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We consider a jamming problem in which a jammer aims to degrade a user’s communication in which the user might differ in applied applications or communication purposes. Such differences are reflected by different communication metrics used by the user. Specifically, signal-to-interference-plus-noise ratio (SINR) is used as a metric to reflect regular data transmission purposes. Meanwhile, as another metric, latency, modeled by the inverse SINR, is used to reflect emergency communication purposes. We consider the most difficult scenario for the jammer where it does not know which application (metric) the user employs. The problem is formulated as a Bayesian game. Equilibrium is found in closed form, and the dependence of equilibrium on network parameters is illustrated.

We consider a multiple access channel (MAC) problem where several users communicate with a base station and in which the users may have different applications or communication purposes for using the network, which is reflected via associated communication metrics. Specifically, we use throughput as the metric to reflect regular data transmission purposes, and latency, modeled by the inverse throughput, is used to reflect data transmission speed as another metric. The problem is formulated as a non-zero sum game. The equilibrium is derived in closed form. Stability in communication for such a heterogeneous network is established by proving the uniqueness of the equilibrium, except for particular cases where stability still can be maintained via cooperation of users with throughput metric or their switching to latency metric.

Wireless networks are susceptible to malicious attacks, especially those involving eavesdropping and jamming. In this paper, we consider a communication scenario involving a transmitter who wishes to communicate secretly and reliably with a receiver, while an adversary wants to obstruct this communication by means of either eavesdropping or jamming. The transmitter as well as the adversary wants to achieve its own goal in a manner that is as unpredictable as possible to its rival. We model this problem by a non-zero sum game. The expected throughput that is delivered secretly and non-jammed to the receiver is considered as the metric that reflects communication secrecy and reliability. The entropy of the player’s strategies is considered as the metric to reflect the player’s unpredictability. The equilibrium is found in closed form, and parameters of the transmitter’s utility supporting both goals are optimized via a proportional fairness approach.

Drug resistance in cancer treatments is a frequent problem that, when it arises, leads to failure in therapeutic efforts. Tumor heterogeneity is the primary reason for resistance emergence and a precise treatment design that takes heterogeneity into account is required to postpone the rise of resistant subpopulations in the tumor environment. In this paper, we present a mathematical framework involving clonal evolution modeling of drug‐sensitive and drug‐resistant clones. Using our framework, we examine delaying the rise of resistance in heterogeneous tumors during control phase of therapy in a containment treatment approach. We apply pharmacokinetic/pharmacodynamic (PKPD) modeling and show that dosage strategies can be designed to control the resistant subpopulation. Our results show that the drug dosage and schedule determine the relative dynamics of sensitive and resistant clones. We present an optimal control problem that finds the dosing strategy that maximizes the delay in resistance emergence for a given period of containment treatment.

In this paper, we investigate the problem of designing a spectrum scanning strategy to detect an intelligent Invader who wants to utilize spectrum undetected for his/her unapproved purposes. To deal with this problem we model the situation as two games, between a Scanner and an Invader, and solve them sequentially. The first game is formulated to design the optimal (in maxmin sense) scanning algorithm, while the second one allows one to find the optimal values of the parameters for the algorithm depending on the parameters of the network. These games provide solutions for two dilemmas that the rivals face. The Invader’s dilemma consists of the following: the more bandwidth the Invader attempts to use leads to a larger payoff if he is not detected, but at the same time also increases the probability of being detected and thus fined. Similarly, the Scanner faces a dilemma: the wider the bandwidth scanned, the higher the probability of detecting the Invader, but at the expense of increasing the cost of building the scanning system. The equilibrium strategies are found explicitly and reveal interesting properties. In particular, we have found a discontinuous dependence of the equilibrium strategies on the network parameters, fine and the type of the Invader’s award. This discontinuity of the fine means that the network provider has to take into account a human/social factor since some threshold values of fine could be very sensible for the Invader, while in other situations simply increasing the fine has a minimal deterrence impact. Also we show how incomplete information about the Invader’s technical characteristics and reward (e.g. motivated by using different type of application, say, video-streaming or downloading files) can be incorporated into the scanning strategy to increase its efficiency.

Treatments consisting of mixtures of pharmacological agents have been shown to have superior effects to treatments involving single compounds. Given the vast amount of possible combinations involving multiple drugs and the restrictions in time and resources required to test all such combinations in vitro, mathematical methods are essential to model the interactive behavior of the drug mixture and the target, ultimately allowing one to better predict the outcome of the combination. In this review, we investigate various mathematical methods that model combination therapies. This survey includes the methods that focus on predicting the outcome of drug combinations with respect to synergism and antagonism, as well as the methods that explore the dynamics of combination therapy and its role in combating drug resistance. This comprehensive investigation of the mathematical methods includes models that employ pharmacodynamics equations, those that rely on signaling and how the underlying chemical networks are affected by the topological structure of the target proteins, and models that are based on stochastic models for evolutionary dynamics. Additionally, this article reviews computational methods including mathematical algorithms, machine learning, and search algorithms that can identify promising combinations of drug compounds. A description of existing data and software resources is provided that can support investigations in drug combination therapies. Finally, the article concludes with a summary of future directions for investigation by the research community.

Sharing of radio spectrum between different types of wireless systems (e.g., different service providers) is the foundation for making more efficient usage of spectrum. Cognitive radio technologies have spurred the design of spectrum servers that coordinate the sharing of spectrum between different wireless systems. These servers receive information regarding the needs of each system, and then provide instructions back to each system regarding the spectrum bands they may use. This sharing of information is complicated by the fact that these systems are often in competition with each other: each system desires to use as much of the spectrum as possible to support its users, and each system could learn and harm the bands of the other system. Three problems arise in such a spectrum-sharing problem: (1) how to maintain reliable performance for each system-shared resource (licensed spectrum); (2) whether to believe the resource requests announced by each agent; and (3) if they do not believe, how much effort should be devoted to inspecting spectrum so as to prevent possible malicious activity. Since this problem can arise for a variety of wireless systems, we present an abstract formulation in which the agents or spectrum server introduces obfuscation in the resource assignment to maintain reliability. We derive a closed form expression for the expected damage that can arise from possible malicious activity, and using this formula we find a tradeoff between the amount of extra decoys that must be used in order to support higher communication fidelity against potential interference, and the cost of maintaining this reliability. Then, we examine a scenario where a smart adversary may also use obfuscation itself, and formulate the scenario as a signaling game, which can be solved by applying a classical iterative forward-induction algorithm. For an important particular case, the game is solved in a closed form, which gives conditions for deciding whether an agent can be trusted, or whether its request should be inspected and how intensely it should be inspected.