Sequence Of Snapshots Research Articles

Com_Tracker: a two-phases framework for detecting and tracking community evolution in dynamic social networks

Purpose This paper aims to introduce a novel modularity-based framework, Com_Tracker, designed to detect and track community structures in dynamic social networks without recomputing them from scratch at each snapshot. Despite extensive research in this area, existing approaches either require repetitive computations or fail to capture key community behavioral events, both of which limit the ability to generate timely and actionable insights. Efficiently tracking community structures is crucial for real-time decision-making in rapidly evolving networks, while capturing behavioral events is necessary for understanding deeper community dynamics. This study addresses these limitations by proposing a more efficient and adaptive solution. It aims to answer the following questions: How can we efficiently track community structures without recomputation? How can we detect significant community events over time? Design/methodology/approach Com_Tracker models dynamic social networks as a sequence of snapshots. First, it detects the community structure of the initial snapshot using a static community detection algorithm. Then, for each subsequent time step, Com_Tracker updates the community structure based on the previous snapshot, allowing it to track communities and detect their changes over time. The locus-based adjacency encoding scheme is adopted, and Pearson’s correlation guides the construction of neighboring solutions. Findings Experiments conducted on various networks demonstrate that Com_Tracker effectively detects community structures and tracks their evolution in dynamic social networks. The results highlight its potential for real-time tracking and provide promising performance outcomes. Practical implications Com_Tracker offers valuable insights into community evolution, helping practitioners across fields such as resource management, public security, marketing and public health. By understanding how communities evolve, decision-makers can better allocate resources, enhance targeted strategies and predict future community behaviors, improving overall responsiveness to changes in network dynamics. Originality/value Com_Tracker addresses critical gaps in existing research by combining the strengths of modularity maximization with efficient tracking of community changes. Unlike previous methods that either recompute structures or fail to capture behavioral events, Com_Tracker provides an incremental, adaptive framework capable of detecting both community evolution and behavioral changes, enhancing real-world applicability in dynamic environments.

Jaccard-constrained dense subgraph discovery

Finding dense subgraphs is a core problem in graph mining with many applications in diverse domains. At the same time many real-world networks vary over time, that is, the dataset can be represented as a sequence of graph snapshots. Hence, it is natural to consider the question of finding dense subgraphs in a temporal network that are allowed to vary over time to a certain degree. In this paper, we search for dense subgraphs that have large pairwise Jaccard similarity coefficients. More formally, given a set of graph snapshots and input parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document}, we find a collection of dense subgraphs, with pairwise Jaccard index at least α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document}, such that the sum of densities of the induced subgraphs is maximized. We prove that this problem is NP-hard and we present a greedy, iterative algorithm which runs in Onk2+m\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}} \\mathopen {} \\left( nk^2 + m\\right)$$\\end{document} time per single iteration, where k is the length of the graph sequence and n and m denote number of vertices and total number of edges respectively. We also consider an alternative problem where subgraphs with large pairwise Jaccard indices are rewarded. We do this by incorporating the indices directly into the objective function. More formally, given a set of graph snapshots and a weight λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}, we find a collection of dense subgraphs such that the sum of densities of the induced subgraphs plus the sum of Jaccard indices, weighted by λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}, is maximized. We prove that this problem is NP-hard. To discover dense subgraphs with good objective value, we present an iterative algorithm which runs in On2k2+mlogn+k3n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}} \\mathopen {}\\left( n^2k^2 + m \\log n + k^3 n\\right)$$\\end{document} time per single iteration, and a greedy algorithm which runs in On2k2+mlogn+k3n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}} \\mathopen {}\\left( n^2k^2 + m \\log n + k^3 n\\right)$$\\end{document} time. We show experimentally that our algorithms are efficient, they can find ground truth in synthetic datasets and provide good results from real-world datasets. Finally, we present two case studies that show the usefulness of our problem.

Trace Semantics for C++11 Memory Model

The C and C++ languages introduced the relaxed-memory concurrency into the language specification for efficiency purposes in 2011. Trace semantics can provide the mathematical foundation for the proposed C++11 memory model, and there is a lack of investigation of trace semantics for C++11. The Promising Semantics (PS) of Kang et al. provides the standard SC-style operational semantics for the C++11 concurrency model, where “SC” refers to “Sequential Consistency”. Inspired by PS, in this paper we first investigate the trace semantics for the relaxed read and write accesses under C++11, acting in the denotational semantics style. In our semantic model, a trace is in the form of a sequence of snapshots, and the snapshots record the modification in the relevant global or local variables, and the thread view. Moreover, the trace semantics for the release/acquire accesses under C++11 is also explored, based on the separated thread views and newly added message views. When considering this trace model, different accesses bring in their unique snapshots, and make distinguished effects on the production of the sequences. For any given program, the proposed trace semantics in this paper produces all the valid traces directly. Further, our trace semantics, together with that for TSO and MCA ARMv8, has the possibility to be the foundation of the meta model of the trace semantics for weak memory models.

Classifier-Based Nonuniform Time Slicing Method for Local Community Evolution Analysis

With the rapid expansion of the scale of a dynamic network, local community evolution analysis attracts much attention because of its efficiency and accuracy. It concentrates on a particularly interested community rather than considering all communities together. A fundamental problem is how to divide time into slices so that a dynamic network is represented as a sequence of snapshots which accurately capture the evolutionary events of the interested community. Existing time slicing methods lead to inaccurate evolution analysis results. The reason is that they usually rely on a linear strategy while the community evolution is a nonlinear process. This paper investigates the problem and proposes a classifier-based time slicing method for local community evolution analysis. First, a classifier is trained for judging whether there is a community in the given network snapshot is identified as the continuing of the community defined by the given node subset. The features for classification include internal cohesion degree and external coupling degree. Second, a time slicing method is proposed based on the trained classifier. As the network evolves, the method continuously uses the classifier to predict whether there is a community in the newest network identified as the continuing of the interested community. Whenever the answer is negative, an evolutionary event is presumed to have occurred and a new time slice is generated. Experimental results show that compared with existing time slicing methods, our proposed method achieves higher recognition rate for given redundancy ratio.

Time-Aware Random Walk Diffusion to Improve Dynamic Graph Learning

How can we augment a dynamic graph for improving the performance of dynamic graph neural networks? Graph augmentation has been widely utilized to boost the learning performance of GNN-based models. However, most existing approaches only enhance spatial structure within an input static graph by transforming the graph, and do not consider dynamics caused by time such as temporal locality, i.e., recent edges are more influential than earlier ones, which remains challenging for dynamic graph augmentation. In this work, we propose TiaRa (Time-aware Random Walk Diffusion), a novel diffusion-based method for augmenting a dynamic graph represented as a discrete-time sequence of graph snapshots. For this purpose, we first design a time-aware random walk proximity so that a surfer can walk along the time dimension as well as edges, resulting in spatially and temporally localized scores. We then derive our diffusion matrices based on the time-aware random walk, and show they become enhanced adjacency matrices that both spatial and temporal localities are augmented. Throughout extensive experiments, we demonstrate that TiaRa effectively augments a given dynamic graph, and leads to significant improvements in dynamic GNN models for various graph datasets and tasks.

Characterization of interactions’ persistence in time-varying networks

Many complex networked systems exhibit volatile dynamic interactions among their vertices, whose order and persistence reverberate on the outcome of dynamical processes taking place on them. To quantify and characterize the similarity of the snapshots of a time-varying network—a proxy for the persistence,—we present a study on the persistence of the interactions based on a descriptor named temporality. We use the average value of the temporality, overline{mathcal {T}}, to assess how “special” is a given time-varying network within the configuration space of ordered sequences of snapshots. We analyse the temporality of several empirical networks and find that empirical sequences are much more similar than their randomized counterparts. We study also the effects on overline{mathcal {T}} induced by the (time) resolution at which interactions take place.

Уолт Уитмен, галерист в Нью-Йорке

In mid-XIX century mechanical reproduction of images through lithography and photography becomes increasingly available — it allows for visual entrepreneurship on a growing scale. In literary artists this trend causes skepticism but in some (like O.W. Holmes) it also inspires creative interest. That the interaction between commercial and technological practices could be productive of aesthetic insight is proved by Walt Whitman’s poetic experiment. Whitman was fascinated by the art of photography – for a daguerreotype he would sit often, willingly and self-consciously, thus turning a portrait into an auto-portrait. Most of the editions of Leaves of Grass contain the author’s images, while Whitman’s form, the very principles his world-building imagination can be best understood through “photographic logic”. Two versions of the poem My Picture Gallery (the one dating back to mid-1850s and the one published in 1881) are being analyzed as instances of Whitman’s lifelong reflection on how the image, the world and the human subject interact. This relationship is full of submerged drama: technical reproducibility makes the image strikingly lifelike but also contributes to the “derealization” or “virtualization” of the world — tends to empower the subject but also to disable one through “the terrible doubt of appearances”. The visual analogue of the “catalogue” technique, representative of Whitman’s early manner, may be a sequence of snapshots and / or that of imperative pointing gestures: see, watch, imagine! Manicules are often used in Whitman’s early manuscripts: this typographic sign (described as “hand” or “printer’s fist”) is pervasive in newspaper advertising of the poet’s time and of particular interest to him — most probably, because giving a sense of forceful, embodied presence, direct contact with the world and the reader alike. In later editions the gesture gets a different representation — a butterfly rests, distractively, upon the index finger using it as a momentary landing grund. This image — Whitman’s newly chosen visual brand – is expressive of the contemplative attitude, indeterminacy and suggestiveness increasingly of import in his poetics.

Temporal networks in biology and medicine: a survey on models, algorithms, and tools.

The use of static graphs for modelling and analysis of biological and biomedical data plays a key role in biomedical research. However, many real-world scenarios present dynamic behaviours resulting in both node and edges modification as well as feature evolution. Consequently, ad-hoc models for capturing these evolutions along the time have been introduced, also referred to as dynamic, temporal, time-varying graphs. Here, we focus on temporal graphs, i.e., graphs whose evolution is represented by a sequence of time-ordered snapshots. Each snapshot represents a graph active in a particular timestamp. We survey temporal graph models and related algorithms, presenting fundamentals aspects and the recent advances. We formally define temporal graphs, focusing on the problem setting and we present their main applications in biology and medicine. We also present temporal graph embedding and the application to recent problems such as epidemic modelling. Finally, we further state some promising research directions in the area. Main results of this study include a systematic review of fundamental temporal network problems and their algorithmic solutions considered in the literature, in particular those having application in computational biology and medicine. We also include the main software developed in this context.

Control energy scaling for target control of complex networks

To control complex networks in practice, recent work has focused on the control energy required to drive the associated system from an initial state to any final state within finite time when it is fully controllable. However, beyond the prohibitively high cost for controlling all nodes of a network, it is usually adequate to control some target nodes of most natural and technological networks. In other words, what we usually need is to implement target control frequently. Yet, understanding the control energy for target control remains an outstanding challenge so far. Here we theoretically present an efficient method to calculate the minimum control energy required for implementing target control of complex networks, which bypasses the sophisticated calculation of the traditional Gramian matrix of the original system. Surprisingly, we uncover that the scaling behavior is only determined by the controllable part of the network. Furthermore, for the upper and lower bounds of the minimum control energy, we systematically derive the exact scaling behavior in terms of the control time. In addition, for controlling temporal networks composed of a sequence of uncontrollable snapshots, we demonstrate that our method offers a more efficient and effective way for analyzing the associated control energy. Our theoretical results are all verified numerically, which paves the way for implementing realistic target control over much broader applications.

Robust and Secure Resource Allocation for ISAC Systems: A Novel Optimization Framework for Variable-Length Snapshots

In this paper, we investigate the robust resource allocation design for secure communication in an integrated sensing and communication (ISAC) system. A multi-antenna dual-functional radar-communication (DFRC) base station (BS) serves multiple single-antenna legitimate users and senses for targets simultaneously, where already identified targets are treated as potential single-antenna eavesdroppers. The DFRC BS scans a sector with a sequence of dedicated beams, and the ISAC system takes a snapshot of the environment during the transmission of each beam. Based on the sensing information, the DFRC BS can acquire the channel state information (CSI) of the potential eavesdroppers. Different from existing works that focused on the resource allocation design for a single snapshot, in this paper, we propose a novel optimization framework that jointly optimizes the communication and sensing resources over a sequence of snapshots with adjustable durations. Besides, artificial noise (AN) is exploited by the BS for joint sensing and physical layer security provisioning. To this end, we jointly optimize the duration of each snapshot, the beamforming vector, and the covariance matrix of the AN for maximization of the system sum secrecy rate over a sequence of snapshots while guaranteeing a minimum required average achievable rate and a maximum information leakage constraint for each legitimate user. The resource allocation algorithm design is formulated as a non-convex optimization problem, where we account for the imperfect CSI of both the legitimate users and the potential eavesdroppers. To make the problem tractable, we derive a bound for the uncertainty region of the potential eavesdroppers’ small-scale fading based on a safe approximation, which facilitates the development of a block coordinate descent-based iterative algorithm for obtaining an efficient suboptimal solution. Simulation results illustrate that the proposed scheme can significantly enhance the physical layer security of ISAC systems compared to three baseline schemes. Moreover, compared to the conventional multi-stage approach for ISAC system design, the proposed approach based on variable-length snapshots not only facilitates a highly-directional offline sensing beam design but also allows us to flexibly prioritize communication or sensing depending on the application scenario.

Correlations of network trajectories

Temporal networks model how the interaction between elements in a complex system evolve over time. Just like complex systems display collective dynamics, here we interpret temporal networks as trajectories performing a collective motion in graph space, following a latent graph dynamical system. Under this paradigm, we propose a way to measure how the network pulsates and collectively fluctuates over time and space. To this aim, we extend the notion of linear correlations function to the case of sequences of network snapshots, i.e. a network trajectory. We construct stochastic and deterministic graph dynamical systems and show that the emergent collective correlations are well captured by simple measures, and illustrate how these patterns are revealed in empirical networks arising in different domains.

A Deep Learning Approach for Flight Delay Prediction Through Time-Evolving Graphs

Flight delay prediction has recently gained growing popularity due to the significant role it plays in efficient airline and airport operation. Most of the previous prediction works consider the single-airport scenario, which overlooks the time-varying spatial interactions hidden in airport networks. In this paper, the flight delay prediction problem is investigated from a network perspective (i.e., multi-airport scenario). To model the time-evolving and periodic graph-structured information in the airport network, a flight delay prediction approach based on the graph convolutional neural network (GCN) is developed in this paper. More specifically, regarding that GCN cannot take both delay time-series and time-evolving graph structures as inputs, a temporal convolutional block based on the Markov property is employed to mine the time-varying patterns of flight delays through a sequence of graph snapshots. Moreover, considering that unknown occasional air routes under emergency may result in incomplete graph-structured inputs for GCN, an adaptive graph convolutional block is embedded into the proposed method to expose spatial interactions hidden in airport networks. Through extensive experiments, it has been shown that the proposed approach outperforms benchmark methods with a satisfying accuracy improvement at the cost of acceptable execution time. The obtained results reveal that deep learning approach based on graph-structured inputs have great potentials in the flight delay prediction problem.

Cross-Temporal Snapshot Alignment for Dynamic Multi-Relational Networks

A dynamic network is often represented as a sequence of snapshots evolving over time. In certain real-world scenarios, the identities of nodes in snapshots of a dynamic network are unknown and need to be figured out. To deal with such a challenge, recently, the task of cross-temporal snapshot alignment for dynamic networks is proposed, which aims to match equivalent nodes across temporal snapshots of a dynamic network given a small set of identified nodes. However, in many dynamic multi-relational networks like temporal knowledge graphs, the relation type information of edges, which can be useful for the alignment task, is neglected by existing methods. In this paper, we focus on a similar task but pay special attention to dynamic multi-relational networks. We propose a Relation-Aware Cross-Temporal Snapshot Alignment model (RCTSA) that incorporates time-dependent topological structure information into temporal node embeddings and temporal relation embeddings. To disentangle time-dependent information and time-independent information of the dynamic multi-relational network, RCTSA maintains a time embedding for each snapshot to preserve the temporal information which is incorporated into entity embeddings and relation embeddings to get the temporal embeddings. After training, the learned entity embeddings of unidentified nodes together with time embeddings can be used for the alignment task. Experimental results on real-world dynamic multi-relational networks demonstrate the effectiveness of our model.

UTP semantics for the MCA ARMv8 architecture

Hardware architectures like x86 and ARM provide relaxed memory models for efficiency reasons. The revised ARMv8 architecture is multi-copy atomic (MCA), which brings relaxed-memory effects through thread-local out-of-order, speculative execution and thread-local buffering. In this paper, we investigate the trace semantics for the MCA ARMv8 architecture, acting in the denotational semantics style based on Unifying Theories of Programming (UTP). In order to present all the valid execution results including reorderings of any program under ARMv8, a trace expressed as a sequence of snapshots is introduced, and it relies heavily on various dependencies among program statements. We also study the algebraic laws for MCA ARMv8, including a set of sequential and parallel expansion laws, which are implemented in the rewriting engine Maude. The concept of head normal form is explored for each program, and every program is described in the form of guarded choice which can model the execution of a program with reorderings. Therefore, the linearizability for ARMv8 is supported. Finally, we provide a strategy for deriving the trace semantics from the algebraic semantics. Using the strategy, the trace semantics for each program can be calculated.

Hurst analysis of dynamic networks.

The sequence of network snapshots with time stamps is an effective tool for describing system dynamics. First, this article constructs a multifractal analysis of a snapshot network, in which the Hurst integral is used to describe the fractal structure hidden in structural dynamics. Second, we adjusted the network model and conducted comparative analysis to clarify the meaning of the Hurst exponent and found that the snapshot network usually includes multiple fractal structures, such as local and global fractal structures. Finally, we discussed the fractal structure of two real network datasets. We found that the real snapshot network also includes rich dynamics, which can be distinguished by the Hurst exponent. In particular, the dynamics of financial networks includes multifractal structures. This article provides a perspective to study the dynamic networks, thereby indirectly describing the fractal characteristics of complex system dynamics.

Online Spatio-Temporal Crowd Flow Distribution Prediction for Complex Metro System

As a key mission of the modern traffic management, crowd flow prediction (CFP) benefits in many tasks of intelligent transportation services. However, most existing techniques focus solely on forecasting entrance and exit flows of metro stations that do not provide enough useful knowledge for traffic management. In practical applications, managers desperately want to solve the problem of getting the potential passenger distributions to help authorities improve transport services, termed as crowd flow distribution (CFD) forecasts. Therefore, to improve the quality of transportation services, we proposed three spatiotemporal models to effectively address the network-wide CFD prediction problem based on the online latent space (OLS) strategy. Our models take into account the various trending patterns and climate influences, as well as the inherent similarities among different stations that are able to predict both CFD and entrance and exit flows precisely. In our online systems, a sequence of CFD snapshots is used as the training data. The latent attribute evolutions of different metro stations can be learned from the previous trend and do the next prediction based on the transition patterns. All the empirical results demonstrate that the three developed models outperform all the other state-of-the-art approaches on three large-scale real-world datasets.

Neural models for the cross-species recognition of dynamic facial expressions

Dynamic facial expression recognition is an essential skill of primate communication. While the neural mechanisms to recognize static facial expressions has been extensively investigated, they remain largely unclear for dynamic facial expressions. We studied plausible neural encoding mechanisms, exploiting highly controlled and realistic stimulus sets generated by computer graphics, which are also used in electrophysiological experiments. METHODS: Combining mechanisms from physiologically plausible neural models for the recognition of dynamic bodies (Giese & Poggio, 2003), static faces (Giese & Leopold, 2005) and architectures from computer vision (Simonyan et al., 2014), we devised models for the recognition of dynamic facial expressions. The first model is example-based, and encodes dynamic expressions as temporal sequences of snapshots, exploiting a sequence-selective recurrent neural network. The second model exploits norm-referenced encoding, where face-space neurons are tuned to the differences between the actual stimulus frame and a reference face, the neutral facial expression. The dynamic expressions are recognized by differentiating the responses of these face-space neurons. We tested the models with high-quality human and monkey avatars, animated with motion capture data from both species, controlling expression by motion morphing. RESULTS: Both models recognize reliably dynamic facial expressions of humans and monkeys. However, the predicted behaviour of face-tuned neurons is very different for both models. The norm-referenced model shows a highly gradual, almost linear dependence of the neuron activity with the expressivity of the stimuli, while the neurons in the example-based model show very limited capability of generalization to expressions with varying strength. We also explored if the models explain the human capability of humans to recognize human expressions on monkey faces (Taubert et al. 2020). CONCLUSIONS: The two physiologically plausible models accomplish the recognition of dynamic faces and make distinguishable predictions for physiological experiments, where norm-referenced encoding might support transfer of expression recognition across different head shapes.

Dynamic graph convolutional networks with attention mechanism for rumor detection on social media

Social media has become an ideal platform for the propagation of rumors, fake news, and misinformation. Rumors on social media not only mislead online users but also affect the real world immensely. Thus, detecting the rumors and preventing their spread became an essential task. Some of the recent deep learning-based rumor detection methods, such as Bi-Directional Graph Convolutional Networks (Bi-GCN), represent rumor using the completed stage of the rumor diffusion and try to learn the structural information from it. However, these methods are limited to represent rumor propagation as a static graph, which isn’t optimal for capturing the dynamic information of the rumors. In this study, we propose novel graph convolutional networks with attention mechanisms, named Dynamic GCN, for rumor detection. We first represent rumor posts with their responsive posts as dynamic graphs. The temporal information is used to generate a sequence of graph snapshots. The representation learning on graph snapshots with attention mechanism captures both structural and temporal information of rumor spreads. The conducted experiments on three real-world datasets demonstrate the superiority of Dynamic GCN over the state-of-the-art methods in the rumor detection task.

Adiabatic waveforms for extreme mass-ratio inspirals via multivoice decomposition in time and frequency

We compute adiabatic waveforms for extreme mass-ratio inspirals (EMRIs) by ``stitching'' together a long inspiral waveform from a sequence of waveform snapshots, each of which corresponds to a particular geodesic orbit. We show that the complicated total waveform can be regarded as a sum of ``voices.'' Each voice evolves in a simple way on long timescales, a property which can be exploited to efficiently produce waveform models that faithfully encode the properties of EMRI systems. We look at examples for a range of different orbital geometries: spherical orbits, equatorial eccentric orbits, and one example of generic (inclined and eccentric) orbits. To our knowledge, this is the first calculation of a generic EMRI waveform that uses strong-field radiation reaction. We examine waveforms in both the time and frequency domains. Although EMRIs evolve slowly enough that the stationary phase approximation (SPA) to the Fourier transform is valid, the SPA calculation must be done to higher order for some voices, since their instantaneous frequency can change from chirping forward ($\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{f}>0$) to chirping backward ($\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{f}<0$). The approach we develop can eventually be extended to more complete EMRI waveform models---for example, to include effects neglected by the adiabatic approximation, such as the conservative self-force and spin-curvature coupling.

Effective Link Prediction with Topological and Temporal Information using Wavelet Neural Network Embedding

AbstractTemporal networks are networks that edges evolve over time, hence link prediction in temporal networks aims at inferring new edges based on a sequence of network snapshots. In this paper, we propose a graph wavelet neural network (TT-GWNN) framework using topological and temporal features for link prediction in temporal networks. To capture topological and temporal features, we develope a second-order weighted random walk sampling algorithm. It combines network snapshots with both first-order and second-order weights into one weighted graph. Moreover, it incorporates a damping factor to assign greater weights to more recent snapshots. Next, we adopt graph wavelet neural networks to embed the vertices and use gated recurrent units for predicting new links. Extensive experiments demonstrate that TT-GWNN can effectively predict links on temporal networks.