Online Manner Research Articles

On adaptive resilient secondary control for DC microgrids under false data injection attacks

AbstractDistributed cooperative control strategies for DC microgrids have been rapidly evolving in recent years. However, introducing a cyber layer to enhance robustness, scalability, and reliability also exposes the system to potential cyber‐attacks. The damage inflicted by such attacks on the system performance can be catastrophic, reaching a point where it may devastate the system normal operation. By using model reference adaptive control (MRAC), this article proposes a resilient approach that does not require an accurate model of the system and despite the uncertainties for detecting false data injections into the reference DC voltage and simultaneously mitigating their adverse effects on the system stability and performance. The proposed technique employs an observer to detect possible false data injections in an online manner. By emulating the behavior of an ideal reference model, the MRAC ensures adaptive adjustments of the control parameters over time to mitigate the negative effects of potential attacks effectively and despite non‐idealities such as measurement noise, parameter variations, and environmental changes in DC microgrids, the MRAC effectively manages false data injection attacks. Simulation studies are conducted using diverse scenarios involving a three‐node DC microgrid to show the effectiveness of the proposed method.

Probabilistic Contrastive Learning for Long-Tailed Visual Recognition.

Long-tailed distributions frequently emerge in real-world data, where a large number of minority categories contain a limited number of samples. Such imbalance issue considerably impairs the performance of standard supervised learning algorithms, which are mainly designed for balanced training sets. Recent investigations have revealed that supervised contrastive learning exhibits promising potential in alleviating the data imbalance. However, the performance of supervised contrastive learning is plagued by an inherent challenge: it necessitates sufficiently large batches of training data to construct contrastive pairs that cover all categories, yet this requirement is difficult to meet in the context of class-imbalanced data. To overcome this obstacle, we propose a novel probabilistic contrastive (ProCo) learning algorithm that estimates the data distribution of the samples from each class in the feature space, and samples contrastive pairs accordingly. In fact, estimating the distributions of all classes using features in a small batch, particularly for imbalanced data, is not feasible. Our key idea is to introduce a reasonable and simple assumption that the normalized features in contrastive learning follow a mixture of von Mises-Fisher (vMF) distributions on unit space, which brings two-fold benefits. First, the distribution parameters can be estimated using only the first sample moment, which can be efficiently computed in an online manner across different batches. Second, based on the estimated distribution, the vMF distribution allows us to sample an infinite number of contrastive pairs and derive a closed form of the expected contrastive loss for efficient optimization. Other than long-tailed problems, ProCo can be directly applied to semi-supervised learning by generating pseudo-labels for unlabeled data, which can subsequently be utilized to estimate the distribution of the samples inversely. Theoretically, we analyze the error bound of ProCo. Empirically, extensive experimental results on supervised/semi-supervised visual recognition and object detection tasks demonstrate that ProCo consistently outperforms existing methods across various datasets.

Graph learning from incomplete graph signals: From batch to online methods

Inferring graph topologies from data is crucial in many graph-related applications. Existing works typically assume that signals are observed at all nodes, which may not hold due to application-specific constraints. The problem becomes more challenging when data are sequentially available and no delay is tolerated. To address these issues, we propose an approach for learning graphs from incomplete data. First, the problem of learning graphs with missing data is formulated as maximizing the posterior distribution with hidden variables from a Bayesian perspective. Then, we propose an expectation maximization (EM) algorithm to solve the induced problem, in which graph learning and graph signal recovery are jointly performed. Furthermore, we extend the proposed EM algorithm to an online version to accommodate the delay-sensitive situations of sequential data. Theoretically, we analyze the dynamic regret of the proposed online algorithm, illustrating the effectiveness of our algorithm in tracking graphs from partial observations in an online manner. Finally, extensive experiments on synthetic and real data are conducted, and the results corroborate that our approach can learn graphs effectively from incomplete data in both batch and online situations.

Electrotactile BCI for Top-Down Somatosensory Training: Clinical Feasibility Trial of Online BCI Control in Subacute Stroke Patients.

This study investigates the feasibility of a novel brain-computer interface (BCI) device designed for sensory training following stroke. The BCI system administers electrotactile stimuli to the user's forearm, mirroring classical sensory training interventions. Concurrently, selective attention tasks are employed to modulate electrophysiological brain responses (somatosensory event-related potentials-sERPs), reflecting cortical excitability in related sensorimotor areas. The BCI identifies attention-induced changes in the brain's reactions to stimulation in an online manner. The study protocol assesses the feasibility of online binary classification of selective attention focus in ten subacute stroke patients. Each experimental session includes a BCI training phase for data collection and classifier training, followed by a BCI test phase to evaluate online classification of selective tactile attention based on sERP. During online classification tests, patients complete 20 repetitions of selective attention tasks with feedback on attention focus recognition. Using a single electroencephalographic channel, attention classification accuracy ranges from 70% to 100% across all patients. The significance of this novel BCI paradigm lies in its ability to quantitatively measure selective tactile attention resources throughout the therapy session, introducing a top-down approach to classical sensory training interventions based on repeated neuromuscular electrical stimulation.

LSGDDN-LCD: An appearance-based loop closure detection using local superpixel grid descriptors and incremental dynamic nodes

Loop Closure Detection (LCD) is an essential component of visual Simultaneous Localization and Mapping (SLAM) systems. It enables the recognition of previously visited scenes to eliminate pose and map estimate drifts arising from long-term exploration. However, current appearance-based LCD methods face significant challenges, including high computational costs, viewpoint changes, and dynamic objects in scenes. This paper introduced an online appearance based LCD using Local Superpixel Grids Descriptor (LSGD) and Dynamic Nodes (DN), i.e., LSGDDN-LCD, to find similarities between scenes via handcrafted features extracted from the LSGD. Additionally, we proposed the adaptive mechanism to group similar scenes called DynamicNodes, which incrementally adjusted the database in an online manner, allowing for efficient and online retrieval of previously viewed images without need of the pre-training. Experimental results confirmed that the LSGDDN-LCD significantly improved LCD precision–recall and efficiency, and outperformed several state-of-the-art (SOTA) approaches on public and our own datasets, indicating its great potential as a generic LCD framework. Our implementation of the LSGDDN-LCD approach and the datasets were open-sourced on GitHub (https://github.com/BaoshengZhang0/LSGDDN-LCD.git).

Online Unmanned Aerial Vehicles Search Planning in an Unknown Search Environment

Unmanned Aerial Vehicles (UAVs) have been widely used in localized data collection and information search. However, there are still many practical challenges in real-world operations of UAV search, such as unknown search environments. Specifically, the payoff and cost at each search point are unknown for the planner in advance, which poses a great challenge to decision making. That is, UAV search decisions should be made sequentially in an online manner thereby adapting to the unknown search environment. To this end, this paper initiates the problem of online decision making in UAV search planning, where the drone has limited energy supply as a constraint and has to make an irrevocable decision to search this area or route to the next in an online manner. To overcome the challenge of unknown search environment, a joint-planning approach is proposed, where both route selection and search decision are made in an integrated online manner. The integrated online decision is made through an online linear programming which is proved to be near-optimal, resulting in high information search revenue. Furthermore, this joint-planning approach can be favorably applied to multi-round online UAV search planning scenarios, showing a great superiority in first-mover dominance of gathering information. The effectiveness of the proposed approach is validated in a widely applied dataset, and experimental results show the superior performance of online search decision making.

Online meta-learning approach for sensor fault diagnosis using limited data

The accurate and timely diagnosis of sensor faults plays a critical role in ensuring the reliability and performance of structural health monitoring (SHM) systems. However, the challenge is detecting, locating, and estimating sensor faults in an online manner using limited training data. To resolve this problem, a novel approach for online sensor fault diagnosis is proposed for SHM. The proposed approach is based on meta-learning, which enables superior model generalization capabilities using limited data. The detection, localization, and estimation of typical sensor faults in an online manner can be achieved efficiently by the proposed approach. First, a one-dimensional convolutional neural network (1D CNN) is designed to detect and locate faulty sensors. The initial model parameters of the 1D CNN are optimized using a model-agnostic meta-learning training strategy. This strategy allows the acquisition of transferable prior knowledge, which can speed up the learning process on new sensor fault detection and localization tasks. The meta-learning strategy also enables efficient and accurate detection and localization of potential faulty sensors with limited data. After detecting and locating the faulty sensors, an online updating algorithm based on a dual Kalman filter is used to estimate the severity of sensor faults and structural states simultaneously. The proposed approach is demonstrated with simulated sensor faults that cover a numerical example and field measurements from the Canton Tower. The results show that the proposed approach is applicable for online sensor fault diagnosis in SHM.

Online Multi-Resource Allocation for Network Slicing in 5G with Distributed Algorithms

With the increasing scale of mobile cellular network applications, 5G mobile network infrastructure provides customizable services to users in the form of network slices. How to effectively allocate existing resources in real dynamic networks with time-varying network utility is a key issue that previous work did not consider. This paper first initializes the multi-resource allocation problem of network slicing in an online manner, where the utility function is set to change over time. Therefore, we propose Metis, an online network slicing resource allocation framework that combines the time-varying nature of the network utility function given bandwidth and processing power constraints with the requirement of virtual network function isolation. The goal is to maximize the cumulative network utility in the long term and specify multiple resource allocation problems by utilizing concave optimization methods. In addition, a distributed algorithm based on the online alternating direction method of multipliers with regret optimization has been developed to achieve optimal resource allocation. Our mathematical analysis proves that Metis can provably converge to the optimal solution and the result of experiments demonstrates a steady state behavior of Metis, which converges in dynamic network settings.

Insight into local defect resonance and its in-situ measurement based on flexible nano-composite sensors

The local defect resonance has been proven to be effective for damage detection, and the methods based on LDR for damage evaluation have demonstrated appealing capabilities of selective assessment and applicability to complex structures. To explain the generation of LDR, models based on vibration theories have been developed in which the defect boundaries are assumed to be fixed. Nevertheless, existing models can only give an accurate prediction of frequency for fundamental LDR mode owing to the deviation of their assumptions from the reality. In addition, the measurement of LDR is currently limited to noncontact technologies, hampering its application to in-situ and online monitoring of inspected structures. To overcome these deficiencies, an analytical model is proposed in this investigation to gain an insight into the generation of LDR from the perspective of wave reflection at defect boundaries and wave superposition. In this model, the interaction of guided waves with defect is scrutinized using a normal mode expansion method to obtain the phase shift of the reflected waves at the defect boundaries. On this basis, the formation of standing waves is analyzed to interpret the occurrence of the resonance of guided waves, whereby the relation of the LDR frequencies and the defect parameters can be obtained. On top of this analytical investigation, the sensing of the LDR using a novel nano-composite sensor is attempted. Flexible and lightweight, these sensors can form a dense sensing network, with which the LDR response in the inspected region can be perceived. Using the LDR-based method and nano-composite sensors, this approach can give a damage characterization in an in-situ and online manner for complex structures. Experimental validations of the proposed approach is performed in which delaminations in composite structures are identified and assessed using the LDR response perceived with the nano-composite sensors.

The moderating role of perseverance and determination in action in the context of self-efficacy and life satisfaction of sportspeople with mobility impairment

Introduction: The article assumes the biopsychosocial model of disability and refers, inter alia, to the assumptions of the concept of empowerment, which recognizes the fact that practicing sports by people with disabilities creates favorable conditions for strengthening resources and developing skills. An attempt was made to develop a model that verifies the moderating importance of mental resilience in the aspect of experiencing a sense of effectiveness and life satisfaction in sportspeople with mobility impairment. Material and method: The research conducted in an encrypted online manner involved 58 people (31 able-bodied sportspeople and 27 sportspeople with physical disabilities). The following tools were used in this study: the Satisfaction with Life Scale (SWLS), the General Self-Efficacy Scale (GSES), the Positivity Scale (P Scale), the Resilience Scale (RS 25) and a demographic questionnaire. The conducted exploratory analyses which ultimately constitute the basis of the mathematically verified model of interactions between the variables identified in the study, as proposed in the article, showed a statistically significant influence of the RS 25 subscale Perseverance and determination in action as a moderator, both in relation to variables, physical disability and life satisfaction, as well as relationships between the variables of motor impairment and self-efficacy. Results: Having taken into consideration group abundance, strength of the effect and statistical significance, it is possible to make attempts to generalize findings of this study into the general population of athletes. Modelling based on subscales turned out to be the most adequate one, as it allowed discovering more in-depth relations between variables. Conclusions: Statistical analysis confirmed the assumed lack of differences between athletes with and without disabilities regarding the life satisfaction variable. It did not confirm that athletes with disabilities had higher scores in the self-efficacy variable (in GSES questionnaire) than regular athletes. It is important to note that physical disability or lack of it moderated by perseverance and determination influences both life satisfaction and self-efficacy in a statistically significant way. Based on conducted statistical analysis, in relations to the initially presented model, the mathematically revised model of confirmed interactions and relations between variables was proposed.

Solar photovoltaic power forecasting system with online manner based on adaptive mode decomposition and multi-objective optimization

Constructing an accurate and reliable solar photovoltaic (PV) power forecasting system is crucial for smart grid management and dispatch. However, due to the intermittent, non-stationary and random nature of solar energy, current methods cannot effectively capture the dynamic change patterns of PV data, resulting in a forecasting accuracy that cannot satisfy the requirement for stable operation of smart grids. To address this issue, in this paper, a new solar PV power forecasting system is proposed based on a new adaptive mode decomposition method that combines machine learning models. First an adaptive mode decomposition method is proposed for adaptively eliminating high-frequency information of PV data, mitigating the impact of high noise on the forecasting performance. Then the powerful mapping ability of machine learning model is utilized to construct a solar PV power generation combination forecasting system. The system adopts a multi-objective optimization strategy to determine the optimal weights of the combination model, which reduces the volatility of the forecasting results and enhances the stability of the forecasting system. Experimental results demonstrate that the proposed system achieves the best overall performance with online manner on 10 state-of-the-art baselines. Furthermore, the evaluation analysis by Diebold–Mariano test, improvement ratio and sensitivity analysis further show that the stability and accuracy of the proposed system outperforms the comparative baselines.

BONES: Near-Optimal Neural-Enhanced Video Streaming

Accessing high-quality video content can be challenging due to insufficient and unstable network bandwidth. Recent advances in neural enhancement have shown promising results in improving the quality of degraded videos through deep learning. Neural-Enhanced Streaming (NES) incorporates this new approach into video streaming, allowing users to download low-quality video segments and then enhance them to obtain high-quality content without violating the playback of the video stream. We introduce BONES, an NES control algorithm that jointly manages the network and computational resources to maximize the quality of experience (QoE) of the user. BONES formulates NES as a Lyapunov optimization problem and solves it in an online manner with near-optimal performance, making it the first NES algorithm to provide a theoretical performance guarantee. Comprehensive experimental results indicate that BONES increases QoE by 5% to 20% over state-of-the-art algorithms with minimal overhead. Our code is available at https://github.com/UMass-LIDS/bones.

Exploiting residual errors in nonlinear online prediction

We introduce a novel online (or sequential) nonlinear prediction approach that incorporates the residuals, i.e., prediction errors in the past observations, as additional features for the current data. Including the past error terms in an online prediction algorithm naturally improves prediction performance significantly since this information is essential for an algorithm to adjust itself based on its past errors. These terms are well exploited in many linear statistical models such as ARMA, SES, and Holts-Winters models. However, the past error terms are rarely or in a certain sense not optimally exploited in nonlinear prediction models since training them requires complex nonlinear state-space modeling. To this end, for the first time in the literature, we introduce a nonlinear prediction framework that utilizes not only the current features but also the past error terms as additional features, thereby exploiting the residual state information in the error terms, i.e., the model’s performance on the past samples. Since the new feature vectors contain error terms that change with every update, our algorithm jointly optimizes the model parameters and the feature vectors simultaneously. We achieve this by introducing new update equations that handle the effects resulting from the changes in the feature vectors in an online manner. We use soft decision trees and neural networks as the nonlinear prediction algorithms since these are the most widely used methods in highly publicized competitions. However, as we show, our methods are generic and any algorithm supporting gradient calculations can be straightforwardly used. We show through our experiments on the well-known real-life competition datasets that our method significantly outperforms the state-of-the-art. We also provide the implementation of our approach including the source code to facilitate reproducibility (https://github.com/ahmetberkerkoc/SDT-ARMA).

Client selection for federated learning using combinatorial multi-armed bandit under long-term energy constraint

In a federated learning system, it is often the case that the more clients it involves, the less increment of the outcome it achieves. It is thus essential to design a client selection strategy to choose an appropriate subset of the clients to participate in federated learning. However, client selection is not easy due to the heterogeneity of clients and the long-term energy budget of each client. Moreover, long-term energy budgets intertwined with the short-term client selection often make the problem NP-hard. In this paper, we propose an online strategy Energy-Aware Client Selection for Federated Learning (EACS-FL) to address this problem. The problem is formulated with a joint energy and delay optimization objective, and the Combinatorial Multi-Armed Bandit (CMAB) is introduced to solve the problem in an online manner. We take advantage of Lyapunov optimization to manage energy consumption of clients, which enables us to deal with independent energy budgets through minimizing virtual energy deficit queues. Theoretical analysis shows that EACS-FL achieves sublinear regret and keeps all queues stable. Experiment results exhibit that the proposed approach outperforms the existing works and achieves close-to-optimal delay and energy consumption performance.

BONES: Near-Optimal Neural-Enhanced Video Streaming

Accessing high-quality video content can be challenging due to insufficient and unstable network bandwidth. Recent advances in neural enhancement have shown promising results in improving the quality of degraded videos through deep learning. Neural-Enhanced Streaming (NES) incorporates this new approach into video streaming, allowing users to download low-quality video segments and then enhance them to obtain high-quality content without violating the playback of the video stream. We introduce BONES, an NES control algorithm that jointly manages the network and computational resources to maximize the quality of experience (QoE) of the user. BONES formulates NES as a Lyapunov optimization problem and solves it in an online manner with near-optimal performance, making it the first NES algorithm to provide a theoretical performance guarantee. Comprehensive experimental results indicate that BONES increases QoE by 5% to 20% over state-of-the-art algorithms with minimal overhead. Our code is available at https://github.com/UMass-LIDS/bones.

Sparsify dynamically expandable network via variational dropout

This paper develops a new method for lifelong learning referred to as Sparsify Dynamically Expandable Network (SDEN) via Variational Dropout, which explores a sparse model while preserving the performance. Dynamically Expandable Network (DEN) can learn a sequence of tasks via performing network retraining, network expansion by adding only the necessary neurons, and network split to effectively prevent semantic drift in an online manner. To overcome point estimation of parameters in DEN, Bayesian Compression for DEN is developed under the Bayesian framework. However, this method demands more time for model training and testing. To improve the model efficiency, we propose SDEN under the efficient sparse learning framework. We validate our SDEN in the lifelong learning scenarios with multiple frequently used benchmarks, on which it can obtain comparable classification accuracy, and less training and testing time compared with the comparison methods. Furthermore, our method can also learn a more sparse network structure which means fewer network parameters.

Modeling Rationality: Toward Better Performance Against Unknown Agents in Sequential Games.

Opponent modeling is necessary for autonomous agents to capture the intents of others during strategic interactions. Most previous works assume that they can access enough interaction history to build the model. However, it may not be realistic. To solve this problem, we present a novel rationality-consistent opponent modeling (ROM) method for games with imperfect information. In our approach, a game-theoretical concept of consistence about rationality is proposed to take advantage of the characteristic of imperfect information sequential games that rational behavior at disjoint information sets is correlated through anticipated opponent's behavior. With the correlation between different information sets, agents could infer the opponents' strategies at information sets correlated to observed behavior. To exploit the correlation, ROM attempts to conduct reasoning from the opponent's perspective and rationalize its past behavior. In this way, ROM acquires the ability to better adapt to different opponents and achieves a more accurate opponent model with insufficient observation history, which is verified by experiments in different settings. A heuristic adaptation approach is also applied in ROM, which updates the opponent model in an online manner and significantly reduces the computation cost. We evaluate ROM in both a grid world game and a poker game. Compared with other opponent modeling methods, ROM shows better performance and has more accurate predictions in both games against different types of opponents with limited action interactions. Experimental results also show that ROM's time cost is significantly reduced through heuristic adaptation.

Intersection control based on Fine-grained Phases for connected and automated vehicles

Traditional traffic signal control is one of the most widely used urban traffic control methods, due to its high efficiency, robustness, and simplicity. However, in the era of connected and automated vehicles (CAVs), it is prospective to enhance traffic control precision and achieve vehicle coordination in a more efficient manner. Focusing on an isolated intersection, this study proposes an innovative concept of Fine-grained Phase (FP) for CAV-enabled traffic control, which realizes more refined right-of-way allocation than traditional signal phases while preserving the simplicity and scalability. The development of FP jointly optimizes traffic control strategy and intersection layout design to fully utilize time-space resources, and multiple forms of FP could be generated in response to various traffic demands; meanwhile, vehicle coordination is achieved in an offline–online manner to balance solution quality and efficiency. Under the FP-based control, each lane is assigned with periodical entry time points using FP design results, then vehicles are supposed to catch up with the appropriate time points to fulfill their trips. Theoretical analyses are conducted under stationary vehicle arrival patterns, where the average delay and the intersection capacity associated with different forms of FP can be analytically acquired. For the implementation of FP-based control, we construct a general offline–online framework, consisting of an offline model that optimizes the geometry of the conflict zone at intersections and the control strategy of vehicles simultaneously, which is formulated as a mixed-integer linear programming problem, and an online FP adoption mechanism that can adapt to varying demand patterns. Under the framework, limited online computation is required, facilitating its practical real-time implementation. Simulation studies under a variety of demand settings show that FP-based control is advantageous over benchmark methods in reducing vehicle delay and also improving intersection capacity in most cases; even for cases with extremely imbalanced demands, FP-based control can admit comparable throughput, while the average delay is much smaller. In addition, results of computation time reveal that FP-based control could realize real-time implementation with negligible computation burden.

Online continual decoding of streaming EEG signal with a balanced and informative memory buffer

Electroencephalography (EEG) based Brain Computer Interface (BCI) systems play a significant role in facilitating how individuals with neurological impairments effectively interact with their environment. In real world applications of BCI system for clinical assistance and rehabilitation training, the EEG classifier often needs to learn on sequentially arriving subjects in an online manner. As patterns of EEG signals can be significantly different for different subjects, the EEG classifier can easily erase knowledge of learnt subjects after learning on later ones as it performs decoding in online streaming scenario, namely catastrophic forgetting. In this work, we tackle this problem with a memory-based approach, which considers the following conditions: (1) subjects arrive sequentially in an online manner, with no large scale dataset available for joint training beforehand, (2) data volume from the different subjects could be imbalanced, (3) decoding difficulty of the sequential streaming signal vary, (4) continual classification for a long time is required. This online sequential EEG decoding problem is more challenging than classic cross subject EEG decoding as there is no large-scale training data from the different subjects available beforehand. The proposed model keeps a small balanced memory buffer during sequential learning, with memory data dynamically selected based on joint consideration of data volume and informativeness. Furthermore, for the more general scenarios where subject identity is unknown to the EEG decoder, aka. subject agnostic scenario, we propose a kernel based subject shift detection method that identifies underlying subject changes on the fly in a computationally efficient manner. We develop challenging benchmarks of streaming EEG data from sequentially arriving subjects with both balanced and imbalanced data volumes, and performed extensive experiments with a detailed ablation study on the proposed model. The results show the effectiveness of our proposed approach, enabling the decoder to maintain performance on all previously seen subjects over a long period of sequential decoding. The model demonstrates the potential for real-world applications.

Heterogeneous Forgetting Rates and Greedy Allocation in Slot-Based Memory Networks Promotes Signal Retention.

A key question in the neuroscience of memory encoding pertains to the mechanisms by which afferent stimuli are allocated within memory networks. This issue is especially pronounced in the domain of working memory, where capacity is finite. Presumably the brain must embed some "policy" by which to allocate these mnemonic resources in an online manner in order to maximally represent and store afferent information for as long as possible and without interference from subsequent stimuli. Here, we engage this question through a top-down theoretical modeling framework. We formally optimize a gating mechanism that projects afferent stimuli onto a finite number of memory slots within a recurrent network architecture. In the absence of external input, the activity in each slot attenuates over time (i.e., a process of gradual forgetting). It turns out that the optimal gating policy consists of a direct projection from sensory activity to memory slots, alongside an activity-dependent lateral inhibition. Interestingly, allocating resources myopically (greedily with respect to the current stimulus) leads to efficient utilization of slots over time. In other words, later-arriving stimuli are distributed across slots in such a way that the network state is minimally shifted and so prior signals are minimally "overwritten." Further, networks with heterogeneity in the timescales of their forgetting rates retain stimuli better than those that are more homogeneous. Our results suggest how online, recurrent networks working on temporally localized objectives without high-level supervision can nonetheless implement efficient allocation of memory resources over time.