Temporal Edge Research Articles

Earliest location of glaucomatous retinal nerve fibre layer damage is determined by intact baseline RNFL thickness profile

Background/aimsTo identify whether an intact retinal nerve fibre layer (RNFL) thickness profile could determine the location of the earliest RNFL defect in glaucoma.MethodsRetrospective longitudinal cohort study of patients with initial...

Visual Acuity and Refractive Status in Congenital Macular Coloboma

Purpose We analysed the refractive state and the factors that influence the best-corrected visual acuity (BCVA) in congenital macular coloboma (CMC) to provide new ideas for improving and predicting the vision of patients with CMC. Methods We reported three patients and reviewed 26 cases of CMC reported in the China National Knowledge Infrastructure (CNKI) database. We measured the BCVA, spherical equivalent refraction (SER), the macular coloboma’s diameter and area, and the distance from the macular coloboma’s nasal edge to the optic disc’s temporal edge (DISTANCE). We analyzed the refractive status of CMC and the factors affecting BCVA. Result The three patients with CMC we reported all had myopia. The study also included 26 patients with CMC reported in the CNKI database (9 unilateral, 17 bilateral) and we analyzed the findings of 26 patients with 43 eyes. The mean age at diagnosis was 22.96 ± 2.32 years. All patients underwent a comprehensive eye examination; 39 eyes (91%) had myopia (44% mild myopia; 28% moderate myopia; 28% high myopia); 23 eyes (53%) had a BCVA ≤6/60 and other 20 eyes (47%)>6/60. No correlation was found between SER or BCVA and the macular coloboma’s diameter or area. BCVA correlated positively with DISTANCE (r = 0.603, p < 0.001). No correlation was found between SER and DISTANCE. The study found a significant difference in SER or BCVA between the affected and fellow eyes in patients with unilateral CMC (n = 9, T=-3.259, p = 0.012; Z=-2.521, p = 0.012, respectively). Conclusion CMC seriously affects visual acuity. The refractive state is mostly myopia. We hypothesize that the DISTANCE is related to the integrity of the papillomacular bundle and affects BCVA.

Predictive Modeling with Temporal Graphical Representation on Electronic Health Records.

Deep learning-based predictive models, leveraging Electronic Health Records (EHR), are receiving increasing attention in healthcare. An effective representation of a patient's EHR should hierarchically encompass both the temporal relationships between historical visits and medical events, and the inherent structural information within these elements. Existing patient representation methods can be roughly categorized into sequential representation and graphical representation. The sequential representation methods focus only on the temporal relationships among longitudinal visits. On the other hand, the graphical representation approaches, while adept at extracting the graph-structured relationships between various medical events, fall short in effectively integrate temporal information. To capture both types of information, we model a patient's EHR as a novel temporal heterogeneous graph. This graph includes historical visits nodes and medical events nodes. It propagates structured information from medical event nodes to visit nodes and utilizes time-aware visit nodes to capture changes in the patient's health status. Furthermore, we introduce a novel temporal graph transformer (TRANS) that integrates temporal edge features, global positional encoding, and local structural encoding into heterogeneous graph convolution, capturing both temporal and structural information. We validate the effectiveness of TRANS through extensive experiments on three real-world datasets. The results show that our proposed approach achieves state-of-the-art performance.

Improving Temporal Treemaps by Minimizing Crossings

AbstractTemporal trees are trees that evolve over a discrete set of time steps. Each time step is associated with a node‐weighted rooted tree and consecutive trees change by adding new nodes, removing nodes, splitting nodes, merging nodes, and changing node weights. Recently, two‐dimensional visualizations of temporal trees called temporal treemaps have been proposed, representing the temporal dimension on the x‐axis, and visualizing the tree modifications over time as temporal edges of varying thickness. The tree hierarchy at each time step is depicted as a vertical, one‐dimensional nesting relationships, similarly to standard, non‐temporal treemaps. Naturally, temporal edges can cross in the visualization, decreasing readability. Heuristics were proposed to minimize such crossings in the literature, but a formal characterization and minimization of crossings in temporal treemaps was left open. In this paper, we propose two variants of defining crossings in temporal treemaps that can be combinatorially characterized. For each variant, we propose an exact optimization algorithm based on integer linear programming and heuristics based on graph drawing techniques. In an extensive experimental evaluation, we show that on the one hand the exact algorithms reduce the number of crossings by a factor of 20 on average compared to the previous algorithms. On the other hand, our new heuristics are faster by a factor of more than 100 and still reduce the number of crossings by a factor of almost three.

Temporal compressive edge imaging enabled by a lensless diffuser camera.

Lensless imagers based on diffusers or encoding masks enable high-dimensional imaging from a single-shot measurement and have been applied in various applications. However, to further extract image information such as edge detection, conventional post-processing filtering operations are needed after the reconstruction of the original object images in the diffuser imaging systems. Here, we present the concept of a temporal compressive edge detection method based on a lensless diffuser camera, which can directly recover a time sequence of edge images of a moving object from a single-shot measurement, without further post-processing steps. Our approach provides higher image quality during edge detection, compared with the "conventional post-processing method." We demonstrate the effectiveness of this approach by both numerical simulation and experiments. The proof-of-concept approach can be further developed with other image post-processing operations or versatile computer vision assignments toward task-oriented intelligent lensless imaging systems.

Static graph approximations of dynamic contact networks for epidemic forecasting.

Epidemic modeling is essential in understanding the spread of infectious diseases like COVID-19 and devising effective intervention strategies to control them. Recently, network-based disease models have integrated traditional compartment-based modeling with real-world contact graphs and shown promising results. However, in an ongoing epidemic, future contact network patterns are not observed yet. To address this, we use aggregated static networks to approximate future contacts for disease modeling. The standard method in the literature concatenates all edges from a dynamic graph into one collapsed graph, called the full static graph. However, the full static graph often leads to severe overestimation of key epidemic characteristics. Therefore, we propose two novel static network approximation methods, DegMST and EdgeMST, designed to preserve the sparsity of real world contact network while remaining connected. DegMST and EdgeMST use the frequency of temporal edges and the node degrees respectively to preserve sparsity. Our analysis show that our models more closely resemble the network characteristics of the dynamic graph compared to the full static ones. Moreover, our analysis on seven real-world contact networks suggests EdgeMST yield more accurate estimations of disease dynamics for epidemic forecasting when compared to the standard full static method.

Exact and approximation algorithms for covering timeline in temporal graphs

AbstractWe consider a variant of vertex cover on temporal graphs that has been recently defined for summarization of timeline activities in temporal graphs. The problem has been proved to be NP-hard, even for several restrictions of the time domain and vertex degree. We present novel algorithmic contributions for the problem and we give an approximation algorithm of factor $$O(T \log {n})$$ O ( T log n ) , on a temporal graph of T timestamps and n vertices. We focus then on the NP-hard restriction of the problem, where at most one temporal edge is defined in each timestamp. For this restriction we present a $$4(T-1)$$ 4 ( T - 1 ) approximation algorithm and a parameterized algorithm (a reduction to kernel) for parameter the cost, called span, of the solution.

Identifying temporal pathways using biomarkers in the presence of latent non-Gaussian components.

Time-series data collected from a network of random variables are useful for identifying temporal pathways among the network nodes. Observed measurements may contain multiple sources of signals and noises, including Gaussian signals of interest and non-Gaussian noises, including artifacts, structured noise, and other unobserved factors (eg, genetic risk factors, disease susceptibility). Existing methods, including vector autoregression (VAR) and dynamic causal modeling do not account for unobserved non-Gaussian components. Furthermore, existing methods cannot effectively distinguish contemporaneous relationships from temporal relations. In this work, we propose a novel method to identify latent temporal pathways using time-series biomarker data collected from multiple subjects. The model adjusts for the non-Gaussian components and separates the temporal network from the contemporaneous network. Specifically, an independent component analysis (ICA) is used to extract the unobserved non-Gaussian components, and residuals are used to estimate the contemporaneous and temporal networks among the node variables based on method of moments. The algorithm is fast and can easily scale up. We derive the identifiability and the asymptotic properties of the temporal and contemporaneous networks. We demonstrate superior performance of our method by extensive simulations and an application to a study of attention-deficit/hyperactivity disorder (ADHD), where we analyze the temporal relationships between brain regional biomarkers. We find that temporal network edges were across different brain regions, while most contemporaneous network edges were bilateral between the same regions and belong to a subset of the functional connectivity network.

Estimates of Temporal Edge Detection Filters in Human Vision

Edge detection is an important process in human visual processing. However, as far as we know, few attempts have been made to map the temporal edge detection filters in human vision. To that end, we devised a user study and collected data from which we derived estimates of human temporal edge detection filters based on three different models, including the derivative of the infinite symmetric exponential function and temporal contrast sensitivity function. We analyze our findings using several different methods, including extending the filter to higher frequencies than were shown during the experiment. In addition, we show a proof of concept that our filter may be used in spatiotemporal image quality metrics by incorporating it into a flicker detection pipeline.

TransformerG2G: Adaptive time-stepping for learning temporal graph embeddings using transformers

Dynamic graph embedding has emerged as a very effective technique for addressing diverse temporal graph analytic tasks (i.e., link prediction, node classification, recommender systems, anomaly detection, and graph generation) in various applications. Such temporal graphs exhibit heterogeneous transient dynamics, varying time intervals, and highly evolving node features throughout their evolution. Hence, incorporating long-range dependencies from the historical graph context plays a crucial role in accurately learning their temporal dynamics. In this paper, we develop a graph embedding model with uncertainty quantification, TransformerG2G, by exploiting the advanced transformer encoder to first learn intermediate node representations from its current state (t) and previous context (over timestamps [t−1,t−l], l is the length of context). Moreover, we employ two projection layers to generate lower-dimensional multivariate Gaussian distributions as each node’s latent embedding at timestamp t. We consider diverse benchmarks with varying levels of “novelty” as measured by the TEA (Temporal Edge Appearance) plots. Our experiments demonstrate that the proposed TransformerG2G model outperforms conventional multi-step methods and our prior work (DynG2G) in terms of both link prediction accuracy and computational efficiency, especially for high degree of novelty. Furthermore, the learned time-dependent attention weights across multiple graph snapshots reveal the development of an automatic adaptive time stepping enabled by the transformer. Importantly, by examining the attention weights, we can uncover temporal dependencies, identify influential elements, and gain insights into the complex interactions within the graph structure. For example, we identified a strong correlation between attention weights and node degree at the various stages of the graph topology evolution.

22 Cognitive Reserve's Relationship to Brain Burden in Parkinson's Disease Without Dementia

Objective:Individuals with Parkinson's disease (PD) have varying trajectories of cognitive decline. One reason for this heterogeneity may be "cognitive reserve": where higher education/IQ/current mental engagement compensates for increasing brain burden (Stern et al., 2020). With few exceptions, most studies examining cognitive reserve in PD fail to include brain metrics. This study's goal was to examine whether cognitive reserve moderated the relationship between neuroimaging indices of brain burden (diffusion free water fraction and T2-weighted white matter changes) and two commonly impaired domains in PD: executive function and memory. We hypothesized cognitive reserve would mitigate the relationship between higher brain burden and worse cognitive performance.Participants and Methods:Participants included 108 individuals with PD without dementia (age mean=67.9±6.3, education mean=16.6±2.5) who were prospectively recruited for two NIH-funded projects at the University of Florida. All received neuropsychological measures of executive function (Trails B, Stroop, Letter Fluency) and memory (delayed recall: Hopkin's Verbal Learning Test-Revised, WMS-III Logical Memory). Domain specific z-score composites were created using data from age/education matched non-PD peer controls (N=62). For the Cognitive Reserve (CR) proxy, a z-score composite included years of education, WASI-II Vocabulary, and Wechsler Test of Adult Reading. At the time of testing, participants completed multiple MRI scans (T1-weighted, diffusion, Fluid Attenuated Inversion Recovery) from which the following were extracted: 1) whole-brain free water within the white matter (a measure of microstructural integrity and neuroinflammation), 2) white matter hyperintensities/white matter total volume (WMH/WMV), and bilaterally-averaged edge weights of white matter connectivity between 3) dorsolateral prefrontal cortex and caudate and 4) entorhinal cortex and hippocampi. Separate linear regressions for each brain metric used executive function and memory composites as dependent variables; predictors were age, CR proxy, respective brain metric, and a residual centered interaction term (brain metric*CR proxy). Identical models were run in dichotomized short and long disease duration groups (median split=6 years).Results:In all models, a lower CR proxy significantly predicted worse executive function (WMH/WMV: beta=0.49, free water: beta=0.54, frontal edge weight: beta=0.49, p's&lt;0.001) and memory (WMH/WMV: beta=0.42, free water: beta=0.35, temporal edge weight: beta=0.39, p's &lt;0.01). For neuroimaging metrics, higher free water significantly predicted worse executive function (beta=-0.39, p=0.002) but not memory. No other brain metrics were significant predictors of either domain. Accounting for PD duration, higher free water predicted worse executive function for those with both short (beta=-0.49, p=0.04) and long disease duration (beta=-0.48, p=0.02). Specifically in those with long disease duration, higher free water (beta=-0.57 p=0.02) and lower edge weights between entorhinal cortex and hippocampi (beta=0.30, p=0.03) predicted worse memory. Overall, no models contained significant interactions between the CR proxy and any brain metric.Conclusions:Results replicate previous work showing that a cognitive reserve proxy relates to cognition. However, cognitive reserve did not moderate brain burden's relationship to cognition. Across the sample, greater neuroinflammation was associated with worse executive function. For those with longer disease duration, higher neuroinflammation and lower medial temporal white matter connectivity related to worse memory. Future work should examine other brain burden metrics to determine whether/how cognitive reserve influences the cognitive trajectory of PD.

Electromagnetic Spatiotemporal Differentiation Meta‐Devices

AbstractSpatiotemporal optical computing devices that can perform mathematical operations in both spatial and temporal domains can provide unprecedented measures to build efficient and real‐time information processing systems. It is particularly important to realize the comprehensive functions in a compact design for better integration with electronic components. In this work, an analog spatiotemporal differentiator in microwaves based on an asymmetrical metasurface that has a phase singularity in the spatiotemporal domain is experimentally demonstrated. It is shown that this structure can give rise to a spatiotemporal transfer function required by an ideal first‐order differentiator in both spatial and temporal domains by tailoring the unidirectional excitation of spoof surface plasmon polaritons (SSPPs). The spatial edge detection is performed utilizing a metallic slit, and the temporal differentiation capability of the device is examined by Gaussian‐like temporal pulses of different widths. It is further confirmed that the differentiator demonstrated here can detect sharp changes in spatiotemporal pulses even with intricate profiles and theoretically estimated the resolution limits of the spatial and temporal edge detection. It is also shown that the pulse input after passing the spatiotemporal differentiator implemented here could carry a transverse orbital angular momentum (OAM) with a fractal topology charge.

FPGN: follower prediction framework for infectious disease prevention

In recent years, how to prevent the widespread transmission of infectious diseases in communities has been a research hot spot. Tracing close contact with infected individuals is one of the most severe problems. In this work, we present a model called Follower Prediction Graph Network (FPGN) to identify high-risk visitors, which is known as follower prediction. The model is designed to identify visitors who may be infected with a disease by tracking their activities at the exact location of infected visitors. FPGN is inspired by the state-of-the-art temporal graph edge prediction algorithm TGN and draws on the shortcomings of existing algorithms. It utilizes graph structure information based on (alpha , beta )-core, time interval statistics by using the statistics of timestamp information, and a GAT-based prediction module to achieve high accuracy in follower prediction. Extensive experiments are conducted on two real datasets, demonstrating the progress of FPGN. The experimental results show that FPGN can achieve the highest results compared with other SOTA baselines. Its AP scores are higher than 0.46, and its AUC scores are higher than 0.62.

Time-Aware Dynamic Graph Embedding for Asynchronous Structural Evolution

Dynamic graphs refer to graphs whose structure dynamically changes over time. Despite the benefits of learning vertex representations (i.e., embeddings) for dynamic graphs, existing works merely view a dynamic graph as a sequence of changes within the vertex connections, neglecting the crucial asynchronous nature of such dynamics where the evolution of each local structure starts at different times and lasts for various durations. To maintain asynchronous structural evolutions within the graph, we innovatively formulate dynamic graphs as temporal edge sequences associated with joining time of vertices (ToV) and timespan of edges (ToE). Then, a time-aware Transformer is proposed to embed vertices' dynamic connections and ToEs into the learned vertex representations. Meanwhile, we treat each edge sequence as a whole and embed its ToV of the first vertex to further encode the time-sensitive information. Extensive evaluations on several datasets show that our approach outperforms the state-of-the-art in a wide range of graph mining tasks. At the same time, it is very efficient and scalable for embedding large-scale dynamic graphs.

Reconfigurable Spatiotemporal Optical Signal Processors

AbstractAnalogue optical computing offers a promising approach for developing super‐fast computation techniques, benefiting from its extraordinary parallel processing capability, low energy consumption, and high integrability compared to digital electronic technologies. In this work, a reconfigurable spatiotemporal optical signal processor using the phase‐change material vanadium dioxide (VO2) to further expand the processing bandwidth and enrich the operation functions is demonstrated. As a specific example, a meta‐device is designed that can switch between a first‐order differentiator and a good reflector in the spatiotemporal domain by controlling the operation temperature. It is shown that the spatiotemporal transfer functions can be precisely engineered to meet the requirements for ideal first‐order differentiation and bright‐field imaging. This approach enables high‐accuracy spatial and temporal signal processing, as demonstrated by inspecting Gaussian signals. The theoretical evaluation determines the resolution limits of spatial and temporal edge detection. It also highlights that the device can perform spatiotemporal signal processing for pulses with complex profiles. The presented reconfigurable spatiotemporal optical signal processor holds great potential in applications such as remote sensing and fast imaging processing, among others.

Stable distance of persistent homology for dynamic graph comparison

Persistent homology theory provides approaches for analyzing topological features, which is now widely applied in graph comparison on social networks, biological networks, and co-location networks. These approaches utilize filtration techniques to extract the topological properties of a graph and construct vectorizations that represent these properties for further computation. However, most existing methods are designed for static scenarios and are unsuitable for the time-varying structure in realistic dynamic graphs. In this paper, we propose the Stable Distance of Persistent Homology (SDPH) to compare and quantify the differences in the topological properties of dynamic graphs. In detail, we design Dynamic Dowker Filtration (DDF) to map dynamic graph to a persistent complex based on the ɛ-interleaved theory, which enables us to trace the structure holes formed by the accumulation of temporal edge via computing the persistent homology. DDF exhibits stability and duality, inducing a time-structure triangle inequality. Based on this inequality, we finally construct Time-interlevel Kernel (TIK) for vectorizing the extracted topological features with an inner product. We conduct the graph clustering and classification experiments on synthetic and real-world datasets. Experimental results show that the proposed SDPH outperforms the baseline methods in these tasks and validate that the proposed SDPH can effectively measure the topological difference of dynamic graphs. Through SDPH, we would provide insight and inspiration on how to apply persistent homology theory to dynamic graph analysis.

Untangling temporal graphs of bounded degree

In this contribution we consider a variant of the vertex cover problem in temporal graphs that has been recently introduced to summarize timeline activities in social networks. The problem is NP-hard, even when the time domain considered consists of two timestamps. We further analyze the complexity of this problem, focusing on temporal graphs of bounded degree. We prove that the problem is NP-hard when (1) each vertex has degree at most one in each timestamp and (2) each vertex is connected with at most three neighbors, has degree at most two in each timestamp and the time domain consists of three timestamps. On the other hand, we prove that the problem is in P when each vertex is connected with at most two neighbors. Then we present a fixed-parameter algorithm for the restriction where we bound the number of interactions in each timestamp and the length of the interval where a vertex has incident temporal edges.

A large-scale data security detection method based on continuous time graph embedding framework

Graph representation learning has made significant strides in various fields, including sociology and biology, in recent years. However, the majority of research has focused on static graphs, neglecting the temporality and continuity of edges in dynamic graphs. Furthermore, dynamic data are vulnerable to various security threats, such as data privacy breaches and confidentiality attacks. To tackle this issue, the present paper proposes a data security detection method based on a continuous-time graph embedding framework (CTDGE). The framework models temporal dependencies and embeds data using a graph representation learning method. A machine learning algorithm is then employed to classify and predict the embedded data to detect if it is secure or not. Experimental results show that this method performs well in data security detection, surpassing several dynamic graph embedding methods by 5% in terms of AUC metrics. Furthermore, the proposed framework outperforms other dynamic baseline methods in the node classification task of large-scale graphs containing 4321477 temporal information edges, resulting in a 10% improvement in the F1 score metric. The framework is also robust and scalable for application in various data security domains. This work is important for promoting the use of continuous-time graph embedding framework in the field of data security.

Temporal SIR-GN: Efficient and Effective Structural Representation Learning for Temporal Graphs

Node representation learning (NRL) generates numerical vectors (embeddings) for the nodes of a graph. Structural NRL specifically assigns similar node embeddings for those nodes that exhibit similar structural roles. This is in contrast with its proximity-based counterpart, wherein similarity between embeddings reflects spatial proximity among nodes. Structural NRL is useful for tasks such as node classification where nodes of the same class share structural roles, though there may exist a distant, or no path between them. Athough structural NRL has been well-studied in static graphs, it has received limited attention in the temporal setting. Here, the embeddings are required to represent the evolution of nodes' structural roles over time. The existing methods are limited in terms of efficiency and effectiveness: they scale poorly to even moderate number of timestamps, or capture structural role only tangentially. In this work, we present a novel unsupervised approach to structural representation learning for temporal graphs that overcomes these limitations. For each node, our approach clusters then aggregates the embedding of a node's neighbors for each timestamp, followed by a further temporal aggregation of all timestamps. This is repeated for (at most) d iterations, so as to acquire information from the d -hop neighborhood of a node. Our approach takes linear time in the number of overall temporal edges, and possesses important theoretical properties that formally demonstrate its effectiveness. Extensive experiments on synthetic and real datasets show superior performance in node classification and regression tasks, and superior scalability of our approach to large graphs.

Decoupled Graph Neural Networks for Large Dynamic Graphs

Real-world graphs, such as social networks, financial transactions, and recommendation systems, often demonstrate dynamic behavior. This phenomenon, known as graph stream, involves the dynamic changes of nodes and the emergence and disappearance of edges. To effectively capture both the structural and temporal aspects of these dynamic graphs, dynamic graph neural networks have been developed. However, existing methods are usually tailored to process either continuous-time or discrete-time dynamic graphs, and cannot be generalized from one to the other. In this paper, we propose a decoupled graph neural network for large dynamic graphs, including a unified dynamic propagation that supports efficient computation for both continuous and discrete dynamic graphs. Since graph structure-related computations are only performed during the propagation process, the prediction process for the downstream task can be trained separately without expensive graph computations, and therefore any sequence model can be plugged-in and used. As a result, our algorithm achieves exceptional scalability and expressiveness. We evaluate our algorithm on seven real-world datasets of both continuous-time and discrete-time dynamic graphs. The experimental results demonstrate that our algorithm achieves state-of-the-art performance in both kinds of dynamic graphs. Most notably, the scalability of our algorithm is well illustrated by its successful application to large graphs with up to over a billion temporal edges and over a hundred million nodes.