Due to the accelerated growth in digital music distribution, it becomes easy to modify, intercept, and distribute material illegally. To overcome the urgent need for copyright protection against piracy, several audio watermarking schemes have been proposed and implemented. These digital audio watermarking schemes have the purpose of embedding inaudible information within the host file to cover copyright and authentication issues. This thesis proposes an audio watermarking model using MATLAB® and Simulink® software for 1K and 2K fast Fourier transform (FFT) lengths. The watermark insertion process is performed in the frequency domain to guarantee the imperceptibility of the watermark to the human auditory system. Additionally, the proposed audio watermarking model was implemented in a Cyclone® II FPGA device from Altera® using the Altera® DSP Builder tool and MATLAB/Simulink® software. To evaluate the performance of the proposed audio watermarking scheme, effectiveness and fidelity performance tests were conducted for the proposed software and hardware-in-the-loop based audio watermarking model.

Unpredictable hardware faults and software bugs lead to application crashes, incorrect computations, unavailability of internet services, data losses, malfunctioning components, and consequently financial losses or even death of people. In particular, faults in microprocessors (CPUs) and memory corruption bugs are among the major unresolved issues of today. CPU faults may result in benign crashes and, more problematically, in silent data corruptions that can lead to catastrophic consequences, silently propagating from component to component and finally shutting down the whole system. Similarly, memory corruption bugs (memory-safety vulnerabilities) may result in a benign application crash but may also be exploited by a malicious hacker to gain control over the system or leak confidential data. Both these classes of errors are notoriously hard to detect and tolerate. Usual mitigation strategy is to apply ad-hoc local patches: checksums to protect specific computations against hardware faults and bug fixes to protect programs against known vulnerabilities. This strategy is unsatisfactory since it is prone to errors, requires significant manual effort, and protects only against anticipated faults. On the other extreme, Byzantine Fault Tolerance solutions defend against all kinds of hardware and software errors, but are inadequately expensive in terms of resources and performance overhead. In this thesis, we examine and propose five techniques to protect against hardware CPU faults and software memory-corruption bugs. All these techniques are hardware-assisted: they use recent advancements in CPU designs and modern CPU extensions. Three of these techniques target hardware CPU faults and rely on specific CPU features: ∆-encoding efficiently utilizes instruction-level parallelism of modern CPUs, Elzar re-purposes Intel AVX extensions, and HAFT builds on Intel TSX instructions. The rest two target software bugs: SGXBounds detects vulnerabilities inside Intel SGX enclaves, and “MPX Explained” analyzes the recent Intel MPX extension to protect against buffer overflow bugs. Our techniques achieve three goals: transparency, practicality, and efficiency. All our systems are implemented as compiler passes which transparently harden unmodified applications against hardware faults and software bugs. They are practical since they rely on commodity CPUs and require no specialized hardware or operating system support. Finally, they are efficient because they use hardware assistance in the form of CPU extensions to lower performance overhead.

Improving the functioning and the safety of the electrical grids is a topic of great concern, given its magnitude and importance in today's world. In this thesis, we focus in these two subjects. In the first part, we study undetectable cyber-physical attacks on power grids, which are attacks that involve physical disruptions, including tripping lines and load modifications, and sensor output alterations. We propose a sophisticated attack model described under the full Alternating Current (AC) power flow equations and show its feasibility on large grids from a test cases library. As counter-measures, we propose different defensive strategies that the network's controller can apply under a suspected cyber attack. These are random, simple and fast procedures that change the voltages across the network and aim to unmask the current status of the system, assuming that the attacker cannot react against their randomness. Secondly, with access to data collected through Phasor Measurement Units (PMUs) by a power utility in the United States, we perform statistical analyses on the frequency and voltage time series that have been recorded at a rate of 30 Hz. We focus on intervals of time where the sampled data shows to be in steady-state conditions and, with the use of appropriate signal processing filters, we are able to extract hidden anomalies such as spatio-temporal correlations between sensors and harmonic distortions.

No description available.

This thesis measured and aligned factors that contribute to the misalignment of the South African National Cybersecurity Policy Framework (SA-NCPF). The exponential growth rate of cyber-attacks and threats has caused more headaches for cybersecurity experts, law enforcement agents, organisations and the global business economy. The emergence of the global Corona Virus Disease-2019 has also contributed to the growth of cyber-attacks and threats thus, requiring concerted efforts from everyone in society to devise appropriate interventions that mitigate unacceptable user behaviour in the reality of cyberspace. In this study, various theories were identified and pooled together into an integrative theoretical framework to provide a better understanding of various aspects of the law-making process more comprehensively. The study identified nine influencing factors that contributed to misalignment of the South African National Cybersecurity Policy Framework. These influencing factors interact with each other continuously producing complex relationships, therefore, it is difficult to measure the degree of influence of each factor, hence the need to look at and measure the relationships as Gestalts. Gestalts view individual interactions between pairs of constructs only as a part of the overall pattern. Therefore, the integrative theoretical framework and Gestalts approach were used to develop a conceptual framework to measure the degree of alignment of influencing factors. This study proposed that the stronger the coherence among the influencing factors, the more aligned the South African National Security Policy Framework. The more coherent the SA-NCPF is perceived, the greater would be the degree of alignment of the country's cybersecurity framework to national, regional and global cyberlaws. Respondents that perceived a strong coherence among the elements also perceived an effective SA-NCPF. Empirically, this proposition was tested using nine constructs. Quantitative data was gathered from respondents using a survey. A major contribution of this study was that it was the first attempt in South Africa to measure the alignment of the SA-NCPF using the Gestalts approach as an effective approach for measuring complex relationships. The study developed the integrative theoretical framework which integrates various theories that helped to understand and explain the South African law making process. The study also made a significant methodological contribution by adopting the Cluster-based perspective to distinguish, describe and predict the degree of alignment of the SA-NCPF. There is a dearth of information that suggests that past studies have adopted or attempted to address the challenge of alignment of the SA-NCPF using the cluster-based and Gestalts perspectives. Practical implications from the study include a review of the law-making process, skills development strategy, a paradigm shift to address the global Covid-19 pandemic and sophisticated cybercrimes simultaneously. The study asserted the importance of establishing an independent cybersecurity board comprising courts, legal, cybersecurity experts, academics and law-makers to provide cybersecurity expertise and advice. From the research findings, government and practitioners can draw lessons to review the NCPF to ensure the country develops an effective national cybersecurity strategy. Limitations and recommendations for future research conclude the discussions of this study.

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The growing adoption of smart manufacturing systems and its related technologies (e.g., embedded sensing, internet-of-things, cyber-physical systems, big data analytics, and cloud computing) is promising a paradigm shift in the manufacturing industry. Such systems enable extracting and exchanging actionable knowledge across the different entities of the manufacturing cyber-physical system and beyond. From a quality control perspective, this allows for more opportunities to realize proactive product design; real-time process monitoring, diagnosis, prognosis, and control; and better product quality characterization. However, a multitude of challenges are arising, with the growing adoption of smart manufacturing, including industrial data characterized by increasing volume, velocity, variety, and veracity, as well as the security of the manufacturing system in the presence of growing connectivity. Taking advantage of these emerging opportunities and tackling the upcoming challenges require creating novel quality control and data analytics methods, which not only push the boundaries of the current state-of-the-art research, but discover new ways to analyze the data and utilize it. One of the key pillars of smart manufacturing systems is real-time automated process monitoring, diagnosis, and control methods for process/product anomalies. For machining applications, traditionally, deterioration in quality measures may occur due to a variety of assignable causes of variation such as poor cutting tool replacement decisions and inappropriate choice cutting parameters. Additionally, due to increased connectivity in modern manufacturing systems, process/product anomalies intentionally induced through malicious cyber-attacks -- aiming at degrading the process performance and/or the part quality -- is becoming a growing concern in the manufacturing industry. Current methods for detecting and diagnosing traditional causes of anomalies are primarily lab-based and require experts to perform initial set-ups and continual fine-tuning, reducing the applicability in industrial shop-floor applications. As for efforts accounting for process/product anomalies due cyber-attacks, these efforts are in early stages. Therefore, more foundational research is needed to develop a clear understanding of this new type of cyber-attacks and their effects on machining processes, to ensure smart manufacturing security both on the cyber and the physical levels. With primary focus on machining processes, the overarching goal of this dissertation work is to explore new ways to expand the use and value of manufacturing data-driven methods for better applicability in industrial shop-floors and increased security of smart manufacturing systems. As a first step toward achieving this goal, the work in this dissertation focuses on adopting this goal in three distinct areas of interest: (1) Statistical Process Monitoring of Time-Between-Events Data (e.g., failure-time data); (2) Defending against Product-Oriented Cyber-Physical Attacks on Intelligent Machining Systems; and (3) Modeling Machining Process Data: Time Series vs. Spatial Point Cloud Data Structures. / PHD / Recent advancements in embedded sensing, internet-of-things, big data analytics, cloud computing, and communication technologies and methodologies are shifting the modern manufacturing industry toward a novel operational paradigm. Several terms have been coined to refer to this new paradigm such as cybermanufacturing, industry 4.0, industrial internet of things, industrial internet, or more generically smart manufacturing (term to be used henceforth). The overarching goal of smart manufacturing is to transform modern manufacturing systems to knowledge-enabled Cyber-Physical Systems (CPS), in which humans, machines, equipment, and products communicate and cooperate together in real-time, to make decentralized decisions resulting in profound improvements in the entire manufacturing ecosystem. From a quality control perspective, this allows for more opportunities to utilize manufacturing process data to realize proactive product design; real-time process monitoring, diagnosis, prognosis, and control; and better product quality characterization. With primary focus on machining processes, the overarching goal of this work is to explore new ways to expand the use and value of manufacturing data-driven methods for better applicability in industrial shop-floors and increased security of smart manufacturing systems. As a first step toward achieving this goal, the work in this dissertation focuses on three distinct areas of interest: (1) Monitoring of time-between-events data of mechanical components replacements (e.g., failure-time data); (2) Defending against cyber-physical attacks on intelligent machining systems aiming at degrading machined parts quality; and (3) Modeling machining process data using two distinct data structures, namely, time series and spatial point cloud data.

Cyber-physical systems (CPSs) are large-scale systems that seamlessly integrate physical and human elements via a cyber layer that enables connectivity, sensing, and data processing. Key examples of CPSs include smart power systems, smart transportation systems, and the Internet of Things (IoT). This wide-scale cyber-physical interconnection introduces various operational benefits and promises to transform cities, infrastructure, and networked systems into more efficient, interactive, and interconnected smart systems. However, this ubiquitous connectivity leaves CPSs vulnerable to menacing security threats as evidenced by the recent discovery of the Stuxnet worm and the Mirai malware, as well as the latest reported security breaches in a number of CPS application domains such as the power grid and the IoT. Addressing these culminating security challenges requires a holistic analysis of CPS security which necessitates: 1) Determining the effects of possible attacks on a CPS and the effectiveness of any implemented defense mechanism, 2) Analyzing the multi-agent interactions -- among humans and automated systems -- that occur within CPSs and which have direct effects on the security state of the system, and 3) Recognizing the role that humans and their decision making processes play in the security of CPSs. Based on these three tenets, the central goal of this dissertation is to enhance the security of CPSs with human actors by developing fool-proof defense strategies founded on novel theoretical frameworks which integrate the engineering principles of CPSs with the mathematical concepts of game theory and human behavioral models. Towards realizing this overarching goal, this dissertation presents a number of key contributions targeting two prominent CPS application domains: the smart electric grid and drone systems. In smart grids, first, a novel analytical framework is developed which generalizes the analysis of a wide set of security attacks targeting the state estimator of the power grid, including observability and data injection attacks. This framework provides a unified basis for solving a broad set of known smart grid security problems. Indeed, the developed tools allow a precise characterization of optimal observability and data injection attack strategies which can target the grid as well as the derivation of optimal defense strategies to thwart these attacks. For instance, the results show that the proposed framework provides an effective and tractable approach for the identification of the sparsest stealthy attacks as well as the minimum sets of measurements to defend for protecting the system. Second, a novel game-theoretic framework is developed to derive optimal defense strategies to thwart stealthy data injection attacks on the smart grid, launched by multiple adversaries, while accounting for the limited resources of the adversaries and the system operator. The analytical results show the existence of a diminishing effect of aggregated multiple attacks which can be leveraged to successfully secure the system; a novel result which leads to more efficiently and effectively protecting the system. Third, a novel analytical framework is developed to enhance the resilience of the smart grid against blackout-inducing cyber attacks by leveraging distributed storage capacity to meet the grid's critical load during emergency events. In this respect, the results demonstrate that the potential subjectivity of storage units' owners plays a key role in shaping their energy storage and trading strategies. As such, financial incentives must be carefully designed, while accounting for this subjectivity, in order to provide effective incentives for storage owners to commit the needed portions of their storage capacity for possible emergency events. Next, the security of time-critical drone-based CPSs is studied. In this regard, a stochastic network interdiction game is developed which addresses pertinent security problems in two prominent time-critical drone systems: drone delivery and anti-drone systems. Using the developed network interdiction framework, the optimal path selection policies for evading attacks and minimizing mission completion times, as well as the optimal interdiction strategies for effectively intercepting the paths of the drones, are analytically characterized. Using advanced notions from Nobel-prize winning prospect theory, the developed framework characterizes the direct impacts of humans' bounded rationality on their chosen strategies and the achieved mission completion times. For instance, the results show that this bounded rationality can lead to mission completion times that significantly surpass the desired target times. Such deviations from the desired target times can lead to detrimental consequences primarily in drone delivery systems used for the carriage of emergency medical products. Finally, a generic security model for CPSs with human actors is proposed to study the diffusion of threats across the cyber and physical realms. This proposed framework can capture several application domains and allows a precise characterization of optimal defense strategies to protect the critical physical components of the system from threats emanating from the cyber layer. The developed framework accounts for the presence of attackers that can have varying skill levels. The results show that considering such differing skills leads to defense strategies which can better protect the system. In a nutshell, this dissertation presents new theoretical foundations for the security of large-scale CPSs, that tightly integrate cyber, physical, and human elements, thus paving the way towards the wide-scale adoption of CPSs in tomorrow's smart cities and critical infrastructure. / Ph. D. / Enhancing the efficiency, sustainability, and resilience of cities, infrastructure, and industrial systems is contingent on their transformation into more interactive and interconnected smart systems. This has led to the emergence of what is known as cyber-physical systems (CPSs). CPSs are widescale distributed and interconnected systems integrating physical components and humans via a cyber layer that enables sensing, connectivity, and data processing. Some of the most prominent examples of CPSs include the smart electric grid, smart cities, intelligent transportation systems, and the Internet of Things. The seamless interconnectivity between the various elements of a CPS introduces a wealth of operational benefits. However, this wide-scale interconnectivity and ubiquitous integration of cyber technologies render CPSs vulnerable to a range of security threats as manifested by recently reported security breaches in a number of CPS application domains. Addressing these culminating security challenges requires the development and implementation of fool-proof defense strategies grounded in solid theoretical foundations. To this end, the central goal of this dissertation is to enhance the security of CPSs by advancing novel analytical frameworks which tightly integrate the cyber, physical, and human elements of a CPS. The developed frameworks and tools enable the derivation of holistic defense strategies by: a) Characterizing the security interdependence between the various elements of a CPS, b) Quantifying the consequences of possible attacks on a CPS and the effectiveness of any implemented defense mechanism, c) Modeling the multi-agent interactions in CPSs, involving humans and automated systems, which have a direct effect on the security state of the system, and d) Capturing the role that human perceptions and decision making processes play in the security of CPSs. The developed tools and performed analyses integrate the engineering principles of CPSs with the mathematical concepts of game theory and human behavioral models and introduce key contributions to a number of CPS application domains such as the smart electric grid and drone systems. The introduced results enable strengthening the security of CPSs, thereby paving the way for their wide-scale adoption in smart cities and critical infrastructure.

The security and resiliency of electric power supply to serve critical facilities are of high importance in today's world. Instead of building large electric power grids and high capacity transmission lines, an intelligent microgrid (or smart grid) can be considered as a promising power supply alternative. In recent years, multi-agent systems have been proposed to provide intelligent energy control and management systems in microgrids. Multi-agent systems offer their inherent benefits of flexibility, extensibility, autonomy, reduced maintenance and more. The implementation of a control network based on multi-agent systems that is capable of making intelligent decisions on behalf of the user has become an area of intense research. Many previous works have proposed multi-agent system architectures that deal with buying and selling of energy within a microgrid and algorithms for auction systems. The others proposed frameworks for multi-agent systems that could be further developed for real life control of microgrid systems. However, most proposed methods ignore the process of sharing energy resources among multiple distinct sets of prioritized loads. It is important to study a scenario that emphasizes on supporting critical loads during outages based on the user's preferences and limited capacity. The situation becomes further appealing when an excess DER capacity after supplying critical loads is allocated to support non-critical loads that belong to multiple users. The previous works also ignore the study of dynamic interactions between the agents and the physical systems. It is important to study the interaction and time delay when an agent issues a control signal to control a physical device in a microgrid and when the command is executed. Agents must be able to respond to the information sensed from the external environment quickly enough to manage the microgrid in a timely fashion. The ability of agents to disconnect the microgrid during emergencies should also be studied. These issues are identified as knowledge gaps that are of focus in this thesis. The objective of this research is to design, develop and implement a multi-agent system that enables real-time management of a microgrid. These include securing critical loads and supporting non-critical loads belonging to various owners with the distributed energy resource that has limited capacity during outages. The system under study consists of physical (microgrid) and cyber elements (multi-agent system). The cyber part or the multi-agent system is of primary focus of this work. The microgrid simulation has been implemented in Matlab/Simulink. It is a simplified distribution circuit that consists of one distributed energy resources (DER), loads and the main grid power supply. For the multi-agent system implementation, various open source agent building toolkits are compared to identify the most suitable agent toolkit for implementation in the proposed multi-agent system. The agent architecture is then designed by dividing overall goal of the system into several smaller tasks and assigning them to each agent. The implementation of multi-agent system was completed by identifying Roles (Role Modeling) and Responsibilities (Social and Domain Responsibilities) of agents in the system, and modeling the Knowledge (Facts), rules and ontology for the agents. Finally, both microgrid simulation and multi-agent system are connected together via TCP/IP using external java programming and a third party TCP server in the Matlab/Simulink environment. In summary, the multi-agent system is designed, developed and implemented in several simulation test cases. It is expected that this work will provide an insight into the design and development of a multi-agent system, as well as serving as a basis for practical implementation of an agent-based technology in a microgrid environment. Furthermore, the work also contributes to new design schemes to increase multi-agent system's intelligence. In particular, these include control algorithms for intelligently managing the limited supply from a DER during emergencies to secure critical loads, and at the same time supporting non-critical loads when the users need the most. / Master of Science

Electric power systems are among the most complex man made systems on the world. Most of the time, they operate under quasi-steady state. With the ever increasing load demand and the advent of the deregulated power market recently, the power systems are pushed more often to operate close to their design limits and with more uncertainty of the system operating mode. With the increasing complexity and more interconnected systems, power systems are operating closer to their performance limits. As a result, maintaining system security and facilitating efficient system operation have been challenging tasks. Transmission systems are considered the most vital components in power systems connecting both generating/substation and consumer areas with several interconnected networks. In the past, they were owned by regulated, vertically integrated utility companies. They have been designed and operated so that conditions in close proximity to security boundaries are not frequently encountered. However, in the new open access environment, operating conditions tend to be much closer to security boundaries, as transmission use is increasing in sudden and unpredictable directions. Transmission unbundling, coupled with other regulatory requirements, has made new transmission facility construction more difficult. Unfortunately these transmission lines are frequently subjected to a wide variety of faults. Thus, providing proper protective functions for them is essential. Generally the protection of Extra High Voltage (EHV) and Ultra High Voltage (UHV) transmission lines are carried out by the use of distance relays in view of the fact that they provide fast fault clearance and system coordination. Transmission line relaying involves detection, classification and location of transmission line faults. Fast detections of faults enable quick isolation of the faulty line from service and hence, protecting it from the harmful effects of fault. Classification of faults means identification of the type of fault and faulted line section, and this information is required for finding the fault location and assessing the extent of repair work to be carried out. Accurate fault location is necessary for facilitating quick repair and restoration of the line, to improve the reliability and availability of the power supply. Generally, the protection system using conventional distance relaying algorithm involves three zones. The first zone (Z1) of the relay is set to detect faults on 80%90% of the protected line without any intentional time delay. The second zone (Z2) is set to protect the remainder of the line plus an adequate margin. Second zone relays are time delayed for 1530 cycles to coordinate with relays at remote bus. The settings of the third zone (Z3) ideally will cover the protected line, plus all of the longest line leaving the remote station. Z3 of a distance relay is used to provide the remote backup protection in case of the failure of the primary protection. Since Z3 covers an adjacent line, a large infeed (outfeed) from the remote terminal causes the relay to underreach (overreach). Thus, a very large load at the remote terminal may cause distance relays to mal-operate. Settings for conventional distance relays are selected to avoid overreach/underreach operation under the worst case scenarios. Studies of significant power system disturbances reported by North American Electric Reliability Council (NERC) indicate that protective relays are involved, one way or another, in 75% of the major disturbances and the most troublesome ones are backup protection relays. With their limited view of the interconnected network based on their locally measured inputs, conventional backup protection relays generally take actions to protect a localized region of the network without considering the impact on the whole network. Relay mal-operations or unintended operations due to overload, power swing, and relay hidden failure are the main factors contributing to the blackouts. Most of the problems are associated with relays tripping too many healthy lines. Since a relay makes the decision automatically to remove a component from the system according to its internal mechanism, the relay mal-operation or unintended operation can make an effective influence on the system stability. Approaches to reduce the relay misbehavior need to be identified. Real time monitoring tools to assess the relay misbehavior are needed, providing the system operator, the accurate information about unfolding events. Existing transmission line protection scheme still has drawbacks. Advanced fault analysis mechanism to enhance the system dependability and security simultaneously is desirable. Relay settings play a significant role in major blackouts. So correct settings should be calculated and coordinated by suitable studies. Attempts are to be made to employ highly accurate AI techniques in protective system implementation. The research work focussed on developing knowledge based intelligent tools for the improving the transmission system security. A process to obtain knowledgebase using SVMs for ready post-fault diagnosis purpose is developed. SVMs are used as Intelligent tool for identifying the faulted line that is emanating from a substation and finding the distance from the substation. The approach uses phasor values of the line voltages and currents after the fault has been detected. The approach is particularly important for post-fault diagnosis of any mal-operation of relays following a disturbance in the neighboring line connected to the same substation. This may help in improving the fault monitoring/diagnosis process and coordination of the protective relays, thus assuring secure operation of the power systems. The approach based on SVMs, exploits the first part of this goal. For comparison, a classifier and regression tools based on the RBFNNs was also investigated. The RBFNNs and SVM networks are introduced and considered as an appropriate tool for pattern recognition problems. Results on a practical 24Bus equivalent EHV transmission system of Indian Southern region and on IEEE39 bus New England system are presented to illustrate the proposed method. In a large connected power network, the number of generators are more in number and their set patterns number will be large. As the line flows are sensitive to generator set patterns, it is difficult to consider all the combinations of generators while simulating the training and testing patterns as input to SVMs. To simulate the training and testing patterns corresponding to possible changes in line flows to meet the load in the present deregulated environment, line flow sensitive generators set to be identified/merit-listed. In this regard, to identify the most sensitive generators for a particular line of interest, a method from the literature is adopted and developed a software program based on the graph theory concepts. Case studies on generator contributions towards loads and transmission lines are illustrated on an equivalent 33bus system, a part of Indian Northern grid with major part of Uttar Pradesh and also with an equivalent 246bus system of practical Indian Southern grid. A distance relay coordination approach is proposed using detailed simulation studies, taking into account various operating conditions and fault resistances. Support Vector Machines as a pattern classifier is used for obtaining distance relay coordination. The scheme uses the apparent impedance values observed during fault as inputs. SVMs are used to build the underlying concept between reach of different zones and the impedance trajectory during fault. An improved performance with the use of SVMs, keeping the reach when faced with different fault conditions as well as line flow changes are illustrated with an equivalent 246bus system of practical Indian Southern grid and also with an equivalent 265bus system of practical Indian Western grid. A strategy of Supportive System is described to aid the conventional protection philosophy in combating situations where protection systems are mal-operated and/or information is missing and provide selective and secure coordination. Highly accurate identification/discrimination of zones plays a key role in effective implementation of the region-wide supportive system. This typically requires a multiclass SVM classifier to effectively analyze/build the underlying concept between reach of different zones and the apparent impedance trajectory during fault. Different multiclass methods are compared for their performance with respect to accuracy, number of iterations, number of support vectors, training and testing time. The performance analysis of these methods is presented on three data sets belonging to the training and testing patterns of three supportive systems for a region, part of a network, which is an equivalent 265bus system of practical Indian Western grid.