The study of intelligent game-playing has gained tremendous attention in the past few decades. The recent development of artificial intelligence (AI) players (e.g., the Go player AlphaGo) has made intelligent game-playing even more prominent in both academia and industry. The performance of state-of-the-art AI players benefits greatly from machine learning techniques, based on which, players can make estimations and decisions even without understanding the games. Although AI machines show great superiority over humans in terms of data processing and complex computation, there remains a vast distance between artificial intelligence and human intelligence with respect to the abilities of context understanding and reasoning. In this paper, we explore the theoretical foundation of intelligent game-playing from a logical perspective. The proposed logic, by considering the computational limits in practical game-playing, drops the ideal assumptions in existing logics for the classical game model. We show that under logical framework, the basis of decision-making for agents in game scenarios can be formally represented and analyzed. Moreover, by characterizing the solutions of games, this logic is able to formalize players’ rational decision-making during practical game-playing.
Since the discovery of the DNA Strand Displacement mechanism, researchers have implemented a lot of applications, such as DNA computing, DNA Circuits, Logic gates, and Chemical Reaction network.To achieve those functions, a well-designed system is essential, among which the toehold domains and migration domains play a vital role.In this paper, we designed three basic logic gates based on the toehold mediates DNA strand displacement mechanism, and utilized them to struct a three-layer multiplexer DNA logic circuit.However, the traditional INHIBIT gate annihilated all the inputs strands which obscure the multiplexer in further applications.Therefore, we improved the INHIBIT gate, so the desired input strand can be selected, and the corresponding output strand can be identified.Lastly, we adjusted the multiplexer and realized a cyclic DNA circuit.The simulation results verified the efficiency and reliability of our multiplexer DNA logic circuits.Our method has the ability in architecting complex DNA integrated circuits.
Graph embedding has been proven to be efficient and effective in facilitating graph analysis. In this paper, we present a novel spectral framework called NOn-Backtracking Embedding (NOBE), which offers a new perspective that organizes graph data at a deep level by tracking the flow traversing on the edges with backtracking prohibited. Further, by analyzing the non-backtracking process, a technique called graph approximation is devised, which provides a channel to transform the spectral decomposition on an edge-to-edge matrix to that on a node-to-node matrix. Theoretical guarantees are provided by bounding the difference between the corresponding eigenvalues of the original graph and its graph approximation. Extensive experiments conducted on various real-world networks demonstrate the efficacy of our methods on both macroscopic and microscopic levels, including clustering and structural hole spanner detection.
Let G=(V,E) be a graph and f:(V ∪ E) → [k] be a proper total k-coloring of G. We say that f is an adjacent vertex distinguishing total coloring if for any two adjacent vertices, the set of colors appearing on the vertex and incident edges are different. We call the smallest k for which such a coloring of G exists the adjacent vertex distinguishing total chromatic number, and denote it by χ at (G). In this paper, we show that χ at (K 19 - E(C 4 )) = 20 and χ at (K 21 -E(C 4 )) = 22.
Denote byγ(G)the domination number of a digraphGandCm□Cnthe Cartesian product ofCmandCn, the directed cycles of lengthm,n≥2. In 2010, Liu et al. determined the exact values ofγ(Cm□Cn)form=2,3,4,5,6. In 2013, Mollard determined the exact values ofγ(Cm□Cn)form=3k+2. In this paper, we give lower and upper bounds ofγ(Cm□Cn)withm=3k+1for different cases. In particular,⌈2k+1n/2⌉≤γ(C3k+1□Cn)≤⌊2k+1n/2⌋+k. Based on the established result, the exact values ofγ(Cm□Cn)are determined form=7and 10 by the combination of the dynamic algorithm, and an upper bound forγ(C13□Cn)is provided.
Given a simple connected graph G, the metric dimension dim(G) (and edge metric dimension edim(G)) is defined as the cardinality of a smallest vertex subset S⊆V(G) for which every two distinct vertices (and edges) in G have distinct distances to a vertex of S. It is an interesting topic to discuss the relation between these two dimensions for some class of graphs. This paper settles two open problems on this topic for unicyclic graphs. We recently learned that Sedlar and Škrekovski settled these problems, but our work presents the results in a completely different way. By introducing four classes of subgraphs, we characterize the structure of a unicyclic graph G such that dim(G) and edim(G) are equal to the cardinality of any minimum branch-resolving set for unicyclic graphs. This generates an approach to determine the exact value of the metric dimension (and edge metric dimension) for a unicyclic graph.
Game theory has become a standard tool for depicting and demonstrating various game-like phenomena by providing appropriate mathematical models and for analyzing and predicting agents' behaviors and their decisions by formalizing solution concepts. The conventional game model mainly concerns ideal systems that would always guarantee optimal responses, which appears unrealistic for practical game scenarios since decision-making usually entails resource costs. Therefore, this study considers players' decision-making in extensive games when the computational cost of searching the strategy space is limited. We start with a new mathematical model of extensive games that features a bound on computational resources during players' decision-making process such that they can only foresee a part of the available alternatives in the future. This model is more appropriate in predicting players' strategies than the conventional model, under which we investigate the effects of computational costs on players' strategies as well as the computational complexity. Furthermore, a simulation experiment is performed to seek the connection between the amount of resources and the goodness of the outcomes. This study is expected to provide a foundation for players' rational decision-making with computational costs.
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