front which corresponds to a stress singularity that is different from the usual linear elastic fracture mechanics solution (LEFM). A new term has been coined, linear elastic hydraulic fracturing (LEHF), to reflect thedifference in the solutions. The use of the LEHF analytical model provides an elegant solution to the numerical problem otherwise associated with modeling the front of a hydraulic fracture. (Note that a 3D crack front becomes a crack tip in 2D.)4.2.1 Review of 2D LEHF SolutionFollowing an approach similar to Spence and Sharp (1985), the Geomechanics Group at SCR (SCR, 1993) has shown that a fluid lag often develops near the crack tip, and this fluid lag negates the influence of the rock fracture toughness. However, by assuming that the fluid reaches the crack tip, a particular singularity develops in both the fluid pressure and the stress field ahead of the crack tip which is unique to hydraulic fracturing (SCR, 1994). This yields an intermediate asymptotic solution for the width and pressure in the crack which is independent of fracture toughness, provided that more energy is dissipated in the fluid than in creating new fracture surface. It is intermediate in the sense that there exists a small region at the very tip of the fracture where a fluid lag develops and LEFM holds, but has little effect on the rest of the solution and is not taken into account.To obtain the general solution for fluid flow in the vicinity of the tip of a hydraulic fracture propagating in an impermeable solid, the following assumptions are made: crack propagation is self-similar and steady-state, the rock mass is a linear elastic solid in plane strain, lubrication theory is valid, and the fluid is incompressible with a power-law shear-thinning consistency. The boundary conditions include the far-field minimum principal stress, the fracture width at the crack tip, which must be zero, and the fluid velocity at the crack tip where the tip is a movingboundary. Details of how the solution is obtained can be found in SCR (1994). The final expressions for the pressure p and crack opening w in the vicinity of the crack tip, are as follows:p −σ3=p h 222+′ n ()π(2−′ n ) L h L ′ n /(2+′ n )−L h ξ ′ n /(2+′ n ) (1)w =ξ2/(2+′ n )L h ′ n /(2+′ n )c 1(′ n )−c 2(′ n )ξL 2+3′ n 4+2′ n (2)whereL h =V ′ K ′ E 1/′ n (3)is a characteristic length particular to hydraulic fracturing andp h =′ E cos((1−α)π)sin(απ) 1+′ n 2′ n +1′ n 2(2+′ n ) ′ n 1(2+′ n ) (4)is a characteristic pressure with α(′ n )=2(2+′ n ) . V is the crack tip speed which is equal to the fluid velocity at the tip. L is the fracture half length and ξ is the position from the crack tip.σ3 is the far-field minimum stress. ′ E =E (1−ν2) is the effective Young's modulus where Eis the Young's modulus and ν is Poisson's ratio. ′ K is the consistency index and ′ n is the power-law exponent. c 1 and c 2 are constants (SCR, 1994) that are evaluated best numerically; for a Newtonian fluid, they are c 1 ≅ 7.21 and c 2 ≅ 3.17. Note that the flow rate at the tip q b is a function of the speed and the crack opening, q b =V ⋅w =f (V ).From these equations, the fluid pressure at the crack tip is found to be singular; for a Newtonian fluid, ′ n =1 and the order of the singularity is 1/3. The stress at the crack tip has the same order of singularity. The order of the singularity depends on the fluid properties only and, within the assumptions made here, is always weaker than the 1/2 obtained from linear elastic fracture mechanics.A similar solution was developed for the permeable case and can be found in Lenoach (1995). It involves a supplementary length scale because of the leak-off process and yields a solution which exhibits yet another singularity, also weaker than that of linear elastic fracture mechanics.4.2.2 Extension of the LEHF Solution to 3DThe behavior of a hydraulic fracture in the vicinity of its propagating front is easily described by the LEHF solution, provided two additional assumptions are made: the crack front is considered to be locally under plane strain conditions, and the local fluid flow parallel to the crack front is negligible. We shall restrict ourselves to the case of a Newtonian fluid, but the process can easily be extended to power-law fluids. The width w in the vicinity of the fracture front is then described by the LEHF solution along any normal to the crack front:w =(2)376()µV ′ E 13ρ23=βV 1 (5)。
2021英语辩题
2021英语辩题2021年的英语辩题有很多，以下是一些例子：1. "The increasing use of AI technology has more positive than negative impacts on individuals."2. "Social media has more negative than positive impacts on society."3. "The current system of higher education is the best system for students."4. "The future of work will be more secure with the rise of automation."5. "Globalization has more negative than positive impacts on the world."6. "The best way to reduce climate change is through government regulation."7. "The best way to improve public health is through increased access to exercise and healthy food."8. "The future of transportation will be dominated by electric vehicles."9. "The best way to solve the problem of income inequality is through government intervention."10. "The best way to improve education is through more technology integration."这些辩题涵盖了科技、社会、政治和经济等多个领域，可以帮助您了解当前社会的一些重要议题，同时提高您的英语辩论技巧。
负折射率隐身衣英文版
Ran Duan,1 Elena Semouchkina,2,* and Ravi Pandey1
1Leabharlann Abstract: The geometric optics principles are used to develop a unidirectional transmission cloak for hiding objects with dimensions substantially exceeding the incident radiation wavelengths. Invisibility of both the object and the cloak is achieved without metamaterials, so that significant widths of the cloaking bands are provided. For the preservation of wave phases, the λ-multiple delays of waves passing through the cloak are realized. Suppression of reflection losses is achieved by using half-λ multiple thicknesses of optical elements. Due to periodicity of phase delay and reflection suppression conditions, the cloak demonstrates efficient multiband performance confirmed by full-wave simulations.
利用网络表征学习辨识复杂网络节点影响力
2021年2月第2期Vol. 42 No. 2 2021小型微 型计算 机系统Journal of Chinese Computer Systems利用网络表征学习辨识复杂网络节点影响力杨旭华，熊帅(浙江工业大学计算机科学与技术学院，杭州310023)E-mail : xhyang@ zjut. edu. cn摘要：发现复杂网络中最具影响力的节点，有助于分析和控制网络中的信息传播，具有重要的理论意义和实用价值.传统的确定节点影响力的方法大多基于网络的邻接矩阵、拓扑结构等，普遍存在数据维度高和数据稀疏的问题，基于网络表征学习，本 文提出了一种局部中心性指标来辨识网络中高影响节点(NLC),首先采用DeepWalk 算法,把高维网络中餉节点映射为一个低维空间的向量表示，并计算局部节点对之间的欧氏距离；接着根据网络的拓扑结构，计算每个节点在信息的传播过程中，对所在 局部的影响力大小，用以识别高影响力节点.在八个真实网络中，以SIR 和SI 传播模型作为评价手段，将NLC 算法和度中心性、接近中心性、介数中心性、邻居核中心性、半局部中心性做了对比，结果表明NLC 算法具有良好的识别高影响力传播节点飴 性能.关键词：节点影响力；网络表征学习；局部节点中心性;复杂网络中图分类号：TP301文献标识码:A 文章编号:1000-1220(2021)02-0418-06Identiflcation of Node Influence Using Network Representation Learning in Complex NetworkYANG Xu-hua,XIONG Shuai(Computer Science and Technology College,Zhejiang University of Technology ,Hangzhou 310023 .China)Abstract ： Finding the most influential propagation nodes in complex networks is helpful to analyze and control the propagation of in formation in the network , which is of great theoretical significance and practical value. Most of the traditional methods for determining the influence of nodes are based on the adjacency matrix and topology of the network , and the problems of high data dimension and da ta sparsity are common. Based on Network Representation Learning , this paper proposes an algorithm to identify the high influence propagation nodes of the network ( NLC). Firstly ,the deepwalk algorithm is used to map the nodes in a high-dimensional network intoa vector representation of a low-dimensional space and calculate the euclidean distance between local node pairs. Then ,according to thetopology of the network,the influence of each node on the local area during the propagation of information is calculated to identify the high-influence nodes. In eight real networks , SIR and SI propagation models are used as evaluation methods , comparing the NLC algo rithm with degree centrality , closeness centrality , betweeness centrality , neighborhood coreness , and semi-local centrality , the resultsshow that NLC algorithm has good performance in identifying high-influence propagation nodes.Key words : node influence ； network representation learning ； node local centrality ； complex network1引言真实世界中的许多系统都可以抽象为复杂网络，比如社 交网络、交通网络、电力网络、通信网络、人物关系网络、流行病传播网络等.辨识网络中有影响力的传播节点，涉及到网络 的结构和功能等属性，包括度分布，平均距离，连通性,信息传 播，鲁棒性等3〕，在实际应用中，能够控制信息在网络中的 传播⑷、做高效的新闻推广⑸、避免电网中故障的传播⑷、分 析蛋白质之间的相互作用⑺等.如何有效辨识网络中节点传播影响力的大小，研究者们 已经有了不少研究成果，这些方法总体上可以分为两种类型： 基于局部信息和基于全局信息的判断节点中心性的方法.基 于局部信息的方法，例如：度中心性⑻把节点连接的边的数量作为衡量的指标;邻居核中心性⑼把节点的一级邻居、二级邻居和三级邻居节点个数之和当做判断影响力大小的指 标;K-shell 分解方法31,是一种基于节点局部拓扑结构的方 法丄iu 等人认为许多真实网络由于局部的紧密连接而存在类核结构，导致许多节点的值不能真实的反映节点在网络中的影响力，他们通过删除冗余边的策略,提高了 K-shell 值 的准确性;郑文萍等人衡量节点在网络连通性中的作用， 通过节点所连边对局部网络连通性的影响来反映该节点在网 络连通性方面的重要性;Chen 等人口结合度中心性和全局信息，提出了一种半局部中心性方法，实验表现与紧密中心性相同,但计算复杂度较低;李维娜等人,基于网络的局部社 团结构和节点度的分布情况，提出了一种重要节点挖掘算法SG-CPMini n &基于网络全局信息的方法往往能获得比基于局部信息的算法更高的精确度，但计算复杂度比较高.例如介数中心收稿日期:2020-02-24 收修改稿日期；2020-04-14 基金项目：国家自然科学基金项目(61773348)资助；浙江省自然科学基金项目 (LY17F030016)资助.作者简介:杨旭华，男，1971年生，博士，教授,CCF 会员，研究方向为机器学习、复杂网络、智能交通；熊0巾，男，1994年生，硕士研究生，研究方向为机器学习、复杂网络.2期杨旭华等:利用网络表征学习辨识复杂网络节点影响力419性和接近中心性:冏，都是基于全局路径的方法，考虑网络中任意节点对之间的路径.谷歌公司提出的PageRank"",通过考虑邻居节点的数量和质量,再进行全局的迭代计算来确定节点的重要性.吕琳環等人提出一种类似于PageRank的算法，在网络中增加了一个背景节点与所有节点进行双向连接,使新的网络成为强连通网络，称作LeaderRank").王斌等人(切考虑网络的结构及属性信息，提出节点信任度的概念，同时将节点信任度引入到PageRank算法中，构建了一种关键节点识别算法TPR(Trust-PageRank)；Lu等人画提出了一种基于信息扩散特性，将节点的局部属性与全局属性相结合的WeiboRank(WR)算法，在微博社交网络数据上表现良好.上述辨识方法,都是建立在传统的网络表示方法之上的，普遍依赖于网络的邻接矩阵和拓扑结构，具有维度高和数据稀疏的特点,计算复杂度高，在大型网络使用中计算代价比较高.随着网络表征学习技术在自然语言处理等领域的发展和广泛应用,研究者们转而探索如何将网络中的节点表示为低维且稠密的向量，提岀了诸多方法.DeepWalk是网络表征学习的先驱0),将词表示学习算法word2vec[22]应用在随机游走序列上,从而生成了节点的低维度表示向量.Lineal针对一阶相似度和二阶相似度，提出了一种边采样算法优化目标函数，进而得到节点的向量表示.N o de2vec[241通过改变随机游走序列生成的方式扩展了DeepWalk算法,将宽度优先搜索和深度优先搜索引入了随机游走序列的生成过程,综合考虑了网络的局部信息和全局信息来表示节点•CANE1251假设每个节点的表示向量由文本表示向量及结构表示向量构成，其中，文本表示向量的生成过程与边上的邻居相关，再利用卷积神经网络和注意力机制对一条边上两个节点的文本信息进行编码，得到节点的表示向量■SDNE1261使用深层神经网络对节点表示间的非线性进行建模，把模型分为两个部分:一个是由Laplace矩阵监督的建模第1级相似度的模块，另一个是由无监督的深层自编码器对第2级相似度关系进行建模，将深层自编码器的中间层输岀作为节点的向量表示.这些算法从不同的角度，采用不同的优化方法，把高维和稀疏的网络映射到低维和稠密的向量空间，保留网络的原有结构，具有计算复杂度低和准确度高等特点.在本文中，我们基于网络表征学习提出了一种辨识网络节点影响力的方法.采用网络表征学习DeepWalk算法把高维的复杂网络映射到低维的向量空间，把网络节点映射为欧式空间中低维的向量表示，然后结合网络拓扑信息提出节点的局部中心性，作为判断节点影响力大小的指标.2基于网络表征学习的节点局部中心性节点在网络中传播信息时,与其局部的拓扑结构有很大的关系.已有研究表明：节点的K-shell值越大，周围的拓扑结构越紧密，节点向周围区域传播信息的效率越高〔勿，同时，信息传递的强度随着节点间距离的增大而迅速衰减皿)，由此,提出一种基于网络表征学习和局部中心性确定任意节点i的影响力指标：NLC(i)=Z心X e-')Ti-X/2(J)其中,Ks,■表示节点i的K-shell值必”分别表示节点ij用DeepWalk网络表征方法映射到低维欧式空间的向量，比-X」表示两个向量之间的欧氏距离，r(i)表示i节点的三级邻域，即i节点的一级邻居、二级邻居以及三级邻居节点的集合j节点属于r(i)集合.网络中节点间的距离，本文没有采用网络的最短路径距离，因为会存在如下的问题，如图1所示,i节点在传播它自身的信息时，首先会影响它的一级邻居节点，比如节点k和节点j,当节点A和/被感染后，由于j节点有更多的连接到外部区域的邻居节点(图1中灰色节点)，尽管同样是节点i的一级邻居节点J比k在传播i节点信息的过程中贡献更大【切，所以，信息在网络中的传播,除了距离以外，还与网络的结构密切相关，最短路径距离的长度不能准确的表示信息在传播过程中的衰减，还要根据网络的拓扑结构，对所求节点的邻域节点做进一步的划分.因为网络表征学习方法不但可以把高维网络映射到低维的向量表示，而且可以同时保持网络的结构，节点间的距离用低维向量间的欧式距离替代后，不仅考虑了最短路径距离，而且包含了图1一个有8个节戌和节点周围的拓扑结构信息，能够9务边的网络更准确的描述信息在网络传播过Fig.1Nitwork with eight程中的衰减因此在本文中，我们....选择应用DeepWalk方法，把网nodes and nine edges络节点映射到低维的向量表示，然后用节点相应的低维向量来计算节点之间的距离.具体地，基于DeepWalk方法，将网络空间映射到欧式空间,把每一个节点表示为一个低维稠密的向量，将具有N个节点的网络G转化为欧氏空间的N个r维向量，一个网络节点及其连边信息对应一个向量，其中任意节点i的向量表示为：Xi=(x.l,X.2,X.3，…，x.,),i=1,2,3,,N,在本文中，『取N/23实验和分析3.1数据集为了评估所提出的方法的性能,我们在8个真实世界的网络中进行了实验，这8个网络都是无向网络，也不考虑权重,它们分别是常见形容词和名词的邻接网络adjnoun f30]、科学家合作网络netscience、Ca-GrQc和hep-th[31H]、新西兰宽吻海豚社会网络dolphin1341、小型的facebook社交网络、爵士音乐人合作网络Jazz匈、美国政治图书网络polbooks1371,表1给出了8个真实数据集的拓扑属性参数.其中,N和E分别表示网络的节点数和边数，〈&〉表示网络的平均度，在本文中，考虑到现实世界中网络的度分布往往存在“重尾效应”，令0”=<*>/<*2>[381，表示SIR模型传播的阈值,c表示网络的平均聚类系数.3.2评价方法和指标3.2.1SIR疾病传播模型SIR属于动态传播算法，结果准确性好但计算复杂度高,420小型微型计算机系统2021年本文提出的NLC算法及其他静态指标方法计算复杂度低，我们用SIR疾病模型做为基准参照模型去评价不同的判断节点影响力静态指标方法性能的优劣（列.在SIR模型中，如果需要判定一个节点在网络中的传播影响力，则把这个节点设定为网络中唯一的感染节点（Infected）,其他节点标记为易感节表1数据集Table1Data setsNetwork N E〈k〉cdolphin62159 5.130.1470.27polbooks1054418.40.0840.488Jazz198274227.700.0260.617adj n oun1124257.5890.0730.1728 netscience15892742 3.4510.1440.6378 facebook40398823443.6910.0090.6055 Ca-GrQc524214496 5.5310.05930.5296 hep-th836115751 3.7680.1150.4420点（Susceptible）,在每个时间步，每个感染态节点会以概率0（0=1.50*）感染其易感邻居节点,0”表示SIR模型传播的阈值,然后以概率“（在本文中，我们设置“=1）从疾病中恢复，变成移除态（Recovered）,移除态节点不会再被感染.这个过程不断迭代直到网络中没有感染节点为止,r时刻网络中移除态和感染态节点的总数量，记为F（r）,F（r），作为评价r时刻该节点传播影响力大小的指标,F（r）越大,该节点影响力越大. 3.2.2SI疾病传播模型在该模型中，节点一旦被感染,状态从S变为I之后不能恢复，其他条件和SIR模型相同，在本文中，易感状态节点被感染的概率为苹".如果在相同的时间步的条件下，一个节点感染的网络节点越多，则说明该节点感染能力越强,影响力越大.3.2.3肯德尔系数不同的方法都可以按照所计算的传播能力，对网络中所有节点从高到低排序，针对不同的感染率0,我们用肯德尔系数7去评价不同的静态指标方法得到的排序列表和SIR动态传播模型生成的排序列表之间的联系I切，t是一个在[-1, 1]之间的一个数,7■越大，两个序列吻合度越高,T被定义为：2(M-NJN(N-1)(2)N c表示两个排序列表相协调元素的数量,M表示二者不协调元素的数量,N表示网络节点总数.3.3数值仿真首先,对八个真实网络的每一个节点在本网络内赋予唯一的编号，比如网络1有N个节点，则网络节点的编号应该是1,2,……,N.3.3.1比较NLC和5种知名中心性方法识别的Top-10高影响力节点的准确性在表2中,我们以SIR模型计算出来的Top-10节点为基准，在4个真实网络上，用NLC方法，度中心性（DC）、接近中心性（CC）、介数中心性（BC）、邻居核中心性（Cnc）、半局部中心性（CL）分别计算ToplO节点，比较不同方法的准确性,考虑到网络的规模和时间复杂度,本文令『=10[41].具体计算方法为:以dolphin网络为例,首先用SIR模型在t=10时刻，计算得到F（10）数值最大的Top-10节点做为基准，然后用NLC方法算出Top-10节点，如果两组节点有9个相同，则NLC算法的准确率为90%.表26种中心性算法和SIR模型对排名前10节点的识别结果Table2Six algorithms and SIR modelsto identify thetop-10nodes网络dolphin算法（准确率）排序DC(70%)BC(60%)cc(60%)Cnc CL(80%)(80%)NLC(90%)F(10) 1153737151515152382414638383834641383846412143438213434214155281521413746618182303046377212184151342830552952525130958523422125110258958173052网络adj n oun算法（准确率）排序DC(70%)BC(60%)CC Cnc CL(70%)(80%)(80%)NLC(80%)F(10) 11818181818181823333352334444525252352452524444444444510510281051051051056108010525512851725105105125101082828272826252592622510552655102292619325160网络polbooks算法（准确率）排序DC(80%)BC(60%)CC Cnc CL(40%)(70%)(90%)NLC(90%)F(10) 193131999921350591313131334108858531734851350473410573731073747346677777743110317744153148585831597367676774912954112745104183248741212网络netscience算法（准确率）排序DC(30%)BC(30%)CC Cnc(20%)(40%)CL(0%)NLC(80%)F(10) 134797934143034552351512823514313556337951715163143255344552827575564656335529521730291714332821336143035152914143413354714317573554143513475781432302132120214361351359631337602951437562762102172041124220143854562在表2中，比较其它5种方法，本文提出的NLC算法在4个数据集中都取得了最高的准确率.接下来，我们比较了各种2期杨旭华等:利用网络表征学习辨识复杂网络节点影响力421静态指标算法与SIR模型得到的Top-10节点排序列表的吻合程度，在小型网络polbooks和adjnoun中,6种中心性算法都有较高的准确率,CL算法和NLC算法有相同的准确率，但NLC得到的序列与SIR模型给出的序列更吻合；在dolphin 和netscience网络中,NLC算法不仅有最高的准确率,而且给出的排序序列与SIR模型给出的序列更吻合；就整体而言，NLC与SIR模型得到的序列保持良好的吻合度.其中实验结果取1000次实验的平均值，最佳准确率用黑体字标出,F(10)表示SIR模型在第10时间步的结果.3.3.2比较NLC与5种知名中心性方法在SIR模型下餉肯德尔系数分别用各种静态指标算法与SIR模型对一个网络中所有节点的影响力排序，然后比较各种静态指标算法得到的节点排序列表和SIR模型得到列表的吻合程度，我们用肯德尔系如图2所示，针对不同的感染率B，使用NLC和5种知名中心性方法计算出网络中所有节点的影响力大小排序列表，与SIR模型生成的排序列表做对比，得到肯德尔系数T.在adjnoun网络中,BC算法表现最差,CL和Cnc算法表现基本相同，NLC算法表现最好；在polbooks网络中，CC和BC 表现最差,NLC、CL、Cnc表现良好;在netscience网络中，表现最差的还是BC算法,CC和CL算法也表现不佳，当B< 0.04.NLC算法表现最好，总体表现良好;在facebook网络中,CC表现最差，当p>0.04,NLC表现最好;在hep-th网络中，当B<0.04时,NLC算法表现最好，当p>0.04,NLC算法在6种方法中排名第二；dolphin网络中，当B在0到0.04以及0.07到0.1这两个区间时,NLC算法表现最好，优于其它算法;在Jazz和Ca-Grtjc网络中，BC算法表现最差，当B >0.03时,NLC算法表现最好;综上所述,NLC在肯德尔系数表示这个吻合程度.0.80数上表现最佳.netscienceinounb0.70l0.60.650.60NLC CC BC DC CL Cnc00.020.04 0.06 0.080.100.020.040.060.080.103NLC CC BC DC CL Cnc图2NLC,8,BC,DC,CL,Cnc算法的肯德尔系数，取1000实验的平均值.横坐标表示节点被感染的概率，纵坐标表示肯德尔系数Fig.2Kendall correlation coefficient of NLC,CC,BC,DC,CL,Cnc algorithm which are taken as the average value of1000 experiments.The horizontal ordinate represents the probability of the node being infected,and the longitudinalordinate represents the Kendall correlation coefficient3.3.3比较NLC和CL、Cnc方法■所选Top-10节点的平均感染能力在8种不同的网络中.NLC算法性能均排前列;BC和CC 算法不仅计算量大,而且表现差;Cnc算法和CL算法,在不同的数据集中,表现极不稳定,在有些数据集中表现较好,在有些数据集中甚至差于BC和CC算法.为进一步比较NLC.CL以及Cnc算法的性能，我们使用SI模型检验3种算法性能.首先用一个算法选出Top-10节点，然后用Top-10节点在第r个时间步之内感染的节点总数与网络节点总数的比值的平均值I(t)诰(3)422小型微型计算机系统2021年做为该算法的性能指标•在式(3)中，n表示网络节点总数,％，表示Top-10节点中第i个节点第1到第r步感染的节点总数.在相同的时间步和感染概率的情况下,哪一种方法选出的Top-10节点感染的节点越多，可以认为该算法表现越好.具体实验结果如图3所示，可以看到，NLC算法在4个网络中都取得了最佳性能.在dolphin网络中，NLC算法表现最好,Cnc算法性能最差;在netscience网络中，当时间步大于15后,NLC算法感染的节点比另外两种算法明显增多，达到 稳定的时间也比另外两种算法早，所选Top-10节点表现最好Ca-GrQc网络中，时间步小于10时,3种算法表现相近，大于10后,NLC算法表现最好，且NLC算法在第33个时间步就达到稳定;在hep-th网络中，Cnc算法表现最差，在第42个时间步才达到稳定,NLC算法表现最好.(d)©图3Top-10节点的感染能力和时间步的关系曲线，取1000次实验的平均值.横坐标表示时间步，纵坐标表示第t个时间步内Top-10节点在SI模型中感染的节点数的平均值与网络节点总数的比值Fig.3Relationship curve of infection ability and time step of Top-10node.The results are taken the average of1000experiments, the horizontal ordinate represents the time step,and the longitudinal ordinate represents the ratio of the average number of nodes infected by Top-10nodes in the SI model to the total number of network nodes within the t time step4总结和分析在本文中,我们基于网络表征学习方法，结合节点的拓扑结构和邻域信息,提出了一种节点局部中心性指标来识别节点影响力的方法•该方法提出网络中的节点的影响力由拓扑结构决定，同时随着距离的增加而衰减•在8个真实网络中，通过和5种知名的中心性方法相比较，在计算Top-10节点、Top-10节点的感染能力和肯德尔系数等方面,NLC算法取得了良好的辨识效果，在分析和控制复杂网络中的信息传播过程中具有广阔的应用前景.References:[1]Albert R,Barabasi A L.Statistical mechanics of complex networks[J].Review of Modem Phy s ics,2001,74(1)：47-97.[2]Boccaletti S,Latora V,Moreno Y,et plex networks:structure and dynamics[J].Complex Systems and Complexity Science, 2006,424(4-5):175-308.[3]Newman M E J.The structure and function of complex networks[J].Siam Review,2003,45(2)：167-256.[4]Wells C R,Galvani A P.Coupled disease-behavior dynamics oncomplex networks:a reviewf J].Physics of Life Reviews,2015,62(15)：55-56.[5]Medo M,Zhang Y C,Zhou T.Adaptive model for recommendationof news[J].Europhysics Letters,2009,88(3)：42-51.[6]Albert Reka,Albert Istvdn,Nakarado G L.Structural vulnerabilityof the North American power grid[J].Physical Review E,2(X)4,69(2):59-73.[7]Li Min,Meng Xiang-mao.The construction,analysis,and applications of dynamic protein-protein interaction networks[J].Journal of Computer Research and Development,2017,54(6):1281-1299.[8]Bonacich P F.Factoring and weighting approaches to status scoresand clique identification[J].Journal of Mathematical Sociology, 1972,2(1)：113-120.[9]Bae J,Kim S.Identifying and ranking influential spreaders in complex networks by neighborhood coreness[J].Physica a Statistical Mechanics&Its Applications,2014,395(4)：549-559.[10]Dorogovtsev S N,Goltsev A V,Mendes J F F.K-core organizationof complex networks[J].Physical Review Letters, 2006,96(4)：40601.1-40601.4.[11]Liu Y,Tang M,Zhou T,et al.Improving the accuracy of the k-shell method by removing redundant links:from a perspective of spreading dynamics[J].Scientific Reports,2015,5(2)：33~46. [12]Zheng Wen-ping,Wu Zhi-kang,Yang Gui.A novel algorithm for i2期杨旭华等:利用网络表征学习辨识复杂网络节点影响力423dentifying critical nodes in networks based on local centrality[J].Journal of Computer Rresearch and Development,2019,56(9)：1872-1880.[13]Chen D,Lii L,Shang M S,et al.Identifying influential nodes incomplex networksf J].Physica a Statistical Mechanics&Its Applications,2012,391(4)：1777-1787.[14]Li Wei-na,Ren Jia-dong.Key node mining in complex softwarenetwork[J].Journal of Chinese Computer Systems,2018,39(9)：2022-2028.[15]Freeman L C.A set of measures of centrality based on betweenness[J].Sociometry,1977,40(1)：35-41.[16]Sabidussi G.The centrality index of a graph[J].Psychometrika,1966,31(4):581-603.[17]Brin S,Page L.The anatomy of a large-scale hypertextual websearch engine[J].Computer Networks&Isdn Systems,1998,30(2):16-34.[18]Lii L,Zhang Y C,Yeung C H,et al.Leaders in social networks,thedelicious case[J].Pios One,2011,23(6)：1-13.[19]Wang Bin,Wang Ya-yun,Sheng Jin-fang,et al.Identifying influential nodes of complex networks based on trust-value[J].Journal of Chinese Computer Sy s tems,2019,40(11)：2337-2342.[20]Jing L,Wanggen W.Identification of key nodes in microblog net-works[J].Etri Journal,2016,38(1):52-61.[21]Perozzi B,Al-Rfou R,Skiena S.Deepwlk:online learning of socialrepresentations[C]//ACM Sigkdd International Conference on Knowledge Discovery&Data Mining,2014.[22]Mikolov T,Sutskever I,Chen K,et al.Distributed representationsof words and phrases and their compositionality[J].Advances in Neural Information Processing Systems,2013,26(2)：3111-3119.[23]Jian T,Meng Q,Wang M,et al.LINE:large-scale information network embedding[C]//24th International Conference on World Wide Web,WWW2015,2015.[24]Aditya Grover J L.node2vec:scalable feature learning for networks[CJ//ACM Sigkdd International Conference on Knowledge Discovery&Data Mining,2016.[25]Tu C C,Liu H,Liu Z Y,et al.CANE:context-aware network embedding for relation modeling[C]//Proceedings of the55th Annual Meeting of the Association for Computational Linguistics,Van-couve,2017：1722-1731.[26]Wang D,Cui P,Zhu W.Structural deep network embedding]C]//Proceedings of the22n d ACM SIGKDD International Conference on Knowledge Discovery and Data Mining,San Francisco,2016：1225-1234[27]Kitsak M,Gallos L K,Havlin S,et al.Identification of influentialspreaders in complex networks[J].Nature Phy s ics,2010,6(11)：888-893.[28]Ma L L,Ma C,Zhang H F,et al.Identifying influential spreaders incomplex networks based on gravity formula[J].Physica a Statistical Mechanics&Its Applications,2016,451(3)：205-212.[29]Liu Y,Tang M,Do Y,et al.Accurate ranking of influential spreaders in networks based on dynamically asymmetric link-impact[J].Physical Review E,2017,96(2)：1-1,doi：10.1103/PhysRevE.96.022323.[30]Newman M E J.Finding community structure in networks using theeigenvectors of matrices[J].Physical Review E,2006,74(3)：51-66.[31]Newman M E J.The structure of scientific collaboration networks[J].Proceedings of the National Academy of Sciences of the United States of America,2001,98(2)：404-409.[32]Leskovec J,Kleinberg J,Faloutsos C.Graph evolution:densifica-tion and shrinking diameters[M].Association for Computing Machinery,ACM,2007.[33]Duncan J Watts,Steven H.Strogatz.Collective dynamics of smallworld networks[J].Nature,1998,393(6684)：440-442.[34]Newman M E J,Watts D J,Strogatz S H.Random graph models ofsocial networks[J].Proceedings of the National Academy of Sciences'^,99(Sup)：2566-2572.[35]McAuley J,Leskovec J.Learning to discover social circles in egonetworks[C]//Conference and Workshop on Neural Information Processing Systems(NIPS),2012.[36]Maridn Bogufid,Pastor-Satorras R,Albert Diaz-Guilera,et al.Models of social networks based on social distance attachment[J].Physical Review E Statistical Nonlinear&Soft Matter Physics, 2004,70(2):2441.[37]Fatiha Souam,Ali Aitelhadj,Riadh Baba-Ali.Dual modularity optimization for detecting overlapping communities in bipartite networks [J].Knowledge&Information Systems,2014,40(2)：455-488. [38]Li Rui-qi,Wang Wei,et al.Review of threshold theoretical analysisabout epidemic spreading dynamics on complex networks[J].Complex Systems and Complexity Science,2016,13(1)：l-39. [39]Garas A,Argyrakis P,Rozenblat C,et al.Worldwide spreading ofeconomic crisis[J].New J Phys,2010,12(11)：69-73.[40]Kendall M G.A new measure of rank correlation[J].Biometrika,1938,30(1-2)：81-93.[41]Wang S,Du Y,Deng Y.A new measure of identifying influentialnodes:efficiency centrality[J].Communications in Nonlinear Science and Numerical Simulation,2017,47(6)：151-163.附中文参考文献:[7]李敏,孟祥茂•动态蛋白质网络的构建、分析及应用研究进展[J].计算机研究与发展,2017,54(6):1281-1299.[12]郑文萍，吴志康，杨贵•一种基于局部中心性的网络关键节点识别算法[J]•计算机研究与发展,2019,56(9):1872-1880. [14]李维娜，任家东•复杂软件群体网络社团中关键节点挖掘算法[J].小型微型计算机系统,2018,39(9):2022-202&[19]王斌，王亚云,盛津芳，等•基于节点信任度的复杂网络关键节点识别[J]•小型微型计算机系统,2019,40(11)：2337-2342.。
环球科学知识点
环球科学知识点As human beings, we are constantly seeking to expand our knowledge and understanding of the world around us. One way in which we do this is through the study of global scientific knowledge. By delving into various scientific disciplines, we can learn about the natural laws that govern our universe and how they apply to different aspects of our lives.作为人类，我们不断寻求拓展自己对周围世界的知识和理解。
其中一种方式是通过学习全球科学知识。
通过深入研究不同的科学学科，我们可以了解统治我们宇宙的自然法则，以及它们如何适用于我们生活的不同方面。
From biology to physics, from chemistry to astronomy, each scientific field offers a unique perspective on how the world works. By studying global scientific knowledge, we can gain a deeper appreciation for the interconnectedness of all living things and the vastness of the cosmos. Whether we are exploring the intricacies of cellular biology or the mysteries of black holes, each discovery adds to our collective understanding of the universe.从生物学到物理学，从化学到天文学，每个科学领域都为我们提供了一个独特的视角来解释世界的运作原理。
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(1)
-4on some interesting spaces modeled on the above. Here d denotes the exterior derivative, ⋆ the Hodge map and ψ a complex scalar field. Since the punctured sphere is conformally flat one may use stereographic projections as charts to map (the real part of) suitable complex analytic functions that solve (1) on the punctured 2-plane, to the punctured sphere. Since one can also solve (1) on the Lorentzian cylinders it is possible to match them across the degeneracy curves to construct a global solution.
-3A non-trivial two dimensional example is the trouser space. It may be realized as a pair of trousers embedded in a Minkowskian spacetime of 3 dimensions such that spacelike circles, disconnected at some time, become connected at another. Such a manifold cannot sustain a global metric with a Lorentzian signature. The domain where the metric becomes degenerate depends on the embedding but cannot be eliminated. One of the fundamental issues that arises in describing fields on such manifolds is the dependence of the field equation on the regularity of the metric tensor field. We adopt a pragmatic approach in this paper and impose natural conditions that enable us to construct non-singular scalar fields that are globally C 1 in the presence of a degenerate C ∞ metric field. An example of a two-dimensional trouser-type manifold with a metric that is singular at a single point may be found in [10]. In our approach we consider manifolds endowed with a smooth everywhere regular covariant metric tensor that is however degenerate. Such manifolds are therefore not causally connected [11], [12], [13]. Since the trousers embedding is only for ease of visualisation one may equivalently consider two (or more) cylinders surgically attached to a punctured 2-sphere. It is then possible with the aid of smooth bump functions to endow such a topological space with a metric that has Euclidean signature on the punctured sphere and has Lorentzian signature on a domain of the cylinders. The transition between Euclidean and Lorentzian signature is handled smoothly by the bump functions. We describe below regular global solutions to the massless scalar field equation
-21. Introduction It is well known that the global structure of a manifold is fundamental in constructing regular solutions to tensor equations. Furthermore field quantisation is sensitive to the topology of the underlying base space [1], [2], [3]. However little attention has been given to the elucidation of classical solutions of field equations on manifolds with degenerate geometries that can accommodate non-trivial topology change in general relativity. Such solutions arise from equations that are not globally hyperbolic. Some of the earliest mathematical work on the study of partial differential equations that change from being hyperbolic to elliptic was done by Tricomi [4]. This early treatise involved considerable technicalities that have not been extensively pursued in the mathematical literature. Even in two dimensions the analysis of second order partial differential equations with indefinite characteristics is often non-trivial and the general theory using modern techniques has only recently been considered in topologically trivial manifolds. [5], [6], [7]. Such techniques are relevant for the general study of (non-linear) equations that can arise on manifolds with a degenerate geometry but need to be supplemented by further data to provide well posed or interesting problems. Kundt first [8] discussed the non-existence of certain topologically non-trivial spacetimes assuming that every geodesic is complete. Geroch [9] exploited the notion of global hyperbolicity to reach a similar conclusion. In this paper we consider two dimensional manifolds with smooth (degenerate) metrics. For the applications that we have in mind we require the existence of asymptotically flat Lorentzian domains foliated by compact space-like hypersurfaces.
Topology Change and the Propagation of Massless Fields
Jonathan Gratus
arXiv:gr-qc/9502016v2 9 Feb 1995
Robin W Tucker School of Physics and Materials, University of Lancaster, Bailrigg, Lancs. LA1 4YB, UK rwt@
We analyse the massless wave equation on a class of two dimensional manifolds consisting of an arbitrary number of topological cylinders connected to one or more topological spheres. Such manifolds are endowed with a degenerate (non-globally hyperbolic) metric. Attention is drawn to the topological constraints on solutions describing monochromatic modes on both compact and non-compact manifolds. Energy and momentum currents are constructed and a new global sum rule discussed. The results offer a rigorous background for the formulation of a field theory of topologically induced particle production.