Central sets in semigroups are known to have very rich combinatorial structure, described by the``Central Sets Theorem''. It has been unknown whether the Central Sets Theorem in fact characterizes central sets, and if not whether some other combinatorial characterization could be found. We derive here a combinatorial characterization of central sets and of the weaker notion of quasi-central sets. We show further that in (N, +) these notions are different and strictly stronger than the characterization provided by the Central Sets Theorem. In addition, we derive an algebraic characterization of sets satisfying the conclusion of the Central Sets Theorem and use this characterization to show that the conclusion of the Central Sets Theorem is a partition regular property in any commutative semigroup.
Typically, the lack of effective stakeholder participation in a project-especially in the initial planning and implementation stages-has a negative impact on the expected performance of the project. These negative consequences require attempts to encourage their effective participation. Nevertheless, there are some challenges ahead, such as conflict of interest among the stakeholders. For more accurate identification of the interests, objectives, and performance of the stakeholders, this paper proposes an accurate and organized model for the analysis of results from the stakeholder impact index. We implemented the proposed model to determine the existing barriers to renewable energy development in Iran, specifically the wind and solar energy sectors. For data collection, we used the opinions of the experts and other people involved in these industries. Data analysis showed that the current implantation conditions of the solar and wind energy sectors were similar from the stakeholders' perspectives as not bad but poor. The required position of each stakeholder to lift the barriers and develop these industries was identified and their current positions from the desirable conditions were assessed. Finally, some recommendations were presented to improve the stakeholders' conditions and eliminate the barriers.
This report presents the results of a friendly competition for formal verification of continuous and hybrid systems with artificial intelligence (AI) components. Specifically, machine learning (ML) components in cyber-physical systems (CPS), such as feedforward neural networks used as feedback controllers in closed-loop systems are considered, which is a class of systems classically known as intelligent control systems, or in more modern and specific terms, neural network control systems (NNCS). We more broadly refer to this category as AI and NNCS (AINNCS). The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2020. In the second edition of this AINNCS category at ARCH-COMP, four tools have been applied to solve seven different benchmark problems, (in alphabetical order): NNV, OVERT, ReachNN*, and VenMAS. This report is a snapshot of the current landscape of tools and the types of benchmarks for which these tools are suited. Due to the diversity of problems, lack of a shared hardware platform, and the early stage of the competition, we are not ranking tools in terms of performance, yet the presented results probably provide the most complete assessment of current tools for safety verification of NNCS.
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