How to Run a Campaign: Optimal Control of SIS and SIR Information Epidemics

Information spreading in a population can be modeled as an epidemic. Campaigners (e.g. election campaign managers, companies marketing products or movies) are interested in spreading a message by a given deadline, using limited resources. In this paper, we formulate the above situation as an optimal control problem and the solution (using Pontryagin's Maximum Principle) prescribes an optimal resource allocation over the time of the campaign. We consider two different scenarios --- in the first, the campaigner can adjust a direct control (over time) which allows her to recruit individuals from the population (at some cost) to act as spreaders for the Susceptible-Infected-Susceptible (SIS) epidemic model. In the second case, we allow the campaigner to adjust the effective spreading rate by incentivizing the infected in the Susceptible-Infected-Recovered (SIR) model, in addition to the direct recruitment. We consider time varying information spreading rate in our formulation to model the changing interest level of individuals in the campaign, as the deadline is reached. In both the cases, we show the existence of a solution and its uniqueness for sufficiently small campaign deadlines. For the fixed spreading rate, we show the effectiveness of the optimal control strategy against the constant control strategy, a heuristic control strategy and no control. We show the sensitivity of the optimal control to the spreading rate profile when it is time varying.Comment: Proofs for Theorems 4.2 and 5.2 which do not appear in the published journal version are included in this version. Published version can be accessed here: http://dx.doi.org/10.1016/j.amc.2013.12.16

Game Theoretic Analysis of Tree Based Referrals for Crowd Sensing Social Systems with Passive Rewards

Participatory crowd sensing social systems rely on the participation of large number of individuals. Since humans are strategic by nature, effective incentive mechanisms are needed to encourage participation. A popular mechanism to recruit individuals is through referrals and passive incentives such as geometric incentive mechanisms used by the winning team in the 2009 DARPA Network Challenge and in multi level marketing schemes. The effect of such recruitment schemes on the effort put in by recruited strategic individuals is not clear. This paper attempts to fill this gap. Given a referral tree and the direct and passive reward mechanism, we formulate a network game where agents compete for finishing crowd sensing tasks. We characterize the Nash equilibrium efforts put in by the agents and derive closed form expressions for the same. We discover free riding behavior among nodes who obtain large passive rewards. This work has implications on designing effective recruitment mechanisms for crowd sourced tasks. For example, usage of geometric incentive mechanisms to recruit large number of individuals may not result in proportionate effort because of free riding.Comment: 6 pages, 3 figures. Presented in Social Networking Workshop at International Conference on Communication Systems and Networks (COMSNETS), Bangalore, India, January 201

Optimal Resource Allocation Over Time and Degree Classes for Maximizing Information Dissemination in Social Networks

We study the optimal control problem of allocating campaigning resources over the campaign duration and degree classes in a social network. Information diffusion is modeled as a Susceptible-Infected epidemic and direct recruitment of susceptible nodes to the infected (informed) class is used as a strategy to accelerate the spread of information. We formulate an optimal control problem for optimizing a net reward function, a linear combination of the reward due to information spread and cost due to application of controls. The time varying resource allocation and seeds for the epidemic are jointly optimized. A problem variation includes a fixed budget constraint. We prove the existence of a solution for the optimal control problem, provide conditions for uniqueness of the solution, and prove some structural results for the controls (e.g. controls are non-increasing functions of time). The solution technique uses Pontryagin's Maximum Principle and the forward-backward sweep algorithm (and its modifications) for numerical computations. Our formulations lead to large optimality systems with up to about 200 differential equations and allow us to study the effect of network topology (Erdos-Renyi/scale-free) on the controls. Results reveal that the allocation of campaigning resources to various degree classes depends not only on the network topology but also on system parameters such as cost/abundance of resources. The optimal strategies lead to significant gains over heuristic strategies for various model parameters. Our modeling approach assumes uncorrelated network, however, we find the approach useful for real networks as well. This work is useful in product advertising, political and crowdfunding campaigns in social networks.Comment: 14 + 4 pages, 11 figures. Author's version of the article accepted for publication in IEEE/ACM Transactions on Networking. This version includes 4 pages of supplementary material containing proofs of theorems present in the article. Published version can be accessed at http://dx.doi.org/10.1109/TNET.2015.251254

Robust Power Allocation and Outage Analysis for Secrecy in Independent Parallel Gaussian Channels

This letter studies parallel independent Gaussian channels with uncertain eavesdropper channel state information (CSI). Firstly, we evaluate the probability of zero secrecy rate in this system for (i) given instantaneous channel conditions and (ii) a Rayleigh fading scenario. Secondly, when non-zero secrecy is achievable in the low SNR regime, we aim to solve a robust power allocation problem which minimizes the outage probability at a target secrecy rate. We bound the outage probability and obtain a linear fractional program that takes into account the uncertainty in eavesdropper CSI while allocating power on the parallel channels. Problem structure is exploited to solve this optimization problem efficiently. We find the proposed scheme effective for uncertain eavesdropper CSI in comparison with conventional power allocation schemes.Comment: 4 pages, 2 figures. Author version of the paper published in IEEE Wireless Communications Letters. Published version is accessible at http://dx.doi.org/10.1109/LWC.2015.249734

Banking risk as an epidemiological model: an optimal control approach

The process of contagiousness spread modelling is well-known in epidemiology. However, the application of spread modelling to banking market is quite recent. In this work, we present a system of ordinary differential equations, simulating data from the largest European banks. Then, an optimal control problem is formulated in order to study the impact of a possible measure of the Central Bank in the economy. The proposed approach enables qualitative specifications of contagion in banking obtainment and an adequate analysis and prognosis within the financial sector development and macroeconomy as a whole. We show that our model describes well the reality of the largest European banks. Simulations were done using MATLAB and BOCOP optimal control solver, and the main results are taken for three distinct scenarios.publishe

HSMA_WOA: A hybrid novel Slime mould algorithm with whale optimization algorithm for tackling the image segmentation problem of chest X-ray images

Recently, a novel virus called COVID-19 has pervasive worldwide, starting from China and moving to all the world to eliminate a lot of persons. Many attempts have been experimented to identify the infection with COVID-19. The X-ray images were one of the attempts to detect the influence of COVID-19 on the infected persons from involving those experiments. According to the X-ray analysis, bilateral pulmonary parenchymal ground-glass and consolidative pulmonary opacities can be caused by COVID-19 — sometimes with a rounded morphology and a peripheral lung distribution. But unfortunately, the specification or if the person infected with COVID-19 or not is so hard under the X-ray images. X-ray images could be classified using the machine learning techniques to specify if the person infected severely, mild, or not infected. To improve the classification accuracy of the machine learning, the region of interest within the image that contains the features of COVID-19 must be extracted. This problem is called the image segmentation problem (ISP). Many techniques have been proposed to overcome ISP. The most commonly used technique due to its simplicity, speed, and accuracy are threshold-based segmentation. This paper proposes a new hybrid approach based on the thresholding technique to overcome ISP for COVID-19 chest X-ray images by integrating a novel meta-heuristic algorithm known as a slime mold algorithm (SMA) with the whale optimization algorithm to maximize the Kapur's entropy. The performance of integrated SMA has been evaluated on 12 chest X-ray images with threshold levels up to 30 and compared with five algorithms: Lshade algorithm, whale optimization algorithm (WOA), FireFly algorithm (FFA), Harris-hawks algorithm (HHA), salp swarm algorithms (SSA), and the standard SMA. The experimental results demonstrate that the proposed algorithm outperforms SMA under Kapur's entropy for all the metrics used and the standard SMA could perform better than the other algorithms in the comparison under all the metrics

Network coding based cooperative communications

Cooperative communications was proposed to enable spatial diversity in small and inexpensive devices. It allows the creation of virtual antenna array through the antennas of the participating users. The benefits offered by cooperation include increase in data rate, robustness against shadowing, decrease in overall transmit power of the system etc. However, when user cooperation is extended to include multiple users or multiple relays, the system suffers from loss in throughput due to increased number of channel use. To overcome this, cooperative communications schemes often make use of network coding which helps trade-off resource allocated for cooperation and system performance. In the first part of the thesis, we propose random network coding based user cooperation scheme in wireless networks. Our scheme is very effective in spreading the information of the pool of cooperating users so that the message can reach the destination via many alternative paths. Also, the proposed scheme is decentralized and the cooperating nodes act independent of the others. Results show that our scheme is resilient to inter-user channel noise and can achieve high diversity gain when number of cooperating users is large. We further enhance the performance of our scheme for bad user-destination channel by protecting the packets by convolutional coding. This version of our scheme performs better than traditional N user cooperation in terms of both outage and throughput for all user-destination channel conditions when inter-user channel is good. It also shows better robustness to inter-user channel than original scheme. In second part of this thesis, we consider analog network coding based bidirectional relaying system. We develop a scheme to optimally allocate power at the relay nodes such that overall data rate in transfer of messages between two user nodes is maximized under uncertain channel conditions. We have proposed an iterative solution for rate maximization problem and solve a geometric program at each step. Results show that bidirectional relaying can achieve significantly more data rate than conventional unidirectional relaying scheme at the cost of reduced diversity. Also, addition of more relays makes the system more robust to imperfections in channel.Applied Science, Faculty ofElectrical and Computer Engineering, Department ofGraduat

DYNAMIC PRIORITY QUEUEING OF HANDOVER CALLS IN WIRELESS NETWORKS: AN ANALYTICAL FRAMEWORK

Abstract. This term paper address the issue of queueing of handover calls in Mobile Networks. There are two priority class for handover calls. The priority of the calls is decided based upon the Received Signal Strength (RSS) and the rate of change of RSS due to mobile velocity. If mobile velocity is large, handover call will be dropped quickly due to degradation in RSS so needs to be put in higher priority class. The facility of priority transition is also provided whereby a second priority handover call can become first order priority call if situation demands. Also, the situation that the call ends in the queue is taken into account. With moinor adjustments, the framework can be modified to analyze First-in-First-Out queueing of handover calls, the schemes that use guard channels to manage handover calls and even networks which handle integrated voice/data transmission. 1

Accelerating Information Diffusion in Social Networks Under the Susceptible-Infected-Susceptible Epidemic Model

Standard Susceptible-Infected-Susceptible (SIS) epidemic models assume that a message spreads from the infected to the susceptible nodes due to only susceptible-infected epidemic contact. We modify the standard SIS epidemic model to include direct recruitment of susceptible individuals to the infected class at a constant rate (independent of epidemic contacts), to accelerate information spreading in a social network. Such recruitment can be carried out by placing advertisements in the media. We provide a closed form analytical solution for system evolution in the proposed model and use it to study campaigning in two different scenarios. In the first, the net cost function is a linear combination of the reward due to extent of information diffusion and the cost due to application of control. In the second, the campaign budget is fixed. Results reveal the effectiveness of the proposed system in accelerating and improving the extent of information diffusion. Our work is useful for devising effective strategies for product marketing and political/social-awareness/crowd-funding campaigns that target individuals in a social network

Degree Based Seed Optimization to Maximize Information Dissemination in Social Networks

We study the problem of optimal seed selection to maximize the fraction of individuals which has received a message in a social network. We have used the Susceptible-Infected (SI) process to model information epidemics. We formulate an optimization problem under a fixed budget constraint on the resource available to recruit individuals in the network to act as seeds, to achieve the above objective. The seeds are decided based on node degrees. This approach will work even when the exact adjacency matrix of the network is unknown and only degrees of the individuals in the network have been estimated. We study effect of the degree distribution of the network on the optimal seed selection strategy and present results for synthetic scale free and Erdos-Renyi networks, and a real scientific collaboration social network. The optimal strategy is compared with two heuristic strategies that (i) selects seeds uniformly among all degrees and (ii) selects highest degree nodes as seeds. Our results show that for a wide range of model parameters, targeting only the highest degree nodes is not optimal for various networks. This work may be of interest to advertisers and campaigners who are interested in spreading a message in a population connected via social networks