This mechanism is common in real datasets, as there will always be missing values. For the WUSTL-IIoTCC-2021 dataset, we take care of missing values using Mean Imputation. In this technique it replaces a missing value with mean of the respective feature. Given a feature xi with missing values, the imputed value for the missing data point ximissing is computed as: (7)ximissing=1n∑i=1nxiwhere n is the number of available values for feature xi. The benefit of this approach is that the dataset is not changed or modified in anyway and the data points are not removed as this would introduce bias to the dataset.

This is done to be sure the features are on the same scale and do not unfairly affect the model. The data is scaled using this technique so that each feature lies between [0, 1]. For a feature xi with minimum value ximin and maximum value ximax, the normalized value xinorm is calculated as: (8)xinorm=xi−ximinximax−ximin

This normalization makes sure any one feature does not overpower others and contribute more to the learning process by its scale.

In order to enhance the performance of this anomaly detection model, we apply the Principal Component Analysis (PCA) in feature extraction. PCA is a method to reduce dimensionality of data such that as much variance as possible is retained. Let X∈Rn×m be the original data matrix with n samples and m features. The principal components are the eigenvectors of the covariance matrix Σ=1n−1XTX, where the eigenvectors correspond to the directions of maximum variance in the dataset. The first few principal components, v1,v2,…,vk, are used to project the data into a lower-dimensional space. The dimensionality-reduced data Xreduced is computed as: (9)Xreduced=X⋅Vkwhere Vk is the matrix of the top k eigenvectors. In this dimensionality reduction, the most important features for anomaly detection are the focus, which improves the computational efficiency of the FedCognis model.

We split the dataset into training, validation and test sets for training and evaluating the FedCognis model. Usually, the data is split in 80-10-10 ratio randomly. Assuming the dataset is represented as D={x1,x2,…,xn}. The training set Dtrain, validation set Dval, and test set Dtest are defined as follows: (10)Dtrain={x1,x2,…,x⌊0.8n⌋} (11)Dval={x⌊0.8n⌋+1,…,x⌊0.9n⌋} (12)Dtest={x⌊0.9n⌋+1,…,xn}

Such evaluation of the model and its performance ensures that the model is tested on data that it hasn’t seen during training, resulting in a more fairer and more realistic assessment of its performance.

As we are using Self Attention Long short term memory (SALSTM) networks as an anomaly detection, we need to be sure that all features are properly scaled for training process. Standardization is applied to each feature, which means our data will have mean of 0 and standard deviation of 1. The standardized value xistd of a feature xi is calculated as: (13)xistd=xi−μiσiwhere μi is the mean of feature xi and σi is its standard deviation. This transformation helps to speed up convergence of the model as the learning rates are identical for all the features and all the data is centered around 0.

Finally the FedCognis model is trained on high quality well prepared dataset by performing the steps like handling missing data, normalization, feature extraction, data splitting as well as feature scaling. The performance of the model should be optimized in order for the model to detect anomalies in IIoTCC environments. By preprocessing in the correct manner, the model is capable of generalizing well to unseen data and adapt to dynamic nature of IIoTCC systems, resulting in higher accuracy and robustness of anomaly detection for real world applications.

Each node in the system model of the network of IIoTCC devices (nodes) generates sensor data and transfers them. The architecture of such a Federated Learning (FL) of the type described above is each IIoTCC device training its own local model with its own private data. Periodically, the local models are aggregated and the global models are taken to detect anomalies in real time.

It is possible to represent the IIoTCC network as a set of nodes 𝒩={1,2,…,N}, where each node i∈𝒩 collects sensor data 𝒟i and trains a local anomaly detection model θi based on its data. The local models are aggregated using a weighted average approach to update the global model θ, as shown below: (14)θt+1=∑i=1NTit|𝒟i|∑j=1NTjt|𝒟j|θitwhere Tit is the trust score of node i at iteration t, and |𝒟i| is the size of the local dataset at node i. The purpose of this aggregation process is to allow the global model to incorporate the learned knowledge from all participating nodes without sharing sensitive data.

The development of the system model takes the following assumptions.

Data Availability: Each IIoTCC node has access to its own sensing data for training of the local model. It will also assume that the dataset is sufficient for training a meaningful anomaly detection model.

Assumptions such as these form the base of the design and implementation of the FedCognis framework and the system model is derived from these. Details of the proposed model are described in the following sections and include how local models are trained, how global model is updated, how security and adaptability are maintained in the system.

In FedCognis, the anomaly detection model is trained in a federated manner. Each IIoTCC node in the network 𝒩={1,2,…,N} maintains a local model θi trained on its own data 𝒟i. Instead of sending raw data to a central server, each node sends only its model updates (i.e., the parameters) to the central server, which aggregates them to form a global model. This ensures data privacy and reduces the communication overhead.

At each iteration t, the global model θ is updated based on the weighted average of the local models: (15)θt+1=∑i=1NTit|𝒟i|∑j=1NTjt|𝒟j|θitwhere Tit is the trust score of node i, and |𝒟i| is the size of the local dataset at node i. This weighted aggregation ensures that nodes with more data or higher trust have a greater influence on the global model.

To protect the federated learning process against malicious updates, such as the model poisoning (e.g., QSA is introduced for Quantum Secure Authentication (QSA) in FedCognis. Using quantum resistant cryptographic techniques, the nodes are authenticated and model updates are authenticated. In a quantum secure authentication protocol, each node’s update is verified before being added in the aggregation process.

We utilize a lattice-based post-quantum digital signature algorithm with 256-bit keys. The average signature size is 2.3 KB per update, with a verification time of 1.7 ms. This lightweight overhead ensures real-time validation under constrained IIoTCC bandwidth without significantly delaying model updates.

Let 𝒮it represent the authentication signature of node i at iteration t, it is generated using a quantum resistant cryptographic algorithm. A verification step is introduced into the global model update process: (16)θt+1=∑i=1NTit|𝒟i|∑j=1NTjt|𝒟j|I(V(𝒮it,θit)=True)θitwhere V(𝒮it,θit) denotes the verification function, which checks whether the update from node i is valid based on the QSA protocol. If the signature is valid, the update is included; otherwise, it is discarded.

FedCognis employs Self-Attention Long Short Term Memory (SALSTM) for improving the performance of anomaly detection. This class of models attains long range dependencies over time in context of time series sensor data, for example they can be used to capture anomalies (in particular long lagged anomalies) that are difficult to discover using conventional machine learning.

Let Xt∈Rd represent the input sequence at time step t, where d is the feature dimension. The SALSTM model consists of two main components: the self-attention mechanism and the LSTM layer.

The self-attention mechanism computes the attention weights αt for each input sequence Xt based on its relevance to previous inputs: (17)αt=softmax(WqXt)where Wq∈Rd×d is α . The softmax function enforces the sum of the attention weights to be 1, and the learned weight matrix.

The inputs are weighted and then passed through an LSTM layer which captures temporal dependencies: (18)ht=LSTM(Xt,ht−1)where ht is the hidden state at time step t, and ht−1 is the hidden state from the previous time step.

Finally, a SALSTM model is used to output which data point is an anomaly. The difference between expected and observed values is used in this prediction: (19)Anomaly Score=∥ht−h^t∥2where h^t is the predicted hidden state from the model, and ∥⋅∥2 represents the L2 norm.

As the environment for dynamic IIoTCC is dynamic, and the data distribution can change over time, this is referred to as concept drift. In order to adapt to these changes FedCognis is fed with recent data and the global model is updated continuously. To handle concept drift, we propose a method to recomputed the trust scores Tit as a function of the difference between a node’s model and the overall model.

The trust score of node i is updated at each iteration t as follows: (20)Tit+1=αTit+(1−α)e−β∥θit−θt−1∥2where α and β are decay parameters that control how quickly trust is updated, and ∥θit−θt−1∥2 is the squared Euclidean distance between the local model and the previous global model. This mechanism prevents nodes with models far away from the global model (as a result of concept drift) to have their trust scores reduced and nodes with models close to the global model to have higher trust scores.

Security Mechanisms for Adversarial Protection

In addition to model poisoning and Byzantine failures, which are further mechanisms used to enhance the security of FedCognis, the system provides the model poisoning and Byzantine failures. This adaptive trust mechanism described earlier will help in detecting and filtering out malicious updates, and only valid model updates shall be incorporated into the global model. Furthermore, QSA integration offers convincing defense against unauthorized updates to the model.

Summary of the workflow of FedCognis mentioned below (Algorithm 1). In each node, the local model is trained, trust scores are computed, updates are authenticated, and the model updates are sent to the central server. The server aggregates the updates with weighted average and updates the global model. The global model is secure and adaptive to the concept drift and the convergence takes place until an anomaly is detected by the global model.

Additionally, in order to enhance the security of FedCognis against adversarial attacks, both model poisoning and Byzantine failures are accounted for. Earlier, we have described that the adaptive trust mechanism can help to identify and filter out the malicious updates and can only contribute to the global model, if they are valid model updates. In addition, the integration of QSA offers strong protection against malicious model update.

Initialize global model θ=θ0

Thus, the workflow of the above algorithm is described above in a nutshell, which is what FedCognis is. Each node trains local model, computes trust scores, authenticates updates and send them to the central server with model updates. The local model is updated according to the weighted average and the global model is updated in terms of the weighted average. Thus, instead of repeating many times over the same training data, it is repeated until convergence to obtain a very good detection of anomalies while ensuring security and the ability to adapt to concept drift.

The main metric, to evaluate how good the classification model is, is accuracy. The ratio of correctly classified instances to the total instances is called its definition. Let TP, TN, FP, and FN. The number of true positives, true negatives, false positives, and false negatives, respectively, are represented by these values. It is given by the accuracy “Acc”: (21)Acc=TP+TNTP+TN+FP+FNwhere: TP is the number of correctly classified anomalies, TN is the number of correctly classified normal instances, FP is the number of normal instances incorrectly classified as anomalies, and FN is the number of anomalies incorrectly classified as normal instances.

Precision is the proportion of true positive predictions out of all the instances predicted as anomalies. Especially when the cost of false positives is high, it is a key metric. The precision P is calculated as: (22)P=TPTP+FP

A high precision means that the model does not usually classify normal instances as anomalies.

Sensitivity or recall measures the proportion of the true positives identified correctly by the model. This matters when the cost of missing an anomaly (false negatives) is high. The recall R is given by: (23)R=TPTP+FN

A high recall means that the model can well identify most of the anomalies in the data.

The F1-score is the harmonic mean of precision and recall, which gives a balanced metric between precision and recall. It is especially useful for imbalanced datasets. The F1-score F1 is defined as: (24)F1=2⋅P⋅RP+Rwhere P is precision and R is recall. The higher F1-score means the overall model performance is better.

An evaluation based on AUC ROC curve is done to determine how well the model can distinguish normal and anomalous instances at different thresholds. The ROC curve plots the true positive rate (recall) against the false positive rate (FPR), where: (25)FPR=FPFP+TN

The area under this ROC curve is the AUC score. The higher the AUC, the better the model will distinguish anomalies from normal instances.

Computational efficiency is crucial for the FedCognis framework as it is designed for IIoTCC environments. Model training time is the primary metric of computational efficiency, which denotes the time it takes to train the model over all involved nodes. Let Ttrain represent the total training time, including both local training at nodes and the aggregation process: (26)Ttrain=Tlocal+Taggregationwhere: Tlocal is the average training time for each node, Taggregation is aggregating model updates and updating the global model requires time, time that I’ll refer to as the time to aggregate model updates or simply the time to aggregate.

Especially for real time anomaly detection systems with high demand of quick decision making, a lower training time is desirable.

We also define the Security Score of the FedCognis framework, which is used to evaluate the model’s resistance to adversarial attacks, e.g., model poisoning. The Quantum Secure Authentication (QSA) and trust-based aggregation mechanisms are measured for the percentage of successful adversarial attacks that are prevented and the security score is calculated. Let Aattacked represent the number of successful adversarial attacks and Aprevented represent the number of attacks prevented by the security mechanisms. The security score Ssecurity is given by: (27)Ssecurity=ApreventedAattacked

A higher value of Ssecurity indicates better protection against adversarial manipulation of the model.

Fig. 3 displays the evolution of anomaly scores over time, with a highlighted concept drift event occurring at round 50. A significant spike in anomaly scores indicates model responsiveness to environmental changes, confirming FedCognis’ ability to detect and adapt to evolving IIoTCC patterns.

The above figure shows the probability distribution of anomaly scores before and after a simulated concept drift at round 50. Before the drift, all the scores are below the decision threshold (2.4), which shows that the system operates stably. However, after the drift event, the distribution moves far to the right and a large amount of scores exceeds the threshold. The change in the distribution of the nodes demonstrates the model’s capability to detect temporal drifts in the behavior of nodes, which is a crucial property for the anomaly detection in dynamic IoT environments.

Fig. 4 contrasts anomaly score distributions pre- and post-drift, showing a rightward shift after drift. This validates the SALSTM’s sensitivity to time-dependent behavioral changes, further enhanced by the trust-aware model updates.

After this, we depict the pairwise cosine similarity between the update vectors of 20 nodes in the federated setup using this heatmap. In the bottom right quadrant we observe a distinct adversarial cluster formed by nodes 15 to 19 that are highly mutually similar and at the same time are not similar to the rest. This implies that the action is coordinated and therefore indicates adversarial intent. It is critical for FedCognis to be able to visualize and detect divergence of this type in order to isolate colluding or compromised nodes, strengthening the system’s robustness.

In Fig. 5, FedCognis’ F1-score is shown across sequential rounds. Two visible dips correspond to simulated drift events. The gradual recovery post-event illustrates the framework’s resilience and ability to restore performance autonomously. The system recovers gradually after both positive and negative drift events, with a post-drift recovery of 37%.

A hexbin plot showing the node by node joint distribution between trust scores and model update magnitudes (L2 norm) of participating nodes is shown. It is obvious that the nodes with higher update magnitudes have lower trust scores. Clearly visible in the bottom right region labeled “Low Trust–High Divergence” are nodes that diverges significantly from normal training behavior. However, for adapting trust scoring to anomalous participants in real time, this is essential.

Fig. 6 reveals a consistent pattern: nodes with high update divergence are penalized with lower trust scores. This correlation supports the use of L2-norm-based filtering for isolating adversarial participants.

In the WUSTL-IIoTCC-2021 dataset, the anomaly score timeline indicates real-time concept drift detection. Around 5 January, the anomaly score goes up significantly, significantly above the detection threshold and within a shaded alert region. This indicates that such a system can adapt to distributional shifts with time and in an autonomous manner, which is crucial for smart factory and critical infrastructure systems to operate without manual intervention.

Fig. 7 visualizes inter-node similarities using cosine similarity. The adversarial cluster forms a coherent block, validating the trust system’s ability to isolate coordinated attacks in the network.

This figure shows the daily F1-score over a three month period with two large drifts. A 15% performance dip occurs from Drift Event 1 and a 12% reduction from Drift Event 2. Despite this, the system is extremely resilient as it recovers post-drift as indicated by a moving average. This confirms that FedCognis can indeed detect (and not just indicate) performance degradation due to drift as well as recover quickly due to trust aware updates and the adaptive filtering.

Fig. 8 demonstrates the dynamic adjustment of trust. The adversarial node’s sharp drop indicates active detection, while gradual recovery reflects the fairness mechanism allowing reintegration of recovered nodes. A drop in trust is observed during malicious activity, followed by partial recovery.

This dual distribution plot represents benign and adversarial nodes update magnitudes. Results on empirical distributions show that adversarial nodes generate much bigger update magnitudes. The dotted vertical line corresponds to the decision threshold (θ = 0.8), and the plot shows the FPR to be 6.4% and the FNR to be 26%. It is shown that the observed distribution gap (Δμ = 1.20) verifies the filtering to separate benign from malicious nodes in the trust pipeline using L2 norm based filtering.

To evaluate the individual contributions of the Quantum Secure Authentication (QSA) module and the Self-Attention Long Short-Term Memory (SALSTM) network to the overall performance of FedCognis, we conducted an ablation study. Three configurations of the model were tested using the WUSTL-IIoTCC-2021 dataset under the same experimental conditions: 1.

FedCognis without QSA—In this setting, model updates are aggregated without quantum authentication. Only trust-based filtering is applied, removing the authentication layer used to validate model integrity.

Performance was evaluated using four core metrics: accuracy, precision, recall, and AUC (Area Under ROC Curve). Results clearly indicate that both QSA and SALSTM contribute significantly to the robustness and effectiveness of the framework. Excluding either component results in reduced detection performance, especially in recall and AUC, which are critical for real-time anomaly detection in IIoTCC networks.

These findings confirm that QSA enhances resilience against malicious updates while SALSTM boosts the model’s ability to capture long-term dependencies and subtle anomalies in sensor data.

Table 3 summarizes the performance impact of removing key components from the FedCognis framework. Without QSA, the model becomes more vulnerable to adversarial updates, reducing its accuracy and AUC. Similarly, removing SALSTM lowers detection quality due to weaker temporal modeling. The full FedCognis model consistently outperforms the ablated versions across all metrics, confirming that both QSA and SALSTM are essential for achieving high anomaly detection performance in IIoTCC environments.

Fig. 9 shows that adversarial nodes typically have much higher update magnitudes than benign ones. The applied threshold effectively separates the two groups, validating the anomaly filter. A trust threshold of 0.8 was effective in distinguishing both groups, with a 6.4% false positive and 26% false negative rate.

This figure compares the bandwidth usage of centralized learning, vanilla FL, and FedCognis. It also shows that FedCognis saves 72% bandwidth from centralized learning and 50% from vanilla FL. In the lower subplot, it is shown that instantaneous bandwidth usage stays low after round 20. The significance of the results lies in the fact that the framework is suitable for bandwidth constrained IoT environments and does not compromise performance.

Fig. 10 ROC curve confirms the model’s capability to distinguish anomalous vs. normal samples under low false positive constraints—key for industrial IoT reliability.

Evolution of the trust score of a benign node and an adversarial node over 100 training rounds, are plotted in this. Adversarial node experiences sharp trust drop immediately when it starts malicious activity and slow recovery after mitigation. The benign node also keeps its trust level stable. FedCognis being able to do this dynamic trust assessment enables isolation of threats quickly and re-evaluating trustworthiness over time improving long term system integrity.

Fig. 11 presents performance metric convergence. The low gap between accuracy and recall ensures balanced detection, minimizing both false alarms and missed threats. The model converges after 27 rounds with accuracy stabilizing at 94.5%.

The evolution of three performance metrics (accuracy, precision, and recall) with training rounds are presented in this figure. It converges by round 27 and the final metrics on all categories exceed 92%. A minimal performance gap between accuracy and precision (2.9%) and accuracy and recall (0.8%) indicates that the model maintains balanced detection capability, that is, that it can still perform well on both false positives and false negatives in anomaly detection.

In Fig. 12, both cumulative and round-wise bandwidth usage are tracked. FedCognis rapidly stabilizes to minimal bandwidth demands, showcasing its suitability for resource-constrained deployments.

This figure’s ROC curve shows the trade-off between true positive rate (TPR) and false positive rate (FPR) for the anomaly detection classifier in FedCognis. The model results in an AUC of 0.896 and optimal threshold of 0.443, which yields a 37% TPR at a strict 5% FPR. This shows that the model is highly discriminative in picking out true anomalies while having low false alert rates under tight constraints.

Fig. 13 highlights the scalability advantage of FedCognis. Even with hundreds of nodes, the runtime remains tractable, validating its applicability to large-scale cognitive cities.

Fig. 13 compares the computational scalability of FedCognis against centralized and vanilla FL architectures. FedCognis has 𝒪(n0.9) complexity which scales much better than centralized learning 𝒪(n1.8). In large networks, the speedup factor exceeds 1000×, proving that FedCognis is able to run on the real time basis even at scale, which makes it a perfect solution for industrial and urban scale IoT deployments.

While FedCognis has demonstrated high accuracy, security resilience, and communication efficiency in moderate-scale deployments, expanding the framework to city-scale networks with thousands of IIoT nodes introduces several non-trivial challenges. Although the system exhibits sublinear computational complexity (𝒪(n^0.9)), which supports scalability in principle, practical issues emerge as the network size grows beyond 1000 nodes.

First, communication bottlenecks may arise due to the increased volume of model updates transmitted during each aggregation round. Even though FedCognis uses selective trust-based filtering, in large networks the cumulative size of authenticated updates and their associated metadata (e.g., trust scores, model parameters) can saturate available bandwidth, especially in edge-constrained environments.

Second, the Quantum Secure Authentication (QSA) process—while lightweight for small networks—can become a computational burden at scale. Each update must be individually signed and verified, and with thousands of nodes participating per round, the cumulative verification latency can degrade real-time responsiveness. This is particularly problematic in time-critical infrastructures like traffic control or power grid management.

Third, managing and updating trust scores dynamically for a massive number of nodes can introduce synchronization delays and require additional memory overhead on the central server. Ensuring consistency and fairness in trust evaluation becomes harder when dealing with diverse device types, varying data quality, and fluctuating participation rates.

To address these challenges, future enhancements of FedCognis will explore several optimization strategies. These include:

Model compression and update sparsification to reduce communication payloads;

In summary, while FedCognis is architecturally capable of supporting large-scale IIoTCC environments, practical scalability will require targeted improvements in communication handling, authentication efficiency, and distributed coordination. Addressing these challenges will be crucial for enabling secure and real-time anomaly detection in future cognitive city deployments involving tens of thousands of devices.

To validate the scalability and robustness of FedCognis in real-world, city-scale deployments, we conducted a large-scale emulated simulation involving 5000 IIoT nodes across three major urban domains: traffic control, smart grid monitoring, and public safety. The simulation was designed to reflect the heterogeneity, communication sparsity, and adversarial dynamics commonly found in cognitive city infrastructures.

Simulation Setup

The 5000-node network was logically divided into:

2000 traffic nodes (e.g., signal controllers, intersection cameras, congestion sensors);

Each node operated on locally partitioned data derived from the WUSTL-IIoTCC-2021 base dataset, with domain-specific temporal perturbations introduced to simulate localized drift and seasonal variation. 10% of the nodes were adversarial, designed to inject poisoned updates intermittently.

The communication topology was semi-synchronous with cluster-based aggregation: nodes were grouped into 50 edge clusters, each containing 100 nodes. Local aggregation was performed at the cluster level before being pushed to the central global server using FedCognis’ trust-weighted, QSA-authenticated update mechanism.

Results and Observations

Runtime and Convergence:

FedCognis converged in 33 global rounds, with each round averaging 6.2 s in total processing time (local training + aggregation + QSA validation), demonstrating linear scalability with minimal degradation compared to smaller-scale runs.

Bandwidth Usage:

Average communication load per cluster dropped by 70%, owing to selective model update participation driven by trust filtering and sparse update scheduling. Total data transmission was reduced from an estimated 4.5 GB (centralized baseline) to 1.3 GB.

Latency Impact:

Average model update latency remained below 1.8 s, even under high node concurrency, due to parallelized QSA verification and the use of hierarchical aggregation.

Accuracy and Resilience:

Detection accuracy held steady at 93.8%, slightly lower than the 94.5% baseline in smaller experiments, with an AUC of 0.887 and adversarial resilience score of 95.3%. This confirms that FedCognis maintains strong performance even as network complexity and adversarial risk scale significantly.

FedCognis supports industry-standard lightweight communication protocols such as MQTT (Message Queuing Telemetry Transport) and OPC-UA (Open Platform Communications Unified Architecture). These protocols allow easy interfacing with IIoT edge devices such as smart meters, traffic sensors, surveillance systems, and programmable logic controllers (PLCs). The trust-aware communication architecture of FedCognis ensures that model updates and anomaly feedback can be securely exchanged over constrained networks using these protocols without protocol modification.

Many current IIoT deployments consist of legacy systems that lack native support for federated learning or cryptographic authentication. To support backward compatibility, FedCognis can operate through lightweight edge gateways that act as federated learning proxies. These gateways can preprocess data, manage QSA authentication, and communicate with the central aggregation server without requiring changes to legacy device firmware or operating systems.

Cognitive city environments demand rapid response to anomalies such as traffic congestion, grid overload, or intrusions. FedCognis’s asynchronous model update mode supports update intervals as low as 1–3 s, with end-to-end detection latency averaging 1.8 s in our WUSTL-IIoTCC simulation. This enables deployment in real-time control systems that require high-frequency updates while still minimizing communication overhead.

To align with real-world operational environments, FedCognis adheres to recognized cybersecurity standards:

NIST SP 800-53: Covers model integrity, access control, and adversarial resilience.

These compliance-ready features make FedCognis suitable for regulated sectors such as energy, public safety, and healthcare infrastructure in smart cities.

The integration roadmap demonstrates that FedCognis is not only a research prototype but a practical solution engineered for real-world IIoT deployments. It addresses the technical and regulatory barriers commonly faced when introducing intelligent anomaly detection systems into existing cognitive city infrastructure.