arXiv subjects

Tamer Başar

Publications and source records attributed to Tamer Başar.

At least 145 records · Page 8Linked to original sources

arXiv2017

Controllability of Conjunctive Boolean Networks with Application to Gene Regulation

A Boolean network is a finite state discrete time dynamical system. At each step, each variable takes a value from a binary set. The value update rule for each variable is a local function which depends only on a selected subset of variables. Boolean networks have been used in modeling gene regulatory networks. We focus in this paper on a special class of Boolean networks, namely the conjunctive Boolean networks (CBNs), whose value update rule is comprised of only logic AND operations. It is known that any trajectory of a Boolean network will enter a periodic orbit. Periodic orbits of a CBN have been completely understood. In this paper, we investigate the orbit-controllability and state-controllability of a CBN: We ask the question of how one can steer a CBN to enter any periodic orbit or to reach any final state, from any initial state. We establish necessary and sufficient conditions for a CBN to be orbit-controllable and state-controllable. Furthermore, explicit control laws are presented along the analysis.

math.DS↗

arXiv2017

Evolution of Social Power in Social Networks with Dynamic Topology

The recently proposed DeGroot-Friedkin model describes the dynamical evolution of individual social power in a social network that holds opinion discussions on a sequence of different issues. This paper revisits that model, and uses nonlinear contraction analysis, among other tools, to establish several novel results. First, we show that for a social network with constant topology, each individual's social power converges to its equilibrium value exponentially fast, whereas previous results only concluded asymptotic convergence. Second, when the network topology is dynamic (i.e., the relative interaction matrix may change between any two successive issues), we show that each individual exponentially forgets its initial social power. Specifically, individual social power is dependent only on the dynamic network topology, and initial (or perceived) social power is forgotten as a result of sequential opinion discussion. Last, we provide an explicit upper bound on an individual's social power as the number of issues discussed tends to infinity; this bound depends only on the network topology. Simulations are provided to illustrate our results.

cs.SI↗

arXiv2017

Multi-Competitive Viruses over Static and Time--Varying Networks

Epidemic processes are used commonly for modeling and analysis of biological networks, computer networks, and human contact networks. The idea of competing viruses has been explored recently, motivated by the spread of different ideas along different social networks. Previous studies of competitive viruses have focused only on two viruses and on static graph structures. In this paper, we consider multiple competing viruses over static and dynamic graph structures, and investigate the eradication and propagation of diseases in these systems. Stability analysis for the class of models we consider is performed and an antidote control technique is proposed.

math.OC↗

arXiv2017

Cash-settled options for wholesale electricity markets

Wholesale electricity market designs in practice do not provide the market participants with adequate mechanisms to hedge their financial risks. Demanders and suppliers will likely face even greater risks with the deepening penetration of variable renewable resources like wind and solar. This paper explores the design of a centralized cash-settled call option market to mitigate such risks. A cash-settled call option is a financial instrument that allows its holder the right to claim a monetary reward equal to the positive difference between the real-time price of an underlying commodity and a pre-negotiated strike price for an upfront fee. Through an example, we illustrate that a bilateral call option can reduce the payment volatility of market participants. Then, we design a centralized clearing mechanism for call options that generalizes the bilateral trade. We illustrate through an example how the centralized clearing mechanism generalizes the bilateral trade. Finally, the effect of risk preference of the market participants, as well as some generalizations are discussed.

math.OC↗

arXiv2017

On the Analysis of the DeGroot-Friedkin Model with Dynamic Relative Interaction Matrices

This paper analyses the DeGroot-Friedkin model for evolution of the individuals' social powers in a social network when the network topology varies dynamically (described by dynamic relative interaction matrices). The DeGroot-Friedkin model describes how individual social power (self-appraisal, self-weight) evolves as a network of individuals discuss a sequence of issues. We seek to study dynamically changing relative interactions because interactions may change depending on the issue being discussed. In order to explore the problem in detail, two different cases of issue-dependent network topologies are studied. First, if the topology varies between issues in a periodic manner, it is shown that the individuals' self-appraisals admit a periodic solution. Second, if the topology changes arbitrarily, under the assumption that each relative interaction matrix is doubly stochastic and irreducible, the individuals' self-appraisals asymptotically converge to a unique non-trivial equilibrium.

cs.SI↗

arXiv2017

Modification of Social Dominance in Social Networks by Selective Adjustment of Interpersonal Weights

According to the DeGroot-Friedkin model of a social network, an individual's social power evolves as the network discusses individual opinions over a sequence of issues. Under mild assumptions on the connectivity of the network, the social power of every individual converges to a constant strictly positive value as the number of issues discussed increases. If the network has a special topology, termed "star topology", then all social power accumulates with the individual at the centre of the star. This paper studies the strategic introduction of new individuals and/or interpersonal relationships into a social network with star topology to reduce the social power of the centre individual. In fact, several strategies are proposed. For each strategy, we derive necessary and sufficient conditions on the strength of the new interpersonal relationships, based on local information, which ensures that the centre individual no longer has the greatest social power within the social network. Interpretations of these conditions show that the strategies are remarkably intuitive and that certain strategies are favourable compared to others, all of which is sociologically expected.

cs.SI↗

arXiv2017

Prospect Theory for Enhanced Cyber-Physical Security of Drone Delivery Systems: A Network Interdiction Game

The use of unmanned aerial vehicles (UAVs) as delivery systems of online goods is rapidly becoming a global norm, as corroborated by Amazon's "Prime Air" and Google's "Project Wing" projects. However, the real-world deployment of such drone delivery systems faces many cyber-physical security challenges. In this paper, a novel mathematical framework for analyzing and enhancing the security of drone delivery systems is introduced. In this regard, a zero-sum network interdiction game is formulated between a vendor, operating a drone delivery system, and a malicious attacker. In this game, the vendor seeks to find the optimal path that its UAV should follow, to deliver a purchase from the vendor's warehouse to a customer location, to minimize the delivery time. Meanwhile, an attacker seeks to choose an optimal location to interdict the potential paths of the UAVs, so as to inflict cyber or physical damage to it, thus, maximizing its delivery time. First, the Nash equilibrium point of this game is characterized. Then, to capture the subjective behavior of both the vendor and attacker, new notions from prospect theory are incorporated into the game. These notions allow capturing the vendor's and attacker's i) subjective perception of attack success probabilities, and ii) their disparate subjective valuations of the achieved delivery times relative to a certain target delivery time. Simulation results have shown that the subjective decision making of the vendor and attacker leads to adopting risky path selection strategies which inflict delays to the delivery, thus, yielding unexpected delivery times which surpass the target delivery time set by the vendor.

cs.GT↗

arXiv2017

Markov-Nash Equilibria in Mean-Field Games with Discounted Cost

In this paper, we consider discrete-time dynamic games of the mean-field type with a finite number $N$ of agents subject to an infinite-horizon discounted-cost optimality criterion. The state space of each agent is a locally compact Polish space. At each time, the agents are coupled through the empirical distribution of their states, which affects both the agents' individual costs and their state transition probabilities. We introduce a new solution concept of the Markov-Nash equilibrium, under which a policy is player-by-player optimal in the class of all Markov policies. Under mild assumptions, we demonstrate the existence of a mean-field equilibrium in the infinite-population limit $N \to \infty$, and then show that the policy obtained from the mean-field equilibrium is approximately Markov-Nash when the number of agents $N$ is sufficiently large.

eess.SY↗

arXiv2017

Team-Optimal Distributed MMSE Estimation in General and Tree Networks

We construct team-optimal estimation algorithms over distributed networks for state estimation in the finite-horizon mean-square error (MSE) sense. Here, we have a distributed collection of agents with processing and cooperation capabilities. These agents observe noisy samples of a desired state through a linear model and seek to learn this state by interacting with each other. Although this problem has attracted significant attention and been studied extensively in fields including machine learning and signal processing, all the well-known strategies do not achieve team-optimal learning performance in the finite-horizon MSE sense. To this end, we formulate the finite-horizon distributed minimum MSE (MMSE) when there is no restriction on the size of the disclosed information, i.e., oracle performance, over an arbitrary network topology. Subsequently, we show that exchange of local estimates is sufficient to achieve the oracle performance only over certain network topologies. By inspecting these network structures, we propose recursive algorithms achieving the oracle performance through the disclosure of local estimates. For practical implementations we also provide approaches to reduce the complexity of the algorithms through the time-windowing of the observations. Finally, in the numerical examples, we demonstrate the superior performance of the introduced algorithms in the finite-horizon MSE sense due to optimal estimation.

eess.SY↗

arXiv2016

Global Stabilization of Triangulated Formations

Formation control deals with the design of decentralized control laws that stabilize mobile, autonomous agents at prescribed distances from each other. We call any configuration of the agents a target configuration if it satisfies the inter-agent distance conditions. It is well known that when the distance conditions are defined by a rigid graph, there is a finite number of target configurations modulo rotations and translations of the entire formation. We can thus recast the objective of formation control as stabilizing one or many of the target configurations. A major issue is that such control laws will also have equilibria corresponding to configurations which do not meet the desired inter-agent distance conditions; we refer to these as undesirable configurations. The undesirable configurations become problematic if they are also stable. Designing decentralized control laws whose stable equilibria are all target configurations in the case of a general rigid graph is still an open problem. We provide here a new point of view on this problem, and propose a partial solution by exhibiting a class of rigid graphs and control laws for which all stable equilibria are target configurations.

math.DS↗

arXiv2016

On the Analysis of a Continuous-Time Bi-Virus Model

Motivated by the spread of opinions on different social networks, we study a distributed continuous-time bi-virus model for a system of groups of individuals. An in-depth stability analysis is performed for more general models than have been previously considered, for the healthy and epidemic states. In addition, we investigate sensitivity properties of some nontrivial equilibria and obtain an impossibility result for distributed feedback control.

math.OC↗

arXiv2015

A Stackelberg Game for Multi-Period Demand Response Management in the Smart Grid

This paper studies a multi-period demand response management problem in the smart grid where multiple utility companies compete among themselves. The user-utility interactions are modeled by a noncooperative game of a Stackelberg type where the interactions among the utility companies are captured through a Nash equilibrium. It is shown that this game has a unique Stackelberg equilibrium at which the utility companies set prices to maximize their revenues (within a Nash game) while the users respond accordingly to maximize their utilities subject to their budget constraints. Closed-form expressions are provided for the corresponding strategies of the users and the utility companies. It is shown that the multi- period scheme, compared with the single-period case, provides more incentives for the users to participate in the game. A necessary and sufficient condition on the minimum budget needed for a user to participate is provided.

math.OC↗

arXiv2015

Context-Aware Wireless Small Cell Networks: How to Exploit User Information for Resource Allocation

In this paper, a novel context-aware approach for resource allocation in two-tier wireless small cell networks~(SCNs) is proposed. In particular, the SCN's users are divided into two types: frequent users, who are regular users of certain small cells, and occasional users, who are one-time or infrequent users of a particular small cell. Given such \emph{context} information, each small cell base station (SCBS) aims to maximize the overall performance provided to its frequent users, while ensuring that occasional users are also well serviced. We formulate the problem as a noncooperative game in which the SCBSs are the players. The strategy of each SCBS is to choose a proper power allocation so as to optimize a utility function that captures the tradeoff between the users' quality-of-service gains and the costs in terms of resource expenditures. We provide a sufficient condition for the existence and uniqueness of a pure strategy Nash equilibrium for the game, and we show that this condition is independent of the number of users in the network. Simulation results show that the proposed context-aware resource allocation game yields significant performance gains, in terms of the average utility per SCBS, compared to conventional techniques such as proportional fair allocation and sum-rate maximization.

cs.GT↗

arXiv2015

Robust Distributed Averaging: When are Potential-Theoretic Strategies Optimal?

We study the interaction between a network designer and an adversary over a dynamical network. The network consists of nodes performing continuous-time distributed averaging. The adversary strategically disconnects a set of links to prevent the nodes from reaching consensus. Meanwhile, the network designer assists the nodes in reaching consensus by changing the weights of a limited number of links in the network. We formulate two Stackelberg games to describe this competition where the order in which the players act is reversed in the two problems. Although the canonical equations provided by the Pontryagin's maximum principle seem to be intractable, we provide an alternative characterization for the optimal strategies that makes connection to potential theory. Finally, we provide a sufficient condition for the existence of a saddle-point equilibrium for the underlying zero-sum game.

eess.SY↗

arXiv2015

Stability of Epidemic Models over Directed Graphs: A Positive Systems Approach

We study the stability properties of a susceptible-infected-susceptible (SIS) diffusion model, so-called the $n$-intertwined Markov model, over arbitrary directed network topologies. As in the majority of the work on infection spread dynamics, this model exhibits a threshold phenomenon. When the curing rates in the network are high, the disease-free state is the unique equilibrium over the network. Otherwise, an endemic equilibrium state emerges, where some infection remains within the network. Using notions from positive systems theory, {we provide novel proofs for the global asymptotic stability of the equilibrium points in both cases over strongly connected networks based on the value of the basic reproduction number, a fundamental quantity in the study of epidemics.} When the network topology is weakly connected, we provide conditions for the existence, uniqueness, and global asymptotic stability of an endemic state, and we study the stability of the disease-free state. Finally, we demonstrate that the $n$-intertwined Markov model can be viewed as a best-response dynamical system of a concave game among the nodes. This characterization allows us to cast new infection spread dynamics; additionally, we provide a sufficient condition for the global convergence to the disease-free state, which can be checked in a distributed fashion. Several simulations demonstrate our results.

eess.SY↗

arXiv2014

Design and Analysis of Distributed Averaging with Quantized Communication

Consider a network whose nodes have some initial values, and it is desired to design an algorithm that builds on neighbor to neighbor interactions with the ultimate goal of convergence to the average of all initial node values or to some value close to that average. Such an algorithm is called generically "distributed averaging," and our goal in this paper is to study the performance of a subclass of deterministic distributed averaging algorithms where the information exchange between neighboring nodes (agents) is subject to uniform quantization. With such quantization, convergence to the precise average cannot be achieved in general, but the convergence would be to some value close to it, called quantized consensus. Using Lyapunov stability analysis, we characterize the convergence properties of the resulting nonlinear quantized system. We show that in finite time and depending on initial conditions, the algorithm will either cause all agents to reach a quantized consensus where the consensus value is the largest quantized value not greater than the average of their initial values, or will lead all variables to cycle in a small neighborhood around the average. In the latter case, we identify tight bounds for the size of the neighborhood and we further show that the error can be made arbitrarily small by adjusting the algorithm's parameters in a distributed manner.

math.OC↗

arXiv2013

A Game-Theoretic Approach to Energy Trading in the Smart Grid

Electric storage units constitute a key element in the emerging smart grid system. In this paper, the interactions and energy trading decisions of a number of geographically distributed storage units are studied using a novel framework based on game theory. In particular, a noncooperative game is formulated between storage units, such as PHEVs, or an array of batteries that are trading their stored energy. Here, each storage unit's owner can decide on the maximum amount of energy to sell in a local market so as to maximize a utility that reflects the tradeoff between the revenues from energy trading and the accompanying costs. Then in this energy exchange market between the storage units and the smart grid elements, the price at which energy is traded is determined via an auction mechanism. The game is shown to admit at least one Nash equilibrium and a novel proposed algorithm that is guaranteed to reach such an equilibrium point is proposed. Simulation results show that the proposed approach yields significant performance improvements, in terms of the average utility per storage unit, reaching up to 130.2% compared to a conventional greedy approach.

cs.GT↗

arXiv2013

Robust Distributed Averaging on Networks with Adversarial Intervention

We study the interaction between a network designer and an adversary over a dynamical network. The network consists of nodes performing continuous-time distributed averaging. The goal of the network designer is to assist the nodes reach consensus by changing the weights of a limited number of links in the network. Meanwhile, an adversary strategically disconnects a set of links to prevent the nodes from converging. We formulate two problems to describe this competition where the order in which the players act is reversed in the two problems. We utilize Pontryagin's Maximum Principle (MP) to tackle both problems and derive the optimal strategies. Although the canonical equations provided by the MP are intractable, we provide an alternative characterization for the optimal strategies that highlights a connection with potential theory. Finally, we provide a sufficient condition for the existence of a saddle-point equilibrium (SPE) for this zero-sum game.

math.OC↗