Visible to the public Biblio

Found 101 results

Filters: Keyword is Stability analysis  [Clear All Filters]
Conference Paper
Halabi, Talal, Haque, Israat, Karimipour, Hadis.  2022.  Adaptive Control for Security and Resilience of Networked Cyber-Physical Systems: Where Are We? 2022 IEEE 4th International Conference on Trust, Privacy and Security in Intelligent Systems, and Applications (TPS-ISA). :239–247.

Cyber-Physical Systems (CPSs), a class of complex intelligent systems, are considered the backbone of Industry 4.0. They aim to achieve large-scale, networked control of dynamical systems and processes such as electricity and gas distribution networks and deliver pervasive information services by combining state-of-the-art computing, communication, and control technologies. However, CPSs are often highly nonlinear and uncertain, and their intrinsic reliance on open communication platforms increases their vulnerability to security threats, which entails additional challenges to conventional control design approaches. Indeed, sensor measurements and control command signals, whose integrity plays a critical role in correct controller design, may be interrupted or falsely modified when broadcasted on wireless communication channels due to cyber attacks. This can have a catastrophic impact on CPS performance. In this paper, we first conduct a thorough analysis of recently developed secure and resilient control approaches leveraging the solid foundations of adaptive control theory to achieve security and resilience in networked CPSs against sensor and actuator attacks. Then, we discuss the limitations of current adaptive control strategies and present several future research directions in this field.

Cai, Chuanjie, Zhang, Yijun, Chen, Qian.  2022.  Adaptive control of bilateral teleoperation systems with false data injection attacks and attacks detection. 2022 41st Chinese Control Conference (CCC). :4407—4412.
This paper studies adaptive control of bilateral teleoperation systems with false data injection attacks. The model of bilateral teleoperation system with false data injection attacks is presented. An off-line identification approach based on the least squares is used to detect whether false data injection attacks occur or not in the communication channel. Two Bernoulli distributed variables are introduced to describe the packet dropouts and false data injection attacks in the network. An adaptive controller is proposed to deal stability of the system with false data injection attacks. Some sufficient conditions are proposed to ensure the globally asymptotical stability of the system under false data injection attacks by using Lyapunov functional methods. A bilateral teleoperation system with two degrees of freedom is used to show the effectiveness of gained results.
Belmouhoub, Amina, Bouzid, Yasser, Medjmadj, Slimane, Derrouaoui, Saddam Hocine, Guiatni, Mohamed.  2022.  Advanced Backstepping Control: Application on a Foldable Quadrotor. 2022 19th International Multi-Conference on Systems, Signals & Devices (SSD). :609–615.
This paper deals with the implementation of robust control, based on the finite time Lyapunov stability theory, to solve the trajectory tracking problem of an unconventional quadrotor with rotating arms (also known as foldable drone). First, the model of this Unmanned Aerial Vehicle (UAV) taking into consideration the variation of the inertia, the Center of Gravity (CoG) and the control matrix is presented. The theoretical foundations of backstepping control enhanced by a Super-Twisting (ST) algorithm are then discussed. Numerical simulations are performed to demonstrate the effectiveness of the proposed control strategy. Finally, a qualitative and quantitative comparative study is made between the proposed controller and the classical backstepping controller. Overall, the results obtained show that the proposed control approach provides better performance in terms of accuracy and resilience.
ISSN: 2474-0446
Pardede, Hilman, Zilvan, Vicky, Ramdan, Ade, Yuliani, Asri R., Suryawati, Endang, Kusumowardani, Renni.  2022.  Adversarial Networks-Based Speech Enhancement with Deep Regret Loss. 2022 5th International Conference on Networking, Information Systems and Security: Envisage Intelligent Systems in 5g//6G-based Interconnected Digital Worlds (NISS). :1–6.
Speech enhancement is often applied for speech-based systems due to the proneness of speech signals to additive background noise. While speech processing-based methods are traditionally used for speech enhancement, with advancements in deep learning technologies, many efforts have been made to implement them for speech enhancement. Using deep learning, the networks learn mapping functions from noisy data to clean ones and then learn to reconstruct the clean speech signals. As a consequence, deep learning methods can reduce what is so-called musical noise that is often found in traditional speech enhancement methods. Currently, one popular deep learning architecture for speech enhancement is generative adversarial networks (GAN). However, the cross-entropy loss that is employed in GAN often causes the training to be unstable. So, in many implementations of GAN, the cross-entropy loss is replaced with the least-square loss. In this paper, to improve the training stability of GAN using cross-entropy loss, we propose to use deep regret analytic generative adversarial networks (Dragan) for speech enhancements. It is based on applying a gradient penalty on cross-entropy loss. We also employ relativistic rules to stabilize the training of GAN. Then, we applied it to the least square and Dragan losses. Our experiments suggest that the proposed method improve the quality of speech better than the least-square loss on several objective quality metrics.
Yaning, Guo, Qianwen, Wang.  2021.  Analysis of Collaborative Co-Governance Path of Public Crisis Emergency Management in An All-Media Environment: —Theoretical Research Based on Multi-Agent. 2021 International Conference on Management Science and Software Engineering (ICMSSE). :235–238.
Multi-Agent system has the advantages of information sharing, knowledge accumulation and system stability, which is consistent with the concept of collaborative co-governance of public crisis management, and provides support for dealing with sudden public crises. Based on the background of the all-media environment, this study introduces the Internet-driven mass data management (“ crowdsourcing” crisis management) as a part of the crisis response system to improve the quality of information resource sharing. Crowdsourcing crisis management and Multi-Agent collaborative co-governance mechanism are combined with each other, so as to achieve a higher level of joint prevention and control mechanism, and explore how to effectively share information resources and emergency management resources across regions and departments in public crisis events.
Pandey, A.K., Agrawal, C.P..  2014.  Analytical Network Process based model to estimate the quality of software components. Issues and Challenges in Intelligent Computing Techniques (ICICT), 2014 International Conference on. :678-682.

Software components are software units designed to interact with other independently developed software components. These components are assembled by third parties into software applications. The success of final software applications largely depends upon the selection of appropriate and easy to fit components in software application according to the need of customer. It is primary requirement to evaluate the quality of components before using them in the final software application system. All the quality characteristics may not be of same significance for a particular software application of a specific domain. Therefore, it is necessary to identify only those characteristics/ sub-characteristics, which may have higher importance over the others. Analytical Network Process (ANP) is used to solve the decision problem, where attributes of decision parameters form dependency networks. The objective of this paper is to propose ANP based model to prioritize the characteristics /sub-characteristics of quality and to o estimate the numeric value of software quality.
 

Ali AL-Jumaili, Ahmed Hadi, Muniyandi, Ravie Chandren, Hasan, Mohammad Kamrul, Singh, Mandeep Jit, Siaw Paw, Johnny Koh.  2022.  Analytical Survey on the Security Framework of Cyber-Physical Systems for Smart Power System Networks. 2022 International Conference on Cyber Resilience (ICCR). :1—8.
Cyber-Physical Power System (CPPS) is one of the most critical infrastructure systems due to deep integration between power grids and communication networks. In the power system, cascading failure is spreading more readily in CPPS, even leading to blackouts as well as there are new difficulties with the power system security simulation and faults brought by physical harm or network intrusions. The current study summarized the cross- integration of several fields such as computer and cyberspace security in terms of the robustness of Cyber-Physical Systems, viewed as Interconnected and secure network systems. Therefore, the security events that significantly influenced the power system were evaluated in this study, besides the challenges and future directions of power system security simulation technologies were investigated for posing both challenges and opportunities for simulation techniques of power system security like building a new power system to accelerate the transformation of the existing energy system to a clean, low-carbon, safe, and efficient energy system which is used to assure power system stability through fusion systems that combine the cyber-physical to integrate the battery power station, power generation and renewable energy resources through the internet with the cyber system that contains Smart energy system control and attacks.
Ibrahim, M., Alsheikh, A..  2018.  Assessing Level of Resilience Using Attack Graphs. 2018 10th International Conference on Electronics, Computers and Artificial Intelligence (ECAI). :1–6.
Cyber-Physical-Systems are subject to cyber-attacks due to existing vulnerabilities in the various components constituting them. System Resiliency is concerned with the extent the system is able to bounce back to a normal state under attacks. In this paper, two communication Networks are analyzed, formally described, and modeled using Architecture Analysis & Design Language (AADL), identifying their architecture, connections, vulnerabilities, resources, possible attack instances as well as their pre-and post-conditions. The generated network models are then verified against a security property using JKind model checker integrated tool. The union of the generated attack sequences/scenarios resulting in overall network compromise (given by its loss of stability) is the Attack graph. The generated Attack graph is visualized graphically using Unity software, and then used to assess the worst Level of Resilience for both networks.
Xia, Hongbing, Bao, Jinzhou, Guo, Ping.  2021.  Asymptotically Stable Fault Tolerant Control for Nonlinear Systems Through Differential Game Theory. 2021 17th International Conference on Computational Intelligence and Security (CIS). :262—266.
This paper investigates an asymptotically stable fault tolerant control (FTC) method for nonlinear continuous-time systems (NCTS) with actuator failures via differential game theory (DGT). Based on DGT, the FTC problem can be regarded as a two-player differential game problem with control player and fault player, which is solved by utilizing adaptive dynamic programming technique. Using a critic-only neural network, the cost function is approximated to obtain the solution of the Hamilton-Jacobi-Isaacs equation (HJIE). Then, the FTC strategy can be obtained based on the saddle point of HJIE, and ensures the satisfactory control performance for NCTS. Furthermore, the closed-loop NCTS can be guaranteed to be asymptotically stable, rather than ultimately uniformly bounded in corresponding existing methods. Finally, a simulation example is provided to verify the safe and reliable fault tolerance performance of the designed control method.
G, Amritha, Kh, Vishakh, C, Jishnu Shankar V, Nair, Manjula G.  2022.  Autoencoder Based FDI Attack Detection Scheme For Smart Grid Stability. 2022 IEEE 19th India Council International Conference (INDICON). :1—5.
One of the major concerns in the real-time monitoring systems in a smart grid is the Cyber security threat. The false data injection attack is emerging as a major form of attack in Cyber-Physical Systems (CPS). A False data Injection Attack (FDIA) can lead to severe issues like insufficient generation, physical damage to the grid, power flow imbalance as well as economical loss. The recent advancements in machine learning algorithms have helped solve the drawbacks of using classical detection techniques for such attacks. In this article, we propose to use Autoencoders (AE’s) as a novel Machine Learning approach to detect FDI attacks without any major modifications. The performance of the method is validated through the analysis of the simulation results. The algorithm achieves optimal accuracy owing to the unsupervised nature of the algorithm.
Wang, Yazhou, Li, Bing, Zhang, Yan, Wu, Jiaxin, Yuan, Pengwei, Liu, Guimiao.  2020.  A Biometric Key Generation Mechanism for Authentication Based on Face Image. 2020 IEEE 5th International Conference on Signal and Image Processing (ICSIP). :231—235.
Facial biometrics have the advantages of high reliability, strong distinguishability and easily acquired for authentication. Therefore, it is becoming wildly used in identity authentication filed. However, there are stability, security and privacy issues in generating face key, which brings great challenges to face biometric authentication. In this paper, we propose a biometric key generation scheme based on face image. On the one hand, a deep neural network model for feature extraction is used to improve the stability of identity authentication. On the other hand, a key generation mechanism is designed to generate random biometric key while hiding original facial biometrics to enhance security and privacy of user authentication. The results show the FAR reach to 0.53% and the FRR reach to 0.57% in LFW face database, which achieves the better performance of biometric identification, and the proposed method is able to realize randomness of the generated biometric keys by NIST statistical test suite.
Shvidkiy, A. A., Savelieva, A. A., Zarubin, A. A..  2021.  Caching Methods Analysis for Improving Distributed Storage Systems Performance. 2021 Systems of Signal Synchronization, Generating and Processing in Telecommunications (SYNCHROINFO. :1—5.
The object of the research is distributed software-defined storage systems, as well as methods of caching disk devices. It is important for improving the performance of storage systems, which is relevant in modern conditions. In this article, an assessment of the possibility of improving performance through the use of various caching methods is made, as well as experimental research and analysis of the results obtained. The parameters of the application's operation with the disk subsystem have been determined. The results of experiments are presented - testing was carried out on a deployed architecture of a distributed storage with two types of caching, the results are combined in graphs. Conclusions are drawn, including on the prospects for further research.
Gupta, A., Johnson, J., Alahi, A., Fei-Fei, L..  2017.  Characterizing and Improving Stability in Neural Style Transfer. 2017 IEEE International Conference on Computer Vision (ICCV). :4087–4096.

Recent progress in style transfer on images has focused on improving the quality of stylized images and speed of methods. However, real-time methods are highly unstable resulting in visible flickering when applied to videos. In this work we characterize the instability of these methods by examining the solution set of the style transfer objective. We show that the trace of the Gram matrix representing style is inversely related to the stability of the method. Then, we present a recurrent convolutional network for real-time video style transfer which incorporates a temporal consistency loss and overcomes the instability of prior methods. Our networks can be applied at any resolution, do not require optical flow at test time, and produce high quality, temporally consistent stylized videos in real-time.

Zhang, Meng, Shen, Chao, Han, Sicong.  2019.  A Compensation Control Scheme against DoS Attack for Nonlinear Cyber-Physical Systems. 2019 Chinese Control Conference (CCC). :144–149.

This paper proposes a compensation control scheme against DoS attack for nonlinear cyber-physical systems (CPSs). The dynamical process of the nonlinear CPSs are described by T-S fuzzy model that regulated by the corresponding fuzzy rules. The communication link between the controller and the actuator under consideration may be unreliable, where Denialof-Service (DoS) attack is supposed to invade the communication link randomly. To compensate the negative effect caused by DoS attack, a compensation control scheme is designed to maintain the stability of the closed-loop system. With the aid of the Lyapunov function theory, a sufficient condition is established to ensure the stochastic stability and strict dissipativity of the closed-loop system. Finally, an iterative linearization algorithm is designed to determine the controller gain and the effectiveness of the proposed approach is evaluated through simulations.

Li, X., Cui, X., Shi, L., Liu, C., Wang, X..  2018.  Constructing Browser Fingerprint Tracking Chain Based on LSTM Model. 2018 IEEE Third International Conference on Data Science in Cyberspace (DSC). :213-218.
Web attacks have increased rapidly in recent years. However, traditional methods are useless to track web attackers. Browser fingerprint, as a stateless tracking technique, can be used to solve this problem. Given browser fingerprint changes easily and frequently, it is easy to lose track. Therefore, we need to improve the stability of browser fingerprint by linking the new one to the previous chain. In this paper, we propose LSTM model to learn the potential relationship of browser fingerprint evolution. In addition, we adjust the input feature vector to time series and construct training set to train the model. The results show that our model can construct the tracking chain perfectly well with average ownership up to 99.3%.
Ouyang, Tinghui, Marco, Vicent Sanz, Isobe, Yoshinao, Asoh, Hideki, Oiwa, Yutaka, Seo, Yoshiki.  2021.  Corner Case Data Description and Detection. 2021 IEEE/ACM 1st Workshop on AI Engineering - Software Engineering for AI (WAIN). :19–26.
As the major factors affecting the safety of deep learning models, corner cases and related detection are crucial in AI quality assurance for constructing safety- and security-critical systems. The generic corner case researches involve two interesting topics. One is to enhance DL models' robustness to corner case data via the adjustment on parameters/structure. The other is to generate new corner cases for model retraining and improvement. However, the complex architecture and the huge amount of parameters make the robust adjustment of DL models not easy, meanwhile it is not possible to generate all real-world corner cases for DL training. Therefore, this paper proposes a simple and novel approach aiming at corner case data detection via a specific metric. This metric is developed on surprise adequacy (SA) which has advantages on capture data behaviors. Furthermore, targeting at characteristics of corner case data, three modifications on distanced-based SA are developed for classification applications in this paper. Consequently, through the experiment analysis on MNIST data and industrial data, the feasibility and usefulness of the proposed method on corner case data detection are verified.
Jiang, Feng, Qi, Buren, Wu, Tianhao, Zhu, Konglin, Zhang, Lin.  2019.  CPSS: CP-ABE based Platoon Secure Sensing Scheme against Cyber-Attacks. 2019 IEEE Intelligent Transportation Systems Conference (ITSC). :3218—3223.

Platoon is one of cooperative driving applications where a set of vehicles can collaboratively sense each other for driving safety and traffic efficiency. However, platoon without security insurance makes the cooperative vehicles vulnerable to cyber-attacks, which may cause life-threatening accidents. In this paper, we introduce malicious attacks in platoon maneuvers. To defend against these attacks, we propose a Cyphertext-Policy Attribute-Based Encryption (CP-ABE) based Platoon Secure Sensing scheme, named CPSS. In the CPSS, platoon key is encapsulated in the access control structure in the key distribution process, so that interference messages sending by attackers without the platoon key could be ignored. Therefore, the sensing data which contains speed and position information can be protected. In this way, speed and distance fluctuations caused by attacks can be mitigated even eliminated thereby avoiding the collisions and ensuring the overall platoon stability. Time complexity analysis shows that the CPSS is more efficient than that of the polynomial time solutions. Finally, to evaluate capabilities of the CPSS, we integrate a LTE-V2X with platoon maneuvers based on Veins platform. The evaluation results show that the CPSS outperforms the baseline algorithm by 25% in terms of distance variations.

Chattopadhyay, Abhiroop, Valdes, Alfonso, Sauer, Peter W., Nuqui, Reynaldo.  2021.  A Cyber Threat Mitigation Approach For Wide Area Control of SVCs using Stability Monitoring. 2021 IEEE Madrid PowerTech. :1–6.
We propose a stability monitoring approach for the mitigation of cyber threats directed at the wide area control (WAC) system used for coordinated control of Flexible AC Transmission Systems (FACTS) used for power oscillation damping (POD) of active power flow on inter-area tie lines. The approach involves monitoring the modes of the active power oscillation on an inter-area tie line using the Matrix Pencil (MP) method. We use the stability characteristics of the observed modes as a proxy for the presence of destabilizing cyber threats. We monitor the system modes to determine whether any destabilizing modes appear after the WAC system engages to control the POD. If the WAC signal exacerbates the POD performance, the FACTS falls back to POD using local measurements. The proposed approach does not require an expansive system-wide view of the network. We simulate replay, control integrity, and timing attacks for a test system and present results that demonstrate the performance of the SM approach for mitigation.
Soper, Braden C..  2019.  A Cyber-Nuclear Deterrence Game. 2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton). :470—479.

The reliability of nuclear command, control and communications has long been identified as a critical component of the strategic stability among nuclear states. Advances in offensive cyber weaponry have the potential to negatively impact this reliability, threatening strategic stability. In this paper we present a game theoretic model of preemptive cyber attacks against nuclear command, control and communications. The model is a modification of the classic two-player game of Chicken, a standard game theoretic model for nuclear brinksmanship. We fully characterize equilibria in both the complete information game and two distinct two-sided incomplete information games. We show that when both players have advanced cyber capabilities conflict is more likely in equilibrium, regardless of information structure. On the other hand, when at most one player has advanced cyber capabilities, strategic stability depends on the information structure. Under complete information, asymmetric cyber capabilities have a stabilizing effect in which the player with strong cyber has the resolve to stand firm in equilibrium. Under incomplete information, asymmetric cyber capabilities can have both stabilizing and destabilizing effects depending on prior beliefs over opponent cyber capabilities.

Han, Weiheng, Cai, Weiwei, Zhang, Guangjia, Yu, Weiguo, Pan, Junjun, Xiang, Longyun, Ning, Tao.  2021.  Cyclic Verification Method of Security Control System Strategy Table Based on Constraint Conditions and Whole Process Dynamic Simulation. 2021 IEEE/IAS Industrial and Commercial Power System Asia (I CPS Asia). :698—703.

The correctness of security control system strategy is very important to ensure the stability of power system. Aiming at the problem that the current security control strategy verification method is not enough to match the increasingly complex large power grid, this paper proposes a cyclic verification method of security control system strategy table based on constraints and whole process dynamic simulation. Firstly, the method is improved based on the traditional security control strategy model to make the strategy model meet certain generalization ability; And on the basis of this model, the cyclic dynamic verification of the strategy table is realized based on the constraint conditions and the whole process dynamic simulation, which not only ensures the high accuracy of strategy verification for the security control strategy of complex large power grid, but also ensures that the power system is stable and controllable. Finally, based on a certain regional power system, the optimal verification of strategy table verification experiment is realized. The experimental results show that the average processing time of the proposed method is 10.32s, and it can effectively guarantee the controllability and stability of power grid.

Li, Mengxue, Zhang, Binxin, Wang, Guangchang, ZhuGe, Bin, Jiang, Xian, Dong, Ligang.  2022.  A DDoS attack detection method based on deep learning two-level model CNN-LSTM in SDN network. 2022 International Conference on Cloud Computing, Big Data Applications and Software Engineering (CBASE). :282–287.
This paper mainly explores the detection and defense of DDoS attacks in the SDN architecture of the 5G environment, and proposes a DDoS attack detection method based on the deep learning two-level model CNN-LSTM in the SDN network. Not only can it greatly improve the accuracy of attack detection, but it can also reduce the time for classifying and detecting network traffic, so that the transmission of DDoS attack traffic can be blocked in time to ensure the availability of network services.
Vekić, Marko, Isakov, Ivana, Rapaić, Milan, Grabić, Stevan, Todorović, Ivan, Porobić, Vlado.  2022.  Decentralized microgrid control "beyond droop". 2022 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe). :1—5.
Various approaches of microgrid operation have been proposed, albeit with noticeable issues such as power-sharing, control of frequency and voltage excursions, applicability on different grids, etc. This paper proposes a goal function-based, decentralized control that addresses the mentioned problems and secures the microgrid stability by constraining the frequency and node deviations across the grid while simultaneously supporting the desired active power exchange between prosumer nodes. The control algorithm is independent of network topology and enables arbitrary node connection, i.e. seamless microgrid expandability. To confirm the effectiveness of the proposed control strategy, simulation results are presented and discussed.
Kanellopoulos, Aris, Vamvoudakis, Kyriakos G., Gupta, Vijay.  2019.  Decentralized Verification for Dissipativity of Cascade Interconnected Systems. 2019 IEEE 58th Conference on Decision and Control (CDC). :3629—3634.

In this paper, we consider the problem of decentralized verification for large-scale cascade interconnections of linear subsystems such that dissipativity properties of the overall system are guaranteed with minimum knowledge of the dynamics. In order to achieve compositionality, we distribute the verification process among the individual subsystems, which utilize limited information received locally from their immediate neighbors. Furthermore, to obviate the need for full knowledge of the subsystem parameters, each decentralized verification rule employs a model-free learning structure; a reinforcement learning algorithm that allows for online evaluation of the appropriate storage function that can be used to verify dissipativity of the system up to that point. Finally, we show how the interconnection can be extended by adding learning-enabled subsystems while ensuring dissipativity.

He, Song, Shi, Xiaohong, Huang, Yan, Chen, Gong, Tang, Huihui.  2022.  Design of Information System Security Evaluation Management System based on Artificial Intelligence. 2022 IEEE 2nd International Conference on Electronic Technology, Communication and Information (ICETCI). :967—970.
In today's society, with the continuous development of artificial intelligence, artificial intelligence technology plays an increasingly important role in social and economic development, and hass become the fastest growing, most widely used and most influential high-tech in the world today one. However, at the same time, information technology has also brought threats to network security to the entire network world, which makes information systems also face huge and severe challenges, which will affect the stability and development of society to a certain extent. Therefore, comprehensive analysis and research on information system security is a very necessary and urgent task. Through the security assessment of the information system, we can discover the key hidden dangers and loopholes that are hidden in the information source or potentially threaten user data and confidential files, so as to effectively prevent these risks from occurring and provide effective solutions; at the same time To a certain extent, prevent virus invasion, malicious program attacks and network hackers' intrusive behaviors. This article adopts the experimental analysis method to explore how to apply the most practical, advanced and efficient artificial intelligence theory to the information system security assessment management, so as to further realize the optimal design of the information system security assessment management system, which will protect our country the information security has very important meaning and practical value. According to the research results, the function of the experimental test system is complete and available, and the security is good, which can meet the requirements of multi-user operation for security evaluation of the information system.
Trajanovski, S., Kuipers, F. A., Hayel, Y., Altman, E., Mieghem, P. Van.  2015.  Designing virus-resistant networks: A game-formation approach. 2015 54th IEEE Conference on Decision and Control (CDC). :294–299.

Forming, in a decentralized fashion, an optimal network topology while balancing multiple, possibly conflicting objectives like cost, high performance, security and resiliency to viruses is a challenging endeavor. In this paper, we take a game-formation approach to network design where each player, for instance an autonomous system in the Internet, aims to collectively minimize the cost of installing links, of protecting against viruses, and of assuring connectivity. In the game, minimizing virus risk as well as connectivity costs results in sparse graphs. We show that the Nash Equilibria are trees that, according to the Price of Anarchy (PoA), are close to the global optimum, while the worst-case Nash Equilibrium and the global optimum may significantly differ for small infection rate and link installation cost. Moreover, the types of trees, in both the Nash Equilibria and the optimal solution, depend on the virus infection rate, which provides new insights into how viruses spread: for high infection rate τ, the path graph is the worst- and the star graph is the best-case Nash Equilibrium. However, for small and intermediate values of τ, trees different from the path and star graphs may be optimal.