Temporal Prediction Research Articles

Using regularity-based temporal predictions to shift our attentional template across time during multiple-target dynamic visual search

Using regularity-based temporal predictions to shift our attentional template across time during multiple-target dynamic visual search

Ensemble data assimilation-based mixed subgrid-scale model for large-eddy simulations

An ensemble Kalman filter (EnKF)-based mixed model (EnKF-MM) is proposed for the subgrid-scale (SGS) closure in the large-eddy simulation (LES) of turbulence. The model coefficients are determined through the EnKF-based data assimilation technique. The direct numerical simulation (DNS) results are filtered to obtain the benchmark data for the LES. Reconstructing the correct kinetic energy spectrum of the filtered DNS (fDNS) data has been adopted as the target for the EnKF to optimize the coefficient of the functional part in the mixed model. The proposed EnKF-MM framework is subsequently tested in the LES of both the incompressible homogeneous isotropic turbulence and turbulent mixing layer. The performance of the LES is comprehensively examined through the predictions of the flow statistics including the velocity spectrum, the probability density functions (PDFs) of the SGS stress, the PDF of the strain rate, and the PDF of the SGS energy flux. The structure functions, the evolution of turbulent kinetic energy, the mean flow, the Reynolds stress profile, and the iso-surface of the Q-criterion are also examined to evaluate the spatial–temporal predictions by different SGS models. The results of the EnKF-MM framework are consistently more satisfying compared to the traditional SGS models, including the dynamic Smagorinsky model, the dynamic mixed model, and the velocity gradient model, demonstrating its great potential in the optimization of SGS models for the LES of turbulence.

Reproducing High Spatiotemporal Resolution Precipitable Water Distributions Using Numerical Prediction Data

Water vapor is an important greenhouse gas that affects regional climatic and weather processes. Atmospheric water vapor content is highly variable spatially and temporally, and continuous quantification over a wide area is problematic. However, existing methods for measuring precipitable water (PW) have advantages and disadvantages in terms of spatiotemporal resolution. This study uses high temporal resolution numerical prediction data and high spatial resolution elevation to reproduce PW distributions with high spatiotemporal resolution. This study also focuses on the threshold for elevation correction, improving temporal resolution, and reproducing PW distributions in near real time. Results show that using the water vapor content in intervals between the ground surface and 1000-hPa isobaric surface as the threshold value for elevation correction and generating hourly numerical prediction data using the Akima spline interpolation method enabled the reproduction of hourly PW distributions for 75% of the global navigation satellite system observation stations in the target region throughout the year with a root mean square error of 3 mm or less. These results suggest that using the mean value of monthly correction coefficients for the past years enables the reproduction of PW distributions in near real time following the acquisition of numerical prediction data.

Improving airport arrival flow prediction considering heterogeneous and dynamic network dependencies

Predicting airport arrival flow serves as a crucial technique in air traffic flow management. Given the unique operational characteristics of air traffic systems, airport arrival flow simultaneously presents complex dynamics in spatial–temporal dimensions, specific spatial heterogeneity, non-rigid periodicity, and robust plannability. These factors pose challenges to existing modeling methods in achieving optimal performance. To address these challenges, we propose a novel large-range air traffic flow prediction model to forecast airport arrival flow. More specifically, a dynamic multi-graph neural network is designed to automatically capture the time-evolving and heterogeneous spatial correlations using convolution and attention operations. In terms of the temporal dimension, a temporal-aware attention module is constructed to extract the temporal transitions of traffic data, considering both the local context and stationarity of the traffic representation sequence. Furthermore, a prior-guided recalibration fusion module is employed to explicitly incorporate the prior knowledge, including historical-periodic and future-scheduled arrival flow features, to recalibrate the temporal module prediction results, thereby enhancing the prediction accuracy. Experimental results on a real-world airport traffic flow dataset demonstrate that the proposed method outperforms the state-of-the-art baselines, and all proposed technical modules contribute to desired performance improvements.

Spatial and temporal variation and prediction of ecological carrying capacity based on machine learning and PLUS model

Ecological carrying capacity is key to evaluating sustainable development capacity, and land use change has varying degrees of impact on ecosystems. This study explores the ecological carrying capacity based on land use change, which is important for the conservation and scientific and rational use of ecosystems. Therefore, in this study, three machine learning classification 3algorithms, namely support vector machine, random forest and artificial neural network, were selected for accuracy comparison and analysis based on multi-source data, using Southwest Guangxi Karst-Beibu Gulf as the study area. The Patch-generating Land Use Simulation Model is used to dissect the spatial and temporal changes in ecological carrying capaciyt from 1990 to 2040 and future trends. The results showed that (1) Coupling multiple sources of data and machine learning classification algorithms can ultimately improve land use classification accuracy. The RF is compared and found to be the optimal classification algorithm for this study. (2) The area of arable and grassland gradually decreases between 1990 and 2040, mainly encroached upon by build land; the area of forested land gradually recovers, the watershed fluctuates up and down, and the area of build land gradually increases. (3) The ecological carrying capacity from 1990 to 2040 shows a trend of decreasing and then increasing, and the area of low and medium–low decreases from 2020 to 2040, with arable land and forest land having a stronger potential to increase ecological carrying capacity. Nanning City, Qinzhou City and Chongzuo City are severely damaged. The framework provides an effective tool for exploring future ecological carrying capacity to support the ecological conservation and future sustainable development of the region.

Metascheduling Using Discrete Particle Swarm Optimization for Fault Tolerance in Time-Triggered IoT-WSN

In time-triggered systems, adaptation is performed by using metascheduling approaches to ensure temporal predictability. Wireless sensor networks (WSNs) are growing to be used as a reliable, an energy-efficient, and a scalable network infrastructure for numerous Internet of Things (IoT) applications. Because of run-time changes because of failure events, a metascheduling system is required to address the changes by precomputing schedules for several context events at design time. Therefore, this paper proposes a metascheduler that solves a new scheduling problem for each adaptation scenario in IoT-WSN using our offline algorithm named discrete particle swarm optimization for reliable task allocation (DPSO-TA), resulting in a multi-schedule graph that combines the repeated schedules. In this work, a time-triggered IoT-WSN metascheduler is proposed that takes into considerations the node or link failures that are common in WSN. Single and two failure events are considered, where a graph for all feasible schedules is formed at the network design time. Such a large number of schedules causes a state space explosion problem, which is managed using a re-convergence method. Different application model sizes and network topologies are used to assess the proposed metascheduler under various failure event scenarios. The results show a reduction in the size of the multi-schedule graph by applying inputs with different deadline values and different number of tasks. Furthermore, the validity suggested by the proposed metascheduler, which is the ratio of valid to invalid schedules, is improved when compared to algorithms that schedule tasks to hosts with the shortest completion time or algorithms that select hosts for a set of sorted tasks based on energy consumed and task arrival time.

Temporal prediction of shallow landslides exploiting soil saturation degree derived by ERA5-Land products

ERA5-Land service has been released recently as an integral and operational component of Copernicus Climate Change Service. Within its set of climatological and atmospheric parameters, it provides soil moisture estimates at different soil depths, represeting an important tool for retrieving saturation degree for predicting natural hazards as shallow landslides. This paper represents an innovative attempt aiming to exploit the use of saturation degree derived from ERA5-Land soil moisture products in a data-driven model to predict the daily probability of occurence of shallow landslides. The study was carried out by investigating a multi-temporal inventory of shallow landslides occurred in Oltrepò Pavese (northern Italy). The achieved results follow: (i) ERA5-Land-derived saturation degree reconstructs well field trends measured in the study area until 1 m from ground; (ii) in agreement with the typical sliding surfaces depth, saturation degree values obtained since ERA5-Land 28–100 cm layer represent a significant predictor for the estimation of temporal probability of occurrence of shallow landslides, able especially to reduce overestimation of triggering events; (iii) saturation degree estimated by ERA5-Land 28–100 cm layer allows to detect soil hydrological conditions leading to triggering in the study area, represented by saturation degree in this layer close to complete saturation. Even if other works of research are required in different geological and geomorphological settings, this study demonstrates that ERA5-Land-derived saturation degree could be implemented to identify triggering conditions and to develop prediction methods of shallow landslides, thanks also to its free availability and constantly updating with a delay of 5 days.

Sex differences in vocal learning ability in songbirds are linked with differences in flexible rhythm pattern perception

Humans readily recognize familiar rhythmic patterns, such as isochrony (equal timing between events) across a wide range of rates. This reflects a facility with perceiving the relative timing of events, not just absolute interval durations. Several lines of evidence suggest this ability is supported by precise temporal predictions arising from forebrain auditory-motor interactions. We have shown previously that male zebra finches, Taeniopygia guttata, which possess specialized auditory-motor networks and communicate with rhythmically patterned sequences, share our ability to flexibly recognize isochrony across rates. To test the hypothesis that flexible rhythm pattern perception is linked to vocal learning, we ask whether female zebra finches, which do not learn to sing, can also recognize global temporal patterns. We find that females can flexibly recognize isochrony across a wide range of rates but perform slightly worse than males on average. These findings are consistent with recent work showing that while females have reduced forebrain song regions, the overall network connectivity of vocal premotor regions is similar to males and may support predictions of upcoming events. Comparative studies of male and female songbirds thus offer an opportunity to study how individual differences in auditory-motor connectivity influence perception of relative timing, a hallmark of human music perception.

Regional electricity market price forecasting based on an adaptive spatial–temporal convolutional network

The accurate prediction of electricity prices has great significance for the power system and the electricity market, regional electricity prices are difficult to predict due to congestion issues in regional transmission lines. A regional electricity price prediction framework is proposed based on an adaptive spatial–temporal convolutional network. The proposed framework is expected to better explore regional electricity prices’ spatial–temporal dynamic characteristics in the electricity spot market and improve the predictive accuracy of regional electricity prices. First, different areas of the electricity market are regarded as nodes. Then, each area’s historical electricity price data are used as the corresponding node’s characteristic information and constructed into a graph. Finally, a graph containing the spatial–temporal information on electricity prices is input to the adaptive spatial–temporal prediction framework to predict the regional electricity price. Operational data from the Australian electricity market are adopted, and the prediction results from the proposed adaptive spatial–temporal prediction framework are compared with those of existing methods. The numerical example results show that the predictive accuracy of the proposed framework is better than the existing baseline and similar methods. In the twelve-step forecast example in this paper, considering the spatial dependence of the spot electricity price can improve the forecast accuracy by at least 10.3% and up to 19.8%.

DyHNet: Learning dynamic heterogeneous network representations

Many real-world networks, such as social networks, contain structural heterogeneity and experience temporal evolution. However, while there has been growing literature on network representation learning, only a few have addressed the need to learn representations for dynamic heterogeneous networks. The objective of our work in this paper is to introduce DyHNet, which learns representations for such networks and distinguishes itself from the state-of-the-art by systematically capturing (1) local node semantics, (2) global network semantics and (3) longer-range temporal associations between network snapshots when learning network representations. Through experiments on four real-world datasets from different domains, namely IMDB with 4,178 movies, AMiner with 10,674 papers, Yelp with 2,693 businesses, and DBLP with 14,376 papers, we demonstrate that our proposed method is able to show consistently better and more robust performance compared to the state-of-the-art techniques on link prediction and node classification tasks. More specifically, we are superior to the best baseline in the temporal link prediction task by approximately 13% and 15% on F1-score for the IMDB and AMiner datasets, respectively. Further, in the node classification task, our findings illustrate that the Micro F1 scores of our proposed model increase by 13% and 17% compared to the runner-up model on the Yelp and DBLP datasets, respectively.1

Feeling the Beat: Temporal Predictability is Associated with Ongoing Changes in Music-Induced Pleasantness.

Music is a complex phenomenon that elicits a range of emotional responses, influenced by numerous variables, such as rhythm, melody and harmony. One interesting aspect of music is listeners' ability to predict its continuation as it unfolds - an inherent attribute hypothesized to contribute to our emotional response to music. In this study, we investigated this link by examining the relationship between temporal predictability - the ability to predict the timing of the next event - and the ongoing changes in music-induced pleasantness. Temporal predictability was operationalized as the degree to which taps of 20 musically trained participants, who tapped to the beat along three naturalistic and highly contrastive musical pieces, were aligned. We then examined the degree to which this measure could explain the ongoing emotional experience, as reflected in continuous measures of arousal and valence, in a separate group of 40 participants that listened to these pieces. Our findings reveal a positive correlation between fluctuations in reported valence and temporal predictability, even when controlling for a set of other musical features, in four out of five musical sections. The only exception being a lyrical slow section. These findings were further supported by a large online database of annotated musical emotions (n = 1780 songs), where a consistent and robust correlation between valence ratings and an automatically extracted feature of pulse clarity was demonstrated. Overall, our findings shed light on the significance of temporal predictability as a contributing factor to the hedonic experience of music, especially within the tempo range of salient beat perception.

Spatial and temporal prediction of secondary crashes combining stacked sparse auto-encoder and long short-term memory

Secondary crashes occur within the spatial and temporal impact area of primary crashes, resulting in traffic delays and safety problems. While most existing studies focus on the likelihood of secondary crashes, predicting the spatio-temporal location of secondary crashes could offer valuable insights for implementing prevention strategies. This includes guiding the deployment of emergency response measures and determining appropriate speed limits. The main objective of this study is to develop a prediction method for the spatial and temporal locations of secondary crashes. A hybrid deep learning model SSAE-LSTM is proposed by combining stacked sparse auto-encoder (SSAE) and long short-term memory network (LSTM). Traffic and crash data on the California I-880 highway covering the period of 2017–2021 are collected. The identification of secondary crashes is performed by the speed contour map method. The time and distance gaps between primary and secondary crashes are modeled using multiple 5-minute interval traffic variables as inputs. Multiple models are developed for benchmarking purposes, including PCA-LSTM, which incorporates principal component analysis (PCA) and LSTM, SSAE-SVM, which incorporates SSAE and support vector machine (SVM), and back propagation neural network (BPNN). The performance comparison indicates that the hybrid SSAE-LSTM model outperforms the other models in terms of both spatial and temporal prediction. In particular, SSAE4-LSTM1 (with 4 SSAE layers and 1 LSTM layer) demonstrates superior spatial prediction performance, while SSAE4-LSTM2 (with 4 SSAE layers and 2 LSTM layers) excels in temporal prediction. A joint spatio-temporal evaluation is also conducted to measure the overall accuracy of the optimal models over different permitted spatio-temporal ranges. Finally, practical suggestions are provided for secondary crash prevention.

DMVC: Decomposed Motion Modeling for Learned Video Compression

Inter prediction is the critical component in hybrid coding framework to deal with the temporal redundancy. Most of the neural video coding methods typically follow the motion compensation based inter coding scheme, establishing motion vector (MV) as the central role. In this paper, we innovatively propose an efficient motion modeling approach by inherently decomposing it into two components, the intrinsic motion and the compensatory motion. The intrinsic motion originates from the implicit spatiotemporal context hidden in the historical sequence, which can be intuitively captured free of bits. On the top of it, the compensatory motion acts a role of structural refinement and texture enhancement as a form of side information. In particular, the inter prediction is performed in the feature space as a manner of progressive temporal transition, conditioned on the decomposed motion. By the motion decomposition paradigm, we innovatively answer the question of motion representation, compensation and coding in the learned video compression framework. With the temporal prediction, the remaining pixel residue is signaled to obtain the reconstruction. Extensive experimental results demonstrate that the proposed method achieves state-of-the-art coding performance on par with other end-to-end coding methods, and outperforms versatile video coding (VVC) under low-delay P (LDP) configuration in terms of MS-SSIM metric.

Mobility-Aware Proactive Edge Caching for Large Files in the Internet of Vehicles

By shifting the requested content to the edge in the Internet of Vehicles (IoV), edge caching is expected to be an effective solution to satisfy the low latency and high reliability requirements of IoV users for multimedia services. However, the edge node’s coverage area and storage space are limited. Moreover, since vehicles have high mobility and in-vehicle multimedia applications require sequential delivery for contents, we need to address two main issues: 1) How to optimize the proactive content caching decision (i.e., the placement of cached content chunks) among edge nodes (ENs) to provide better Quality of Services (QoS) for IoV users. 2) How to ensure that vehicles can download the required contents sequentially to improve Quality of Experience (QoE). In this paper, we propose a mobility-aware proactive edge caching scheme (MSTPS), where the spatial and temporal prediction of vehicles are taken into account for content deployment and scheduling. Specifically, we optimize the caching decision based on predicting the vehicle’s driving trajectory and travel preference. The scheme learns the vehicle’s travel preferences to cope with mobility uncertainty by combining users with similar travel patterns. Meanwhile, the proposed scheme can support the sequential downloading of content chunks. Furthermore, in order to deal with the dynamic characteristics and unpredictable challenges of the IoV, we design a system recovery strategy, which can avoid the degradation of the proposed scheme due to the failure of prediction. Finally, by using real mobility datasets and scenarios, we explore the impact of the number of ENs deployed in advance for each vehicle’s request when the cache needs to be updated on system performance. In addition, we evaluate the effectiveness of the proposed scheme. Our proposed scheme can achieve the best cache hit ratio and decrease caching costs compared to the existing mobility-aware caching schemes.

Are Surprise Questions and Probabilistic Questions by Nurses Useful in Home Palliative Care? A Prospective Study.

Background: Surprise questions (SQs) are used as screening tools in palliative care. Probabilistic questions (PQs) are more accurate than temporal predictions. However, no study has examined the usefulness of SQs and PQs assessed by nurses. Objectives: To examine the accuracy of nurses' SQ and PQ assessments in patients with advanced cancer receiving home palliative care. Design: A prospective single-center cohort study. Setting/Subjects: Adult patients with advanced cancer who received palliative care at home in South Korea between 2019 and 2020. Measurements: Palliative care specialized nurses were asked the SQ, "Would you be surprised if the patient died in a specific timeframe?" and PQ, "What is the probability that this patient will be alive (0 to 100%) within a specific timeframe?" at the 1-, 2-, 4-, and 6-week timeframes at enrollment. We calculated the sensitivities and specificities of the SQs and PQs. Results: 81 patients were recruited with 47days of median survival. The sensitivity, specificity, and overall accuracy (OA) of the 1-week SQ were 50.0, 93.2, and 88.9%, respectively. The accuracies for the 1-week PQ were 12.5, 100.0, and 91.3%, respectively. The 6-week SQ showed sensitivity, specificity, and OA of 84.6, 42.9, and 62.9%, respectively; the accuracies for the 6-week PQ were 59.0, 66.7, and 63.0%, respectively.Conclusion: The SQ and PQ showed acceptable accuracy in home palliative care patients. Interestingly, PQ showed higher specificity than SQ at all timeframes. The SQ and PQ assessed by nurses may be useful in providing additional prognostic information for home palliative care.

Predicting Temporal Sets with Simplified Fully Connected Networks

Given a sequence of sets, where each set contains an arbitrary number of elements, temporal sets prediction aims to predict which elements will appear in the subsequent set. Existing methods for temporal sets prediction are developed on sophisticated components (e.g., recurrent neural networks, attention or gating mechanisms, and graph neural networks), which inevitably increase the model complexity due to more trainable parameters and higher computational costs. Moreover, the involved nonlinear activation may contribute little or even degrade the performance. In this paper, we present a succinct architecture that is solely built on the Simplified Fully Connected Networks (SFCNs) for temporal sets prediction to bring both effectiveness and efficiency together. In particular, given a user's sequence of sets, we employ SFCNs to derive representations of the user by learning inter-set temporal dependencies, intra-set element relationships, and intra-embedding channel correlations. Two families of general functions are introduced to preserve the permutation-invariant property of each set and the permutation-equivariant property of elements in each set. Moreover, we design a user representations adaptive fusing module to aggregate user representations according to each element for improving the prediction performance. Experiments on four benchmarks show the superiority of our approach over the state-of-the-art under both transductive and inductive settings. We also theoretically and empirically demonstrate that our model has lower space and time complexity than baselines. Codes and datasets are available at https://github.com/yule-BUAA/SFCNTSP.

Predicting Crop Growth Patterns with Spatial–Temporal Deep Feature Exploration for Early Mapping

The timely and accurate mapping of crops over large areas is essential for alleviating food crises and formulating agricultural policies. However, most existing classical crop mapping methods usually require the whole-year historical time-series data that cannot respond quickly to the current planting information, let alone for future prediction. To address this issue, we propose a novel spatial–temporal feature and deep integration strategy for crop growth pattern prediction and early mapping (STPM). Specifically, the STPM first learns crop spatial–temporal evolving patterns from historical data to generate future remote sensing images based on the current observations. Then, a robust crop type recognition model is applied by combining the current early data with the predicted images for early crop mapping. Compared to existing spatial–temporal prediction models, our proposed model integrates local, global, and temporal multi-modal features comprehensively. Not only does it achieve the capability to predict longer sequence lengths (exceeding 100 days), but it also demonstrates a significant improvement in prediction accuracy for each time step. In addition, this paper analyses the impact of feature dimensionality and initial data length on prediction and early crop mapping accuracy, demonstrating the necessity of multi-modal feature fusion for spatial–temporal prediction of high-resolution remote sensing data and the benefits of longer initial time-series (i.e., longer crop planting time) for crop identification. In general, our method has the potential to carry out early crop mapping on a large scale and provide information to formulate changes in agricultural conditions promptly.

P3-like signatures of temporal predictions: a computational EEG study.

Many cognitive processes, ranging from perception to action, depend on the ability to predict the timing of forthcoming events. Yet, how the brain uses predictive models in the temporal domain is still an unsolved question. In previous work, we began to explore the neural correlates of temporal predictions by using a computational approach in which an ideal Bayesian observer learned the temporal probabilities of target onsets in a simple reaction time task. Because the task was specifically designed to disambiguate updating of predictive models and surprise, changes in temporal probabilities were explicitly cued. However, in the real world, we are usually incidentally exposed to changes in the statistics of the environment. Here, we thus aimed to further investigate the electroencephalographic (EEG) correlates of Bayesian belief updating and surprise associated with incidental learning of temporal probabilities. In line with our previous EEG study, results showed distinct P3-like modulations for updating and surprise. While surprise was indexed by an early fronto-central P3-like modulation, updating was associated with a later and more posterior P3 modulation. Moreover, updating was associated with a P2-like potential at centro-parietal electrodes, likely capturing integration processes between prior beliefs and likelihood of the observed event. These findings support previous evidence of trial-by-trial variability of P3 amplitudes as an index of dissociable inferential processes. Coupled with our previous findings, the present study strongly bolsters the view of the P3 as a key brain signature of temporal Bayesian inference. Data and scripts are shared on OSF: osf.io/sdy8j/.

Spatial and temporal characteristics analysis and prediction model of PM2.5 concentration based on SpatioTemporal-Informer model.

The primary cause of hazy weather is PM2.5, and forecasting PM2.5 concentrations can aid in managing and preventing hazy weather. This paper proposes a novel spatiotemporal prediction model called SpatioTemporal-Informer (ST-Informer) in response to the shortcomings of spatiotemporal prediction models commonly used in studies for long-input series prediction. The ST-Informer model implements parallel computation of long correlations and adds an independent spatiotemporal embedding layer to the original Informer model. The spatiotemporal embedding layer captures the complex dynamic spatiotemporal correlations among the input information. In addition, the ProbSpare Self-Attention mechanism in this model can focus on extracting important contextual information of spatiotemporal data. The ST-Informer model uses weather and air pollutant concentration data from numerous stations as its input data. The outcomes of the trials indicate that (1) The ST-Informer model can sharply capture the peaks and sudden changes in PM2.5 concentrations. (2) Compared to the current models, the ST-Informer model shows better prediction performance while maintaining high-efficiency prediction [Formula: see text]. (3) The ST-Informer model has universal applicability, and the model was applied to the concentration of other pollutants prediction with good results.

Automatic temporal clothing deformation prediction: applicable to variable shape and motion

Simulating temporal three-dimensional (3D) deformations of clothing worn by the human body is a core technology in computer graphics that plays a vital role in various fields, such as computer games, animation, and movies. Physics-based simulation and data-driven methods are two mainstream technologies used to generate clothing deformation. However, when it is necessary to quickly generate clothing animations of different body shapes and motions, the existing methods cannot balance efficiency and effectiveness. In this paper, we present a learning-based method, given human body shape and motion, which automatically synthesizes temporal 3D deformations of clothing in real-time. A temporal framework based on the transformer is designed to capture the correlation between clothing deformation and shape features of the moving human body, as well as the frame-level dependency. A feature fusion strategy is an innovation used to fuse the two features of shape and motion. We also perform post-processing on the penetration of clothing and the human body, generating collision-free cloth deformation sequences. To evaluate the method, we build a human motion dataset based on the large-scale public human body dataset AMASS, and further develop a clothing deformation dataset. We qualitatively and quantitatively demonstrate that our approach outperforms existing methods in terms of temporal clothing deformation with variable shape and motion, as well as producing realistic deformation at interactive rates.