Annals of Mathematics and Artificial Intelligence最新文献

A digital plane is a digitization of a Euclidean plane. A plane is specified by its normal, which is a 3D vector with integer coordinates, as considered in this case. It is established here that a 3D digital straight line segment, shifted by an integer amount, can produce the digitized plane. 3D plane’s normals are classified based on the Greatest Common Divisor (GCD) of its components, and the net code is calculated separately for each case. Experimental results are provided for several normals. Also, we show that the digital plane segment generated is a connected digital plane. The proposed method mainly involves integer arithmetic.

Hedonic games are a prominent model of coalition formation, in which each agent’s utility only depends on the coalition she resides. The subclass of hedonic games that models the formation of general partnerships (Larson 2018), where all affiliates receive the same utility, is referred to as hedonic games with common ranking property (HGCRP). Aside from their economic motivation, HGCRP came into prominence since they are guaranteed to have core stable solutions that can be found efficiently (Farrell and Scotchmer Q. J. Econ. 103(2), 279–297 1988). We improve upon existing results by proving that every instance of HGCRP has a solution that is Pareto optimal, core stable, and individually stable. The economic significance of this result is that efficiency is not to be totally sacrificed for the sake of stability in HGCRP. We establish that finding such a solution is NP-hard even if the sizes of the coalitions are bounded above by 3; however, it is polynomial time solvable if the sizes of the coalitions are bounded above by 2. We show that the gap between the total utility of a core stable solution and that of the socially-optimal solution (OPT) is bounded above by n, where n is the number of agents, and that this bound is tight. Our investigations reveal that computing OPT is inapproximable within better than (O(n^{1-epsilon })) for any fixed (epsilon > 0), and that this inapproximability lower bound is polynomially tight. However, OPT can be computed in polynomial time if the sizes of the coalitions are bounded above by 2.

Many recent studies have shown that Fractal Dimension (FD), a ratio for figuring out the complexity of a system given its measurements, can be used as an useful index to provide information about certain brain disease. Our research focuses on the Alzheimer’s disease changes in white and grey brain matters detected through the FD indexes of their contours. Data used in this study were obtained from the Alzheimer’s Disease (AD) Neuroimaging Initiative database (Normal Condition, N = 57, and Alzheimer’s Disease, N = 60). After standard preprocessing pipeline, the white and grey matter 3D FD indexes are computed for the two groups. A statistical analysis shows that only grey matter 3D FD indexes are able to differentiate healthy and AD subjects. Although white matter 3D FD indexes do not, it is remarkable that their presence enhance the separation capability of previous ones. In order to valuate the classification capability of these indexes on healthy and AD subjects, we define several Neural Networks models. The performances of these models vary according to the statistical analysis and reach their best performances when each 3D FD input index is changed into a sequence of 2D FD indexes of (a subset of) the horizontal slices of the white and grey matter volumes.

Deciphering gene regulatory networks’ functioning is an essential step for better understanding of life, as these networks play a fundamental role in the control of cellular processes. Boolean networks have been widely used to represent gene regulatory networks. They allow to describe the dynamics of complex gene regulatory networks straightforwardly and efficiently. The attractors are essential in the analysis of the dynamics of a Boolean network. They explain that a particular cell can acquire specific phenotypes that may be transmitted over several generations. In this work, we consider a new representation of Boolean networks’ dynamics based on a new semantics used in Answer Set Programming (ASP). We use logic programs and ASP to express and deal with gene regulatory networks seen as Boolean networks, and develop a method to detect all the attractors of such networks. We first show how to represent and deal with general Boolean networks for the synchronous and asynchronous updates modes, where the computation of attractors requires a simulation of these networks’ dynamics. Then, we propose an approach for the particular case of circular networks where no simulation is needed. This last specific case plays an essential role in biological systems. We show several theoretical properties; in particular, simple attractors of the gene networks are represented by the stable models of the corresponding logic programs and cyclic attractors by its extra-stable models. These extra-stable models correspond to the extra-extensions of the new semantics that are not captured by the semantics of stable models. We then evaluate the proposed approach for general Boolean networks on real biological networks and the one dedicated to the case of circular networks on Boolean networks generated randomly. The obtained results for both approaches are encouraging.

Nguyen et al. (2016) introduced altruistic hedonic games in which agents’ utilities depend not only on their own preferences but also on those of their friends in the same coalition. We propose to extend their model to coalition formation games in general, considering also the friends in other coalitions. Comparing our model to altruistic hedonic games, we argue that excluding some friends from the altruistic behavior of an agent is a major disadvantage that comes with the restriction to hedonic games. After introducing our model and showing some desirable properties, we additionally study some common stability notions and provide a computational analysis of the associated verification and existence problems.

A Digital Twin (DT) is a frequently updated virtual representation of a physical or a digital instance that captures its properties of interest. Incorporating both cyber and physical parts to build a digital twin is challenging due to the high complexity of the requirements that should be addressed and satisfied during the design, implementation and operation. In this context, we introduce the MADTwin (Multi-Agent Digital Twin) framework driven by a Multi-agent Systems (MAS) paradigm and supported by flexible architecture and extendible upper ontology for modelling agent-based digital twins. A comprehensive case study of a smart warehouse supported by multi-robots has been presented to show the feasibility and applicability of this framework. The introduced framework powered by intelligent agents integrated with enabler technologies enabled us to cope with parts of the challenges imposed by modelling and integrating Cyber-Physical Systems (CPS) with digital twins for multi-robots of the smart warehouse. In this framework, different components of CPS (robots) are represented as autonomous physical agents with their digital twin agents in the digital twin environment. Agents act autonomously and cooperatively to achieve their local goals and the objectives of the whole system. Eventually, we discuss the framework’s strengths and identify areas of improvement and plans for future work.