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Accurate and timely forecasting of traffic on local road networks is crucial for deploying effective dynamic traffic control, advanced route planning, and navigation services. This task is particularly challenging due to complex spatio-temporal dependencies arising from non-Euclidean spatial relations in road networks and non-linear temporal dynamics influenced by changing road conditions. This paper introduces the spatio-temporal network embedding (STNE) model, a novel deep learning framework tailored for learning and forecasting graph-structured traffic data over extended input sequences. Unlike traditional convolutional neural networks (CNNs), the model employs graph convolutional networks (GCNs) to capture the spatial characteristics of local road network topologies. Moreover, the segmentation of very long input traffic data into multiple sub-sequences, based on significant temporal properties such as closeness, periodicity, and trend, is performed. Multi-dimensional long short-term memory neural networks (MDLSTM) are utilized to flexibly access multi-dimensional context. Experimental results demonstrate that the STNE model surpasses state-of-the-art traffic forecasting benchmarks on two large-scale real-world traffic datasets.

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This study advances the field of infectious disease forecasting by introducing a novel approach to micro-level contact modeling, leveraging human movement patterns to generate realistic temporal-dynamic networks. Through the incorporation of human mobility models and parameter tuning, this research presents an innovative method for simulating micro-level encounters that closely mirror infection dynamics within confined spaces. Central to our methodology is the application of Bayesian optimization for parameter selection, which refines our models to emulate both the properties of real-world infection curves and the characteristics of network properties. Typically, large-scale epidemiological simulations overlook the specifics of human mobility within confined spaces or rely on overly simplistic models. By focusing on the distinct aspects of infection propagation within specific locations, our approach strengthens the realism of such pandemic simulations. The resulting models shed light on the role of spatial encounters in disease spread and improve the capability to forecast and respond to infectious disease outbreaks. This work not only contributes to the scientific understanding of micro-level transmission patterns but also offers a new perspective on temporal network generation for epidemiological modeling.

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Brain dynamics can be modeled as a temporal brain network starting from the activity of different brain regions in functional magnetic resonance imaging (fMRI) signals. When validating hypotheses about temporal networks, it is important to use an appropriate statistical null model that shares some features with the treated empirical data. The purpose of this work is to contribute to the theory of temporal null models for brain networks by introducing the random temporal hyperbolic (RTH) graph model, an extension of the random hyperbolic (RH) graph, known in the study of complex networks for its ability to reproduce crucial properties of real-world networks. We focus on temporal small-worldness which, in the static case, has been extensively studied in real-world complex networks and has been linked to the ability of brain networks to efficiently exchange information. We compare the RTH graph model with standard null models for temporal networks and show it is the null model that best reproduces the small-worldness of resting brain activity. This ability to reproduce fundamental features of real brain networks, while adding only a single parameter compared with classical models, suggests that the RTH graph model is a promising tool for validating hypotheses about temporal brain networks.

We show that the random temporal hyperbolic (RTH) graph is a suitable null model for testing hypotheses about brain dynamics, after comparing it with the current state of the art and two other geometric null models. The static version of this theoretical model captures properties of various real-world networks, and its temporal version exhibits the temporal small-world property, for which we propose a new proper temporal definition. In particular, we show that the model best reproduces the temporal small-worldness measured in the empirical temporal network extracted from fMRI signals.

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Recent empirical studies have revealed that social interactions among agents in realistic networks merely exist intermittently and occur in a particular sequential order. However, it remains unexplored how to theoretically describe evolutionary dynamics of multiple strategies on temporal networks. Herein, we develop a deterministic theory for studying evolutionary dynamics of any [Formula: see text] pairwise games in structured populations where individuals are connected and organized by temporally activated edges. In the limit of weak selection, we derive replicator-like equations with a transformed payoff matrix characterizing how the mean frequency of each strategy varies over time, and then obtain critical conditions for any strategy to be evolutionarily stable on temporal networks. Interestingly, the re-scaled payoff matrix is a linear combination of the original payoff matrix with an additional one describing local competitions between any pair of different strategies, whose weights are solely determined by network topology and selection intensity. As a particular example, we apply the deterministic theory to analysing the impacts of temporal networks in the mini-ultimatum game, and find that temporally networked population structures result in the emergence of fairness. Our work offers theoretical insights into the subtle effects of network temporality on evolutionary game dynamics.

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OBJECTIVE: The recent SARS-CoV-2 pandemic has exhibited diverse patterns of spread across countries and communities, emphasizing the need to consider the underlying population dynamics in modeling its progression and the importance of evaluating the effectiveness of non-pharmaceutical intervention strategies in combating viral transmission within human communities. Such an understanding requires accurate modeling of the interplay between the community dynamics and the disease propagation dynamics within the community. METHODS: We build on an interaction-driven model of an airborne disease over contact networks that we have defined. Using the model, we evaluate the effectiveness of temporal, spatial, and spatiotemporal social distancing policies. Temporal social distancing involves a pure dilation of the timeline while preserving individual activity potential and thus prolonging the period of interaction; spatial distancing corresponds to social distancing pods; and spatiotemporal distancing pertains to the situation in which fixed subgroups of the overall group meet at alternate times. We evaluate these social distancing policies over real-world interactions' data and over history-preserving synthetic temporal random networks. Furthermore, we evaluate the policies for the disease's with different number of initial patients, corresponding to either the phase in the progression of the infection through a community or the number of patients infected together at the initial infection event. We expand our model to consider the exposure to viral load, which we correlate with the meetings' duration. RESULTS: Our results demonstrate the superiority of decreasing social interactions (i.e., time dilation) within the community over partial isolation strategies, such as the spatial distancing pods and the spatiotemporal distancing strategy. In addition, we found that slow-spreading pathogens (i.e., pathogens that require a longer exposure to infect) spread roughly at the same rate as fast-spreading ones in highly active communities. This result is surprising since the pathogens may follow different paths. However, we demonstrate that the dilation of the timeline considerably slows the spread of the slower pathogens. CONCLUSIONS: Our results demonstrate that the temporal dynamics of a community have a more significant effect on the spread of the disease than the characteristics of the spreading processes.

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Complexity science provides a powerful framework for understanding physical, biological and social systems, and network analysis is one of its principal tools. Since many complex systems exhibit multilateral interactions that change over time, in recent years, network scientists have become increasingly interested in modelling and measuring dynamic networks featuring higher-order relations. At the same time, while network analysis has been more widely adopted to investigate the structure and evolution of law as a complex system, the utility of dynamic higher-order networks in the legal domain has remained largely unexplored. Setting out to change this, we introduce temporal hypergraphs as a powerful tool for studying legal network data. Temporal hypergraphs generalize static graphs by (i) allowing any number of nodes to participate in an edge and (ii) permitting nodes or edges to be added, modified or deleted. We describe models and methods to explore legal hypergraphs that evolve over time and elucidate their benefits through case studies on legal citation and collaboration networks that change over a period of more than 70 years. Our work demonstrates the potential of dynamic higher-order networks for studying complex legal systems, and it facilitates further advances in legal network analysis. This article is part of the theme issue 'A complexity science approach to law and governance'.

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Population structure has been known to substantially affect evolutionary dynamics. Networks that promote the spreading of fitter mutants are called amplifiers of selection, and those that suppress the spreading of fitter mutants are called suppressors of selection. Research in the past two decades has found various families of amplifiers while suppressors still remain somewhat elusive. It has also been discovered that most networks are amplifiers of selection under the birth-death updating combined with uniform initialization, which is a standard condition assumed widely in the literature. In the present study, we extend the birth-death processes to temporal (i.e., time-varying) networks. For the sake of tractability, we restrict ourselves to switching temporal networks, in which the network structure deterministically alternates between two static networks at constant time intervals or stochastically in a Markovian manner. We show that, in a majority of cases, switching networks are less amplifying than both of the two static networks constituting the switching networks. Furthermore, most small switching networks, i.e., networks on six nodes or less, are suppressors, which contrasts to the case of static networks.

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In network analysis, real-world systems may be represented via graph models, where nodes and edges represent the set of biological objects (e.g., genes, proteins, molecules) and their interactions, respectively. This representative knowledge-graph model may also consider the dynamics involved in the evolution of the network (i.e., dynamic networks), in addition to a classic static representation (i.e., static networks). Bioinformatics solutions for network analysis allow knowledge extraction from the features related to a single network of interest or by comparing networks of different species. For instance, we may align a network related to a well known species to a more complex one in order to find a match able to support new hypotheses or studies. Therefore, the network alignment is crucial for transferring the knowledge between species, usually from simplest (e.g., rat) to more complex (e.g., human). Methods: In this paper, we present Dynamic Network Alignment based on Temporal Embedding (DANTE), a novel method for pairwise alignment of dynamic networks that applies the temporal embedding to investigate the topological similarities between the two input dynamic networks. The main idea of DANTE is to consider the evolution of interactions and the changes in network topology. Briefly, the proposed solution builds a similarity matrix by integrating the tensors computed via the embedding process and, subsequently, it aligns the pairs of nodes by performing its own iterative maximization function. Results: The performed experiments have reported promising results in terms of precision and accuracy, as well as good robustness as the number of nodes and time points increases. The proposed solution showed an optimal trade-off between sensitivity and specificity on the alignments produced on several noisy versions of the dynamic yeast network, by improving by ∼18.8% (with a maximum of 20.6%) the Area Under the Receiver Operating Characteristic (ROC) Curve (i.e., AUC or AUROC), compared to two well known methods: DYNAMAGNA++ and DYNAWAVE. From the point of view of quality, DANTE outperformed these by ∼91% as nodes increase and by ∼75% as the number of time points increases. Furthermore, a ∼23.73% improvement in terms of node correctness was reported with our solution on real dynamic networks.

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The large-scale real-time sequencing of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) genomes has allowed for rapid identification of concerning variants through phylogenetic analysis. However, the nature of phylogenetic reconstruction is typically static, in that the relationships between taxonomic units, once defined, are not subject to alterations. Furthermore, most phylogenetic methods are intrinsically batch mode in nature, requiring the presence of the entire data set. Finally, the emphasis of phylogenetics is on relating taxonomical units. These characteristics complicate the application of classical phylogenetics methods to represent relationships in molecular data collected from rapidly evolving strains of an etiological agent, such as SARS-CoV-2, since the molecular landscape is updated continuously as samples are collected. In such settings, variant definitions are subject to epistemological constraints and may change as data accumulate. Furthermore, representing within-variant molecular relationships may be as important as representing between variant relationships. This article describes a novel data representation framework called dynamic epidemiological networks (DENs) along with algorithms that underpin its construction to address these issues. The proposed representation is applied to study the molecular development underlying the spread of the COVID-19 (coronavirus disease 2019) pandemic in two countries: Israel and Portugal spanning a 2-year period from February 2020 to April 2022. The results demonstrate how this framework could be used to provide a multiscale representation of the data by capturing molecular relationships between samples as well as those between variants, automatically identifying the emergence of high frequency variants (lineages), including variants of concern such as Alpha and Delta, and tracking their growth. Additionally, we show how analyzing the evolution of the DEN can help identify changes in the viral population that could not be readily inferred from phylogenetic analysis.

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The temporal organization of biological systems is key for understanding them, but current methods for identifying this organization are often ad hoc and require prior knowledge. We present Phasik, a method that automatically identifies this multiscale organization by combining time series data (protein or gene expression) and interaction data (protein-protein interaction network). Phasik builds a (partially) temporal network and uses clustering to infer temporal phases. We demonstrate the method's effectiveness by recovering well-known phases and sub-phases of the cell cycle of budding yeast and phase arrests of mutants. We also show its general applicability using temporal gene expression data from circadian rhythms in wild-type and mutant mouse models. We systematically test Phasik's robustness and investigate the effect of having only partial temporal information. As time-resolved, multiomics datasets become more common, this method will allow the study of temporal regulation in lesser-known biological contexts, such as development, metabolism, and disease.

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Understanding the evolutionary patterns of real-world complex systems such as human interactions, biological interactions, transport networks, and computer networks is important for our daily lives. Predicting future links among the nodes in these dynamic networks has many practical implications. This research aims to enhance our understanding of the evolution of networks by formulating and solving the link-prediction problem for temporal networks using graph representation learning as an advanced machine learning approach. Learning useful representations of nodes in these networks provides greater predictive power with less computational complexity and facilitates the use of machine learning methods. Considering that existing models fail to consider the temporal dimensions of the networks, this research proposes a novel temporal network-embedding algorithm for graph representation learning. This algorithm generates low-dimensional features from large, high-dimensional networks to predict temporal patterns in dynamic networks. The proposed algorithm includes a new dynamic node-embedding algorithm that exploits the evolving nature of the networks by considering a simple three-layer graph neural network at each time step and extracting node orientation by using Given's angle method. Our proposed temporal network-embedding algorithm, TempNodeEmb, is validated by comparing it to seven state-of-the-art benchmark network-embedding models. These models are applied to eight dynamic protein-protein interaction networks and three other real-world networks, including dynamic email networks, online college text message networks, and human real contact datasets. To improve our model, we have considered time encoding and proposed another extension to our model, TempNodeEmb++. The results show that our proposed models outperform the state-of-the-art models in most cases based on two evaluation metrics.

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Valued in hundreds of billions of Malaysian ringgit, the Bursa Malaysia Financial Services Index's constituents comprise several of the strongest performing financial constituents in Bursa Malaysia's Main Market. Although these constituents persistently reside mostly within the large market capitalization (cap), the existence of the individual constituent's causal influence or intensity relative to each other's performance during uncertain or even certain times is unknown. Thus, the key purpose of this paper is to identify and analyze the individual constituent's causal intensity, from early 2018 (pre-COVID-19) to the end of the year 2021 (post-COVID-19) using Granger causality and Schreiber transfer entropy. Furthermore, network science is used to measure and visualize the fluctuating causal degree of the source and the effected constituents. The results show that both the Granger causality and Schreiber transfer entropy networks detected patterns of increasing causality from pre- to post-COVID-19 but with differing causal intensities. Unexpectedly, both networks showed that the small- and mid-caps had high causal intensity during and after COVID-19. Using Bursa Malaysia's sub-sector for further analysis, the Insurance sub-sector rapidly increased in causality as the year progressed, making it one of the index's largest sources of causality. Even after removing large amounts of weak causal intensities, Schreiber transfer entropy was still able to detect higher amounts of causal sources from the Insurance sub-sector, whilst Granger causal sources declined rapidly post-COVID-19. The method of using directed temporal networks for the visualization of temporal causal sources is demonstrated to be a powerful approach that can aid in investment decision making.

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Pig farming in Ecuador represents an important economic and cultural sector, challenged by classical swine fever (CSF). Recently, the National Veterinary Service (NVS), has dedicated its efforts to control the disease by implementing pig identification, mandatory vaccination against CSF and movement control. Our objective was to characterise pig premises according to risk criteria, to model the effect of movement restriction strategies and to consider the temporal evolution of the network. Social network analysis (SNA), SIRS (susceptible, infected, recovered, susceptible) network modelling and temporal analysis were used. The network contained 751,003 shipments and 6 million pigs from 2017 to 2019. Participating premises consisted of 144,118 backyard farms, 138 industrial farms, 21,337 traders and 51 markets. The 10 most influential markets, in the Andean highlands, received between 500 and 4600 pigs each week. The 10 most influential traders made about 3 shipments with 17 pigs per week. Simulations without control strategy resulted in an average CSF prevalence of 14.4 %; targeted movement restriction reduced the prevalence to 7.2 %, while with random movement restriction it was 13 %. Targeting the top 10 national traders and markets and one of the high-risk premises in every parish was one of the best strategies with the surveillance infrastructure available, highlighting its major influence and epidemiological importance in the network. When comparing the static network with its temporal counterpart, causal fidelity (c = 0.62) showed a 38 % overestimation in the number of transmission paths, also traversing the network required 4.39 steps, lasting approximately 233 days. In conclusion, NVS surveillance strategies could be more efficient by targeting the most at-risk premises, and in particular, taking into account the temporal information would make the risk assessment much more precise. This information could contribute to implement risk-based surveillance reducing the time to eradicate CSF and other infectious animal diseases.

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Effective contact tracing is crucial to containing epidemic spreading without disrupting societal activities, especially during a pandemic. Large gatherings play a key role, potentially favouring superspreading events. However, the effects of tracing in large groups have not been fully assessed so far. We show that in addition to forward tracing, which reconstructs to whom the disease spreads, and backward tracing, which searches from whom the disease spreads, a third 'sideward' tracing is always present, when tracing gatherings. This is an indirect tracing that detects infected asymptomatic individuals, even if they have been neither directly infected by nor directly transmitted the infection to the index case. We analyse this effect in a model of epidemic spreading for SARS-CoV-2, within the framework of simplicial activity-driven temporal networks. We determine the contribution of the three tracing mechanisms to the suppression of epidemic spreading, showing that sideward tracing induces a non-monotonic behaviour in the tracing efficiency, as a function of the size of the gatherings. Based on our results, we suggest an optimal choice for the sizes of the gatherings to be traced and we test the strategy on an empirical dataset of gatherings on a university campus.

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Modern theoretical models of Alcohol Use Disorder (AUD) highlight the different functional roles played by various mechanisms associated with different symptoms. Symptom network models (SNMs) offer one approach to modeling AUD symptomatology in a way that could reflect these processes and provide important information on the progression and persistence of disorder. However, much of the research conducted using SNMs relies on cross-sectional data, which has raised questions regarding the extent they reflect dynamic processes. The current study aimed to (a) examine symptom networks of AUD and (b) compare the extent to which cross-sectional network models had similar structures and interpretations as longitudinal network models. 17,360 participants from Wave 1 (2001-2002) and Wave 2 (2003-2004) of the National Epidemiological Survey on Alcohol and Related Conditions (NESARC) were used to model cross-sectional and longitudinal AUD symptom networks. The cross-sectional analyses demonstrate high replicability across waves and central symptoms consistent with other cross-sectional studies on addiction networks. The longitudinal network shared much less similarity than the cross-sectional networks and had a substantially different structure. Given the increasing attention given to the network perspective in psychopathology research, the results of this study raise concerns about interpreting cross-sectional symptom networks as representative of temporal changes occurring within a psychological disorder. We conclude that the psychological symptom network literature should be bolstered with additional research on longitudinal network models.

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Many tasks in graph machine learning, such as link prediction and node classification, are typically solved using representation learning. Each node or edge in the network is encoded via an embedding. Though there exists a lot of network embeddings for static graphs, the task becomes much more complicated when the dynamic (i.e., temporal) network is analyzed. In this paper, we propose a novel approach for dynamic network representation learning based on Temporal Graph Network by using a highly custom message generating function by extracting Causal Anonymous Walks. We provide a benchmark pipeline for the evaluation of temporal network embeddings. This work provides the first comprehensive comparison framework for temporal network representation learning for graph machine learning problems involving node classification and link prediction in every available setting. The proposed model outperforms state-of-the-art baseline models. The work also justifies their difference based on evaluation in various transductive/inductive edge/node classification tasks. In addition, we show the applicability and superior performance of our model in the real-world downstream graph machine learning task provided by one of the top European banks, involving credit scoring based on transaction data.

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A discrete-time deterministic epidemic model is proposed to better understand the contagious dynamics and the behaviour observed in the incidence of real infectious diseases. For this purpose, we analyse a SIRS model both in a random-mixing approach and in a small-world network formulation. The models include the basic parameters that characterize an epidemic: infection and recovery times, as well as mechanisms of contagion. Depending on the parameters, the random-mixing model has different types of behaviour of an epidemic: pathogen extinction; endemic infection; sustained oscillations and dynamic extinction. Spatial effects are included in our network-based approach, where each individual of a population is represented by a node of a small-world network. Our network-based approach includes rewiring connections to account for time-varying network structure, a consequence of the natural response to the emergence of an epidemic (e.g. avoiding contacts with infected individuals). Random and adaptive rewiring conditions are analysed and numerical simulation are made. A comparison of model predictions with the actual effects of COVID-19 infection on population that occurred in Italy and France is produced. Results of the time series of infected people show that our adaptive evolving networks represent effective strategies able to decrease the epidemic spreading.

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Networks are well-established representations of social systems, and temporal networks are widely used to study their dynamics. However, going from temporal network data (i.e. a stream of interactions between individuals) to a representation of the social group's evolution remains a challenge. Indeed, the temporal network at any specific time contains only the interactions taking place at that time and aggregating on successive time-windows also has important limitations. Here, we present a new framework to study the dynamic evolution of social networks based on the idea that social relationships are interdependent: as the time we can invest in social relationships is limited, reinforcing a relationship with someone is done at the expense of our relationships with others. We implement this interdependence in a parsimonious two-parameter model and apply it to several human and non-human primates' datasets to demonstrate that this model detects even small and short perturbations of the networks that cannot be detected using the standard technique of successive aggregated networks. Our model solves a long-standing problem by providing a simple and natural way to describe the dynamic evolution of social networks, with far-reaching consequences for the study of social networks and social evolution.

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Ongoing COVID-19 pandemic poses many challenges to the research of artificial intelligence. Epidemics are important in network science for modeling disease spread over networks of contacts between individuals. To prevent disease spread, it is desirable to introduce prioritized isolation of the individuals contacting many and unspecified others, or connecting different groups. Finding such influential individuals in social networks, and simulating the speed and extent of the disease spread are what we need for combating COVID-19. This article focuses on the following topics, and discusses some of the traditional and emerging research attempts: (1) topics related to epidemics in network science, such as epidemic modeling, influence maximization and temporal networks, (2) recent research of network science for COVID-19 and (3) datasets and resources for COVID-19 research.

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PURPOSE: In adolescent idiopathic scoliosis (AIS), non-invasive surgical techniques such as anterior vertebral body tethering (AVBT) enable to treat patients with mild and severe degrees of deformity while maintaining lower lumbar motion by avoiding spinal fusion. However, multiple features and characteristics affect the overall patient outcome, notably the 3D spine geometry and bone maturity, but also from decisions taken intra-operatively such as the selected tethered vertebral levels, which makes it difficult to anticipate the patient response. METHODS: We propose here a forecasting method which can be used during AVBT surgery, exploiting the spatio-temporal features extracted from a dynamic networks. The model learns the corrective effect from the spine's different segments while taking under account the time differences in the initial diagnosis and between the serial acquisitions taken before and during surgery. Clinical parameters are integrated through an attention-based decoder, allowing to associate geometrical features to patient status. Long-term relationships allow to ensure regularity in geometrical curve prediction, using a manifold-based smoothness term to regularize geometrical outputs, capturing the temporal variations of spine correction. RESULTS: A dataset of 695 3D spine reconstructions was used to train the network, which was evaluated on a hold-out dataset of 72 scoliosis patients using the baseline 3D reconstruction obtained prior to surgery, yielding an overall reconstruction error of [Formula: see text]mm based on pre-identified landmarks on vertebral bodies. The model was also tested prospectively on a separate cohort of 15 AIS patients, demonstrating the integration within the OR theatre. CONCLUSION: The proposed predictive network allows to intra-operatively anticipate the geometrical response of the spine to AVBT procedures using the dynamic features.

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