scholarly journals Containing Misinformation Spread: A Collaborative Resource Allocation Strategy for Knowledge Popularization and Expert Education

2022 ◽  
Vol 2022 ◽  
pp. 1-14
Author(s):  
Linhong Li ◽  
Kaifan Huang ◽  
Xiaofan Yang

With the prevalence of online social networks, the potential threat of misinformation has greatly enhanced. Therefore, it is significant to study how to effectively control the spread of misinformation. Publishing the truth to the public is the most effective approach to controlling the spread of misinformation. Knowledge popularization and expert education are two complementary ways to achieve that. It has been proven that if these two ways can be combined to speed up the release of the truth, the impact caused by the spread of misinformation will be dramatically reduced. However, how to reasonably allocate resources to these two ways so as to achieve a better result at a lower cost is still an open challenge. This paper provides a theoretical guidance for designing an effective collaborative resource allocation strategy. First, a novel individual-level misinformation spread model is proposed. It well characterizes the collaborative effect of the two truth-publishing ways on the containment of misinformation spread. On this basis, the expected cost of an arbitrary collaborative strategy is evaluated. Second, an optimal control problem is formulated to find effective strategies, with the expected cost as the performance index function and with the misinformation spread model as the constraint. Third, in order to solve the optimal control problem, an optimality system that specifies the necessary conditions of an optimal solution is derived. By solving the optimality system, a candidate optimal solution can be obtained. Finally, the effectiveness of the obtained candidate optimal solution is verified by a series of numerical experiments.

2016 ◽  
Vol 21 (2) ◽  
pp. 223-240 ◽  
Author(s):  
Xiaopeng Zhao ◽  
Jinde Cao

In this paper, for the BCF model describing crystal surface growth, the optimal control problem is considered, the existence of optimal solution is proved and the optimality system is established.


2014 ◽  
Vol 11 (03) ◽  
pp. 477-491 ◽  
Author(s):  
Adimurthi ◽  
Shyam Sundar Ghoshal ◽  
G. D. Veerappa Gowda

The optimal control problem for Burgers equation was first considered by Castro, Palacios and Zuazua. They proved the existence of a solution and proposed a numerical scheme to capture an optimal solution via the method of "alternate decent direction". In this paper, we introduce a new strategy for the optimal control problem for scalar conservation laws with convex flux. We propose a new cost function and by the Lax–Oleinik explicit formula for entropy solutions, the nonlinear problem is converted to a linear problem. Exploiting this property, we prove the existence of an optimal solution and, by a backward construction, we give an algorithm to capture an optimal solution.


1977 ◽  
Vol 9 (01) ◽  
pp. 55-68 ◽  
Author(s):  
P. Nash ◽  
J. C. Gittins

The problem of scheduling items for service with random service times is formulated as an optimal control problem. Pontryagin's maximum principle is used to determine the optimal schedule in certain cases.


2008 ◽  
Vol 13 (3) ◽  
pp. 351-377 ◽  
Author(s):  
S. S. Ravindran

In this paper we study the long time behavior of solutions for an optimal control problem associated with the viscous incompressible electrically conducting fluid modeled by the magnetohydrodynamic (MHD) equations in a bounded two dimensional domain through the adjustment of distributed controls. We first construct a quasi-optimal solution for the MHD systems which possesses exponential decay in time. We then derive some preliminary estimates for the long-time behavior of all admissible solutions of the MHD systems. Next we prove the existence of a solution for the optimal control problem for both finite and infinite time intervals. Finally, we establish the long-time decay properties of the solutions for the optimal control problem.


Author(s):  
Juan López-Ríos ◽  
Élder J. Villamizar-Roa

In this paper, we study an optimal control problem associated to a 3D-chemotaxis-Navier-Stokes model. First we prove the existence of global weak solutions of the state equations with a linear reaction term on the chemical concentration equation, and an external source on the velocity equation, both acting as controls on the system. Second, we establish aregularity criterion to get global-in-time strong solutions. Finally, we prove the existence of an optimal solution, and we establish a first-order optimality condition.


2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Jian-Ping Sun ◽  
Qiu-Yan Ren ◽  
Ya-Hong Zhao

In this paper, we are concerned with a class of optimal control problem governed by nonlinear first order dynamic equation on time scales. By imposing some suitable conditions on the related functions, for any given control policy, we first obtain the existence of a unique solution for the nonlinear controlled system. Then, we study the existence of an optimal solution for the optimal control problem.


Author(s):  
Agnes Lamacz-Keymling ◽  
Irwin Yousept

This article examines a linear-quadratic elliptic optimal control problem in which the cost functional and the state equation involve a highly oscillatory periodic coefficient $A^\eps$. The small parameter $\eps>0$ denotes the periodicity length. We propose a high-order effective control problem with constant coefficients that provides an approximation of the original one with error $O(\eps^M)$, where $M\in\N$ is as large as one likes. Our analysis relies on a Bloch wave expansion of the optimal solution and is performed in two steps. In the first step, we expand the lowest Bloch eigenvalue in a Taylor series to obtain a high-order effective optimal control problem. In the second step, the original and the effective problem are rewritten in terms of the Bloch and the Fourier transform, respectively. This allows for a direct comparison of the optimal control problems via the corresponding variational inequalities, leading to our main theoretical result on the high-oder approximation.


1977 ◽  
Vol 9 (1) ◽  
pp. 55-68 ◽  
Author(s):  
P. Nash ◽  
J. C. Gittins

The problem of scheduling items for service with random service times is formulated as an optimal control problem. Pontryagin's maximum principle is used to determine the optimal schedule in certain cases.


2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
H. Zarei ◽  
A. V. Kamyad ◽  
M. H. Farahi

This present study proposes an optimal control problem, with the final goal of implementing an optimal treatment protocol which could maximize the survival time of patients and minimize the cost of drug utilizing a system of ordinary differential equations which describes the interaction of the immune system with the human immunodeficiency virus (HIV). Optimal control problem transfers into a modified problem in measure space using an embedding method in which the existence of optimal solution is guaranteed by compactness of the space. Then the metamorphosed problem is approximated by a linear programming (LP) problem, and by solving this LP problem a suboptimal piecewise constant control function, which is more practical from the clinical viewpoint, is achieved. The comparison between the immune system dynamics in treated and untreated patients is introduced. Finally, the relationships between the healthy cells and virus are shown.


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