Пространство мифа: о возможности топологического анализа мифологического мышления (часть 2)
The paper is devoted to the concept of mythological thinking and its special characteristic – mythological space. The category of space is considered as ontological and stated in mythological history and order. We introduce the topological method as a method for studying the mythological space, partly borrowed from the branch of mathematics – topology, partly drawn from the experience within the scholarship. The paper provides the essential features of mythological thinking.
A new type of massless Dirac fermions in crystalline three_dimensional topological insulators (three_dimen_sional two_dimensional situation) has been predicted. The spectrum has fourfold degeneracy at the top of the two_dimensional Brillouin zone (M point) and twofold degeneracy near the M point. Crystal symmetry along with the time reversal invariance in three_dimensional topological insulators allows fourfold degenerate Dirac cones, which are absent in the classification of topological features in R._J. Slager et al., Nat. Phys. 9, 98 (2013). The Hamiltonian in the cited work does not contain Dirac singularities with more than twofold degeneracy. For this reason, the corresponding topological classification is incomplete. The longitudinal magnetic field in the spinless case holds the massless dispersion law of fermions and does not lift fourfold degeneracy. In the spinor case, the magnetic field lifts fourfold degeneracy, holding only twofold degeneracy, and results in the appearance of a band gap in the spectrum of fermions.
Recently much attention has been devoted to the optimization of transportation networks in a given geographic area. One assumes the distributions of population and of services/workplaces (i.e. the network's sources and sinks) are known, as well as the costs of movement with/without the network, and the cost of constructing/maintaining it. Both the long-term optimization and the short-term, "who goes where" optimization are considered. These models can also be adapted for the optimization of other types of networks, such as telecommunications, pipeline or drainage networks. In the monograph we study the most general problem settings, namely, when neither the shape nor even the topology of the network to be constructed is known a priori.
The paper presents the implementation of a dynamic routing algorithm intended for use in networks-on-chip with a circulant topology with three generatrices of type C(N; s1, s2, s3) for finding the shortest routes between any two network nodes. The algorithm can be implemented as a RTL state machine in routers for NoCs. The proposed algorithm was tested on sets of optimal circulants. Compared with the classical algorithms A* or Dijkstra, the proposed algorithm does not require to calculate the entire path of the packet, but calculates the port number to which the packet should be sent so that it can reach the destination node. This makes it possible to significantly simplify the structure of the NoC router.
The problem from the area of Personology of Self, being the most important part of general personology, is studied in this paper. The paper offers the model of basic features and abilities of Self. The role of ability of Self to be its own ability, the ability which integrates many intentions of “I can” type depending on life tasks faced by the personality, is stressed. Existential value of the task to be effective in dialog based on the intention “I express myself” is substantiated. The model of narration, the model of author’s reflection in the moment of narration and three-dimensional topological model of ability of Self to express itself in the dialog are offered.
We propose a model that evaluates how much a network has changed over time in terms of its structure and a set of central elements. The difference of structure is evaluated in terms of node-to-node influence using known nodes correspondence models. To analyze the changes in nodes centralities we adapt an idea of interval orders to the network theory. Our approach can be used to investigate dynamic changes in temporal networks and to identify suspicious or abnormal effects in terms of the topology and its critical members. We can also transform the stability measure to the similarity measure in order to cluster the network in some homogeneous periods. To test our model, we consider the international migration network from 1970 to 2015 and attempt to analyze main changes in migration patterns.