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1. Epistemic Argumentation Framework

   https://doi.org/10.1007/978-3-030-29908-8_56  

   Sakama, S; Son, Tran C (August 2019, Pacific Rim International Conference on Artificial Intelligence)

   The paper introduces the notion of an epistemic argumentation framework (EAF) as a means to integrate the beliefs of a reasoner with argumentation. Intuitively, an EAF encodes the beliefs of an agent who reasons about arguments. Formally, an EAF is a pair of an argumentation framework and an epistemic constraint. The semantics of the EAF is defined by the notion of an -epistemic labelling set, where is complete, stable, grounded, or preferred, which is a set of -labellings that collectively satisfies the epistemic constraint of the EAF. The paper shows how EAF can represent different views of reasoners on the same argumentation framework. It also includes representing preferences in EAF and multi-agent argumentation. Finally, the paper discusses the complexity of the problem of determining whether or not an -epistemic labelling set exists. 

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2. Epistemic Argumentation Framework: Theory and Computation

   https://doi.org/https://doi.org/10.1613/jair.1.12121  

   Sakama, Chiaki; Son, Tran C. (December 2020, Journal of artificial intelligence research)

   null (Ed.)

   The paper introduces the notion of an epistemic argumentation framework (EAF) as a means to integrate the beliefs of a reasoner with argumentation. Intuitively, an EAF encodes the beliefs of an agent who reasons about arguments. Formally, an EAF is a pair of an argumentation framework and an epistemic constraint. The semantics of the EAF is defined by the notion of an ω-epistemic labelling set, where ω is complete, stable, grounded, or preferred, which is a set of ω-labellings that collectively satisfies the epistemic constraint of the EAF. The paper shows how EAF can represent different views of reasoners on the same argumentation framework. It also includes representing preferences in EAF and multi-agent argumentation. Finally, the paper discusses complexity issues and computation using epistemic logic programming. 

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3. Derivation of the ion equation

   Grenier, E (March 2020, Quarterly of applied mathematics)

   We consider the classical Euler-Poisson system for electrons and ions, interacting through an electrostatic field. The mass ratio of an electron and an ion is small and we establish an asymptotic expansion of solutions, where the main term is obtained from a solution to a self-consistent equation involving only the ion variables. Moreover, on R^3, the validity of such an expansion is established even with \ill-prepared" Cauchy data, by including an additional initial layer correction. 

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4. Two-stage linear decision rules for multi-stage stochastic programming

   https://doi.org/10.1007/s10107-018-1339-4  

   Bodur, Merve; Luedtke, James R. (October 2018, Mathematical Programming)

   Multi-stage stochastic linear programs (MSLPs) are notoriously hard to solve in general. Linear decision rules (LDRs) yield an approximation of an MSLP by restricting the decisions at each stage to be an affine function of the observed uncertain parameters. Finding an optimal LDR is a static optimization problem that provides an upper bound on the optimal value of the MSLP, and, under certain assumptions, can be formulated as an explicit linear program. Similarly, as proposed by Kuhn et al. (Math Program 130(1):177–209, 2011) a lower bound for an MSLP can be obtained by restricting decisions in the dual of the MSLP to follow an LDR. We propose a new approximation approach for MSLPs, two-stage LDRs. The idea is to require only the state variables in an MSLP to follow an LDR, which is sufficient to obtain an approximation of an MSLP that is a two-stage stochastic linear program (2SLP). We similarly propose to apply LDR only to a subset of the variables in the dual of the MSLP, which yields a 2SLP approximation of the dual that provides a lower bound on the optimal value of the MSLP. Although solving the corresponding 2SLP approximations exactly is intractable in general, we investigate how approximate solution approaches that have been developed for solving 2SLP can be applied to solve these approximation problems, and derive statistical upper and lower bounds on the optimal value of the MSLP. In addition to potentially yielding better policies and bounds, this approach requires many fewer assumptions than are required to obtain an explicit reformulation when using the standard static LDR approach. A computational study on two example problems demonstrates that using a two-stage LDR can yield significantly better primal policies and modestly better dual policies than using policies based on a static LDR. 

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5. Graph Exploration by Energy-Sharing Mobile Agents

   Czyzowicz, J.; Dobrev, S.; Killick, R.; Kranakis, E.; Krizanc, D.; Narayanan, L.; Opatrny, J; Pankratov, D.; Shende, S. (July 2021, 28th International Colloquium on Structural Information and Communication Complexity (SIROCCO))

   null (Ed.)

   We consider the problem of collective exploration of a known n- node edge-weighted graph by k mobile agents that have limited energy but are capable of energy transfers. The agents are initially placed at an arbitrary subset of nodes in the graph, and each agent has an initial, possibly different, amount of energy. The goal of the exploration problem is for every edge in the graph to be traversed by at least one agent. The amount of energy used by an agent to travel distance x is proportional to x. In our model, the agents can share energy when co-located: when two agents meet, one can transfer part of its energy to the other. For an n-node path, we give an O(n+k) time algorithm that either nds an exploration strategy, or reports that one does not exist. For an n-node tree with l leaves, we give an O(n+lk^2) algorithm that finds an exploration strategy if one exists. Finally, for the general graph case, we show that the problem of deciding if exploration is possible by energy-sharing agents is NP-hard, even for 3-regular graphs. In addition, we show that it is always possible to find an exploration strategy if the total energy of the agents is at least twice the total weight of the edges; moreover, this is asymptotically optimal. 

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