Traffic Optimization to Control Epidemic Outbreaks in Metapopulation Models

We propose a novel framework to study viral spreading processes in metapopulation models. Large subpopulations (i.e., cities) are connected via metalinks (i.e., roads) according to a metagraph structure (i.e., the traffic infrastructure). The problem of containing the propagation of an epidemic outbreak in a metapopulation model by controlling the traffic between subpopulations is considered. Controlling the spread of an epidemic outbreak can be written as a spectral condition involving the eigenvalues of a matrix that depends on the network structure and the parameters of the model. Based on this spectral condition, we propose a convex optimization framework to find cost-optimal approaches to traffic control in epidemic outbreaks

Worst-Case Scenarios for Greedy, Centrality-Based Network Protection Strategies

The task of allocating preventative resources to a computer network in order to protect against the spread of viruses is addressed. Virus spreading dynamics are described by a linearized SIS model and protection is framed by an optimization problem which maximizes the rate at which a virus in the network is contained given finite resources. One approach to problems of this type involve greedy heuristics which allocate all resources to the nodes with large centrality measures. We address the worst case performance of such greedy algorithms be constructing networks for which these greedy allocations are arbitrarily inefficient. An example application is presented in which such a worst case network might arise naturally and our results are verified numerically by leveraging recent results which allow the exact optimal solution to be computed via geometric programming

Accelerated Backpressure Algorithm

We develop an Accelerated Back Pressure (ABP) algorithm using Accelerated Dual Descent (ADD), a distributed approximate Newton-like algorithm that only uses local information. Our construction is based on writing the backpressure algorithm as the solution to a network feasibility problem solved via stochastic dual subgradient descent. We apply stochastic ADD in place of the stochastic gradient descent algorithm. We prove that the ABP algorithm guarantees stable queues. Our numerical experiments demonstrate a significant improvement in convergence rate, especially when the packet arrival statistics vary over time.Comment: 9 pages, 4 figures. A version of this work with significantly extended proofs is being submitted for journal publicatio

From Curved Bonding to Configuration Spaces

Bonding curves are continuous liquidity mechanisms which are used in market design for cryptographically-supported token economies. Tokens are atomic units of state information which are cryptographically verifiable in peer-to-peer networks. Bonding curves are an example of an enforceable mechanism through which participating agents influence this state. By designing such mechanisms, an engineer may establish the topological structure of a token economy without presupposing the utilities or associated actions of the agents within that economy. This is accomplished by introducing configuration spaces, which are proper subsets of the global state space representing all achievable states under the designed mechanisms. Any global properties true for all points in the configuration space are true for all possible sequences of actions on the part of agents. This paper generalizes the notion of a bonding curve to formalize the relationship between cryptographically enforced mechanisms and their associated configuration spaces, using invariant properties of conservation functions. We then proceed to apply this framework to analyze the augmented bonding curve design, which is currently under development by a project in the non-profit funding sector.Series: Working Paper Series / Institute for Cryptoeconomics / Interdisciplinary Researc

Economic Games as Estimators

Discrete event games are discrete time dynamical systems whose state transitions are discrete events caused by actions taken by agents within the game. The agents’ objectives and associated decision rules need not be known to the game designer in order to impose struc- ture on a game’s reachable states. Mechanism design for discrete event games is accomplished by declaring desirable invariant properties and restricting the state transition functions to conserve these properties at every point in time for all admissible actions and for all agents, using techniques familiar from state-feedback control theory. Building upon these connections to control theory, a framework is developed to equip these games with estimation properties of signals which are private to the agents playing the game. Token bonding curves are presented as discrete event games and numerical experiments are used to investigate their signal processing properties with a focus on input-output response dynamics.Series: Working Paper Series / Institute for Cryptoeconomics / Interdisciplinary Researc

Fast, Distributed Optimization Strategies for Resource Allocation in Networks

Many challenges in network science and engineering today arise from systems composed of many individual agents interacting over a network. Such problems range from humans interacting with each other in social networks to computers processing and exchanging information over wired or wireless networks. In any application where information is spread out spatially, solutions must address information aggregation in addition to the decision process itself. Intelligently addressing the trade off between information aggregation and decision accuracy is fundamental to finding solutions quickly and accurately. Network optimization challenges such as these have generated a lot of interest in distributed optimization methods. The field of distributed optimization deals with iterative methods which perform calculations using locally available information. Early methods such as subgradient descent suffer very slow convergence rates because the underlying optimization method is a first order method. My work addresses problems in the area of network optimization and control with an emphasis on accelerating the rate of convergence by using a faster underlying optimization method. In the case of convex network flow optimization, the problem is transformed to the dual domain, moving the equality constraints which guarantee flow conservation into the objective. The Newton direction can be computed locally by using a consensus iteration to solve a Poisson equation, but this requires a lot of communication between neighboring nodes. Accelerated Dual Descent (ADD) is an approximate Newton method, which significantly reduces the communication requirement. Defining a stochastic version of the convex network flow problem with edge capacities yields a problem equivalent to the queue stability problem studied in the backpressure literature. Accelerated Backpressure (ABP) is developed to solve the queue stabilization problem. A queue reduction method is introduced by merging ideas from integral control and momentum based optimization

Traffic Control for Network Protection Against Spreading Processes

Epidemic outbreaks in human populations are facilitated by the underlying transportation network. We consider strategies for containing a viral spreading process by optimally allocating a limited budget to three types of protection resources: (i) Traffic control resources, (ii), preventative resources and (iii) corrective resources. Traffic control resources are employed to impose restrictions on the traffic flowing across directed edges in the transportation network. Preventative resources are allocated to nodes to reduce the probability of infection at that node (e.g. vaccines), and corrective resources are allocated to nodes to increase the recovery rate at that node (e.g. antidotes). We assume these resources have monetary costs associated with them, from which we formalize an optimal budget allocation problem which maximizes containment of the infection. We present a polynomial time solution to the optimal budget allocation problem using Geometric Programming (GP) for an arbitrary weighted and directed contact network and a large class of resource cost functions. We illustrate our approach by designing optimal traffic control strategies to contain an epidemic outbreak that propagates through a real-world air transportation network.Comment: arXiv admin note: text overlap with arXiv:1309.627

Foundations of Cryptoeconomic Systems

Blockchain networks and similar cryptoeconomic networks aresystems, specifically complex systems. They are adaptive networkswith multi-scale spatiotemporal dynamics. Individual actions towards a collective goal are incentivized with "purpose-driven" tokens. These tokens are equipped with cryptoeconomic mechanisms allowing a decentralized network to simultaneously maintain a universal state layer, support peer-to-peer settlement, andincentivize collective action. These networks therefore provide a mission-critical and safety-critical regulatory infrastructure for autonomous agents in untrusted economic networks. They also provide a rich, real-time data set reflecting all economic activities in their systems. Advances in data science and network sciencecan thus be leveraged to design and analyze these economic systems in a manner consistent with the best practices of modern systems engineering. Research that reflects all aspects of these socioeconomic networks needs (i) a complex systems approach, (ii) interdisciplinary research, and (iii) a combination of economic and engineering methods, here referred to as "economic systems engineering", for the regulation and control of these socio-economicsystems. This manuscript provides foundations for further research activities that build on these assumptions, including specific research questions and methodologies for future research in this field.Series: Working Paper Series / Institute for Cryptoeconomics / Interdisciplinary Researc

Optimal Vaccine Allocation to Control Epidemic Outbreaks in Arbitrary Networks

We consider the problem of controlling the propagation of an epidemic outbreak in an arbitrary contact network by distributing vaccination resources throughout the network. We analyze a networked version of the Susceptible-Infected-Susceptible (SIS) epidemic model when individuals in the network present different levels of susceptibility to the epidemic. In this context, controlling the spread of an epidemic outbreak can be written as a spectral condition involving the eigenvalues of a matrix that depends on the network structure and the parameters of the model. We study the problem of finding the optimal distribution of vaccines throughout the network to control the spread of an epidemic outbreak. We propose a convex framework to find cost-optimal distribution of vaccination resources when different levels of vaccination are allowed. We also propose a greedy approach with quality guarantees for the case of all-or-nothing vaccination. We illustrate our approaches with numerical simulations in a real social network