基于TOPSIS模型的机场网络节点重要度评估

在机场网络中单个机场节点的失效往往会对其他的节点产生影响,特别是关键节点的失效会波及整个网络.准确客观的识别重要节点机场关乎整个机场网络的安全运营.本文分析了机场网络拓扑特性中的度、集聚系数和接近度指标,考虑了机场旅客吞吐量和所在城市人口等交通经济特性指标,使用熵权法确定权重的基础上,应用TOPSIS法构建综合评价体系模型,最后以华东地区机场网络为例进行节点重要度排序.结果表明与单一指标的评估结果相比,该方法更加全面客观的确定不同属性指标的权重,避免了不同指标取值的差异性,使评价更加全面,更符合机场网络实际运营情况.     

Finite groups with a given number of relative centralizers

We will study all finite groups and their subgroups with at most four relative centralizers.     

浙江省旅游用海质量时空变化特征分析

考虑海洋旅游发展程度、区域经济社会发展水平以及海域环境条件等因素，构建旅游用海质量评价指标体系，依据官方渠道采集的统计数据，采用信息熵模型量化指标权重，根据TOPSIS法原理对沿海县（市、区）旅游海域质量进行排序并应用系统聚类法划分海域等级。结果表明：（1）人均海洋旅游总产值、海洋生物多样性指数以及海水质量指数3个评价因子对旅游用海质量影响显著，海水质量指数有反向影响。（2）2007―2016年，浙江省沿海18个县（市、区）旅游用海等级变动较大，“北强南弱”特征明显。（3）比较2007年标准，第二、三、四等级县（市、区）数量有较大幅度增加，五、六等级县（市、区）数量明显减少，旅游海域质量等级整体提高，等级数量变化与沿海县（市、区）海洋旅游发展态势和海洋生态环境变动相吻合。     

Some extensions of the operator entropy type inequalities

In this paper, we define the generalised relative operator entropy and investigate some of its properties such as subadditivity and homogeneity. As application of our result, we obtain the information inequality. In continuation, we establish some reverses of the operator entropy inequalities under certain conditions by using the Mond–Pe?ari? method.     

The Role of Information in Managing Interactions from a Multifractal Perspective

In the framework of the multifractal hydrodynamic model, the correlations informational entropy–cross-entropy manages attractive and repulsive interactions through a multifractal specific potential. The classical dynamics associated with them imply Hubble-type effects, Galilei-type effects, and dependences of interaction constants with multifractal degrees at various scale resolutions, while the insertion of the relativistic amendments in the same dynamics imply multifractal transformations of a generalized Lorentz-type, multifractal metrics invariant to these transformations, and an estimation of the dimension of the multifractal Universe. In such a context, some correspondences with standard cosmologies are analyzed. Since the same types of interactions can also be obtained as harmonics mapping between the usual space and the hyperbolic plane, two measures with uniform and non-uniform temporal flows become functional, temporal measures analogous with Milne’s temporal measures in a more general manner. This work furthers the analysis published recently by our group in “Towards Interactions through Information in a Multifractal Paradigm”.     

Revisiting the structural and electronic properties of neutral,mono- and di-anionic titanium-doped silicon clusters TiSin0/−/2− (n = 6-16)

The systematic structures search for neutral and Zintl anionic Ti-doped silicon clusters TiSi_n^0/−/2− (n = 6-16) have been carried out using the ABCluster global search technique combined with a double-hybrid density functional method. Based on the predicted energies, adiabatic electron affinities, vertical detachment energies and the consistency between simulated and experimental photoelectron spectroscopy, the true global minimum structures are confirmed. The results show that structural growth pattern of neutral TiSi_n clusters is from linked structures (n = 10-12) to encapsulated configurations (n = 13-16). In contrast, the evolution pattern of Zintl anionic TiSi_n^−/2− clusters begins with the pentagonal bipyramid structure (n = 6). As the Si atoms increase, these Si atoms attach to the surface adjacent to Ti atom, and gradually surround Ti atom. Eventually, the encapsulated structure is formed when n = 12. Moreover, two extra electrons not only perfect the structure of TiSi₁₂ but also improve its chemical and thermodynamic stability.     

Compressibility of random walker trajectories on growing networks

We find that the simple coupling of network growth to the position of a random walker on the network generates a traveling wave in the probability distribution of nodes visited by the walker. We argue that the entropy of this probability distribution is bounded as the network size tends to infinity. This means that the growth of a space coupled to a random walker situated in it constrains its dynamics to a set of typical random walker trajectories, and walker trajectories inside the growing space are compressible.     

On Entropic Uncertainty Relations for Measurements of Energy and Its “Complement”

Heisenberg's uncertainty principle in application to energy and time is a powerful heuristics. This statement plays an important role in foundations of quantum theory and statistical physics. If some state exists for a finite interval of time, then it cannot have a completely definite value of energy. It is well known that the case of energy and time principally differs from more familiar examples of two non‐commuting observables. Since quantum theory was originated, many approaches to energy–time uncertainties have been proposed. Entropic way to formulate the uncertainty principle is currently the subject of active researches. Using the Pegg concept of complementarity of the Hamiltonian, uncertainty relations of the “energy–time” type are obtained in terms of Rényi and Tsallis entropies. Although this concept is somehow restricted in scope, derived relations can be applied to systems typically used in quantum information processing. Both the state‐dependent and state‐independent formulations are of interest. Some of the derived state‐independent bounds are similar to the results obtained within a more general approach on the basis of sandwiched relative entropies. The developed method allows us to address the case of detection inefficiencies.     

Order-Stability in Complex Biological,Social, and AI-Systems from Quantum Information Theory

This paper is our attempt, on the basis of physical theory, to bring more clarification on the question “What is life?” formulated in the well-known book of Schrödinger in 1944. According to Schrödinger, the main distinguishing feature of a biosystem’s functioning is the ability to preserve its order structure or, in mathematical terms, to prevent increasing of entropy. However, Schrödinger’s analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schrödinger also appealed to the ambiguous notion of negative entropy. We apply quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of classical entropy. We consider a complex biosystem S composed of many subsystems, say proteins, cells, or neural networks in the brain, that is, S=(Si). We study the following problem: whether the compound system S can maintain “global order” in the situation of an increase of local disorder and if S can preserve the low entropy while other Si increase their entropies (may be essentially). We show that the entropy of a system as a whole can be constant, while the entropies of its parts rising. For classical systems, this is impossible, because the entropy of S cannot be less than the entropy of its subsystem Si. And if a subsystems’s entropy increases, then a system’s entropy should also increase, by at least the same amount. However, within the quantum information theory, the answer is positive. The significant role is played by the entanglement of a subsystems’ states. In the absence of entanglement, the increasing of local disorder implies an increasing disorder in the compound system S (as in the classical regime). In this note, we proceed within a quantum-like approach to mathematical modeling of information processing by biosystems—respecting the quantum laws need not be based on genuine quantum physical processes in biosystems. Recently, such modeling found numerous applications in molecular biology, genetics, evolution theory, cognition, psychology and decision making. The quantum-like model of order stability can be applied not only in biology, but also in social science and artificial intelligence.