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. (C) 2014 Elsevier Inc. All rights reserved.

Vertical structure and horizontal gradients of aerosol extinction coefficients over coastal India inferred from airborne lidar measurements during the Integrated Campaign for Aerosol, Gases and Radiation Budget (ICARB) field campaign

Quantitative estimates of the vertical structure and the spatial gradients of aerosol extinction coefficients have been made from airborne lidar measurements across the coastline into offshore oceanic regions along the east and west coasts of India. The vertical structure revealed the presence of strong, elevated aerosol layers in the altitude region of similar to 2-4 km, well above the atmospheric boundary layer (ABL). Horizontal gradients also showed a vertical structure, being sharp with the e(-1) scaling distance (D-0H) as small as similar to 150 km in the well-mixed regions mostly under the influence of local source effects. Above the ABL, where local effects are subdued, the gradients were much shallower (similar to 600-800 km); nevertheless, they were steep compared to the value of similar to 1500-2500 km reported for columnar AOD during winter. The gradients of these elevated layers were steeper over the east coast of India than over the west coast. Near-simultaneous radio sonde (Vaisala, Inc., Finland) ascents made over the northern Bay of Bengal showed the presence of convectively unstable regions, first from surface to similar to 750-1000 m and the other extending from 1750 to 3000 m separated by a stable region in between. These can act as a conduit for the advection of aerosols and favor the transport of continental aerosols in the higher levels (> 2 km) into the oceans without entering the marine boundary layer below. Large spatial gradient in aerosol optical and hence radiative impacts between the coastal landmass and the adjacent oceans within a short distance of < 300 km (even at an altitude of 3 km) during summer and the premonsoon is of significance to the regional climate.

Aerosol characteristics and radiative impacts over the Arabian Sea during the intermonsoon season: Results from ARMEX field campaign

During the second phase of the Arabian Sea Monsoon Experiment (ARMEX-II), extensive measurements of spectral aerosol optical depth, mass concentration, and mass size distribution of ambient aerosols as well as mass concentration of aerosol black carbon (BC) were made onboard a research vessel during the intermonsoon period (i.e., when the monsoon winds are in transition from northeasterlies to westerlies/ southwesterlies) over the Arabian Sea (AS) adjoining the Indian Peninsula. Simultaneous measurements of spectral aerosol optical depths (AODs) were made at different regions over the adjoining Indian landmass. Mean AODs (at 500-nm wavelength) over the ocean (similar to0.44) were comparable to those over the coastal land (similar to0.47), but were lower than the values observed over the plateau regions of central Indian Peninsula (similar to0.61). The aerosol properties were found to respond distinctly with respect to change in the trajectories, with higher optical depths and flatter AOD spectra associated with trajectories indicating advection from west Asia, and northwest and west-coastal India. On average, BC constituted only similar to2.2% to total aerosol mass compared to the climatological values of similar to6% over the coastal land during the same season. These data are used to characterize the physical properties of aerosols and to assess the resulting short-wave direct aerosol forcing. The mean values were similar to27 W m(-2) at the surface and -12 W m(-2) at the top of the atmosphere (TOA), resulting in a net atmospheric forcing of +15 W m(-2). The forcing also depended on the region from where the advection predominates. The surface and atmospheric forcing were in the range -40 to -57 W m(-2) and +27 to +39 W m(-2), respectively, corresponding to advection from the west Asian and western coastal India where they were as low as -19 and +10 W m(-2), respectively, when the advection was mainly from the Bay of Bengal and from central/peninsular India. In all these cases, the net atmospheric forcing (heating) efficiency was lower than the values reported for northern Indian Ocean during northern winter, which is attributed to the reduced BC mass fraction.

A game theoretical multiple resource interaction approach to resource allocation in an air campaign

In this paper we propose a multiple resource interaction model in a game-theoretical framework to solve resource allocation problems in theater level military campaigns. An air raid campaign using SEAD aircraft and bombers against an enemy target defended by air defense units is considered as the basic platform. Conditions for the existence of saddle point in pure strategies is proved and explicit feedback strategies are obtained for a simplified model with linear attrition function limited by resource availability. An illustrative example demonstrates the key features.

Influence limitation in multi-campaign social networks: A Shapley value based approach

We investigate the problem of influence limitation in the presence of competing campaigns in a social network. Given a negative campaign which starts propagating from a specified source and a positive/counter campaign that is initiated, after a certain time delay, to limit the the influence or spread of misinformation by the negative campaign, we are interested in finding the top k influential nodes at which the positive campaign may be triggered. This problem has numerous applications in situations such as limiting the propagation of rumor, arresting the spread of virus through inoculation, initiating a counter-campaign against malicious propaganda, etc. The influence function for the generic influence limitation problem is non-submodular. Restricted versions of the influence limitation problem, reported in the literature, assume submodularity of the influence function and do not capture the problem in a realistic setting. In this paper, we propose a novel computational approach for the influence limitation problem based on Shapley value, a solution concept in cooperative game theory. Our approach works equally effectively for both submodular and non-submodular influence functions. Experiments on standard real world social network datasets reveal that the proposed approach outperforms existing heuristics in the literature. As a non-trivial extension, we also address the problem of influence limitation in the presence of multiple competing campaigns.

Optimal control of information epidemics modeled as Maki Thompson rumors

We model the spread of information in a homogeneously mixed population using the Maki Thompson rumor model. We formulate an optimal control problem, from the perspective of single campaigner, to maximize the spread of information when the campaign budget is fixed. Control signals, such as advertising in the mass media, attempt to convert ignorants and stiflers into spreaders. We show the existence of a solution to the optimal control problem when the campaigning incurs non-linear costs under the isoperimetric budget constraint. The solution employs Pontryagin's Minimum Principle and a modified version of forward backward sweep technique for numerical computation to accommodate the isoperimetric budget constraint. The techniques developed in this paper are general and can be applied to similar optimal control problems in other areas. We have allowed the spreading rate of the information epidemic to vary over the campaign duration to model practical situations when the interest level of the population in the subject of the campaign changes with time. The shape of the optimal control signal is studied for different model parameters and spreading rate profiles. We have also studied the variation of the optimal campaigning costs with respect to various model parameters. Results indicate that, for some model parameters, significant improvements can be achieved by the optimal strategy compared to the static control strategy. The static strategy respects the same budget constraint as the optimal strategy and has a constant value throughout the campaign horizon. This work finds application in election and social awareness campaigns, product advertising, movie promotion and crowdfunding campaigns. (C) 2014 Elsevier B.V. All rights reserved.

Sources of black carbon aerosols in South Asia and surrounding regions during the Integrated Campaign for Aerosols, Gases and Radiation Budget (ICARB)

This study examines differences in the surface black carbon (BC) aerosol loading between the Bay of Bengal (BoB) and the Arabian Sea (AS) and identifies dominant sources of BC in South Asia and surrounding regions during March-May 2006 (Integrated Campaign for Aerosols, Gases and Radiation Budget, ICARB) period. A total of 13 BC tracers are introduced in the Weather Research and Forecasting Model coupled with Chemistry to address these objectives. The model reproduced the temporal and spatial variability of BC distribution observed over the AS and the BoB during the ICARB ship cruise and captured spatial variability at the inland sites. In general, the model underestimates the observed BC mass concentrations. However, the model-observation discrepancy in this study is smaller compared to previous studies. Model results show that ICARB measurements were fairly well representative of the AS and the BoB during the pre-monsoon season. Elevated BC mass concentrations in the BoB are due to 5 times stronger influence of anthropogenic emissions on the BoB compared to the AS. Biomass burning in Burma also affects the BoB much more strongly than the AS. Results show that anthropogenic and biomass burning emissions, respectively, accounted for 60 and 37% of the average +/- standard deviation (representing spatial and temporal variability) BC mass concentration (1341 +/- 2353 ng m(-3)) in South Asia. BC emissions from residential (61 %) and industrial (23 %) sectors are the major anthropogenic sources, except in the Himalayas where vehicular emissions dominate. We find that regional-scale transport of anthropogenic emissions contributes up to 25% of BC mass concentrations in western and eastern India, suggesting that surface BC mass concentrations cannot be linked directly to the local emissions in different regions of South Asia.