minimal spanning tree
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Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1211
Author(s):  
Peter Tsung-Wen Yen ◽  
Kelin Xia ◽  
Siew Ann Cheong

In econophysics, the achievements of information filtering methods over the past 20 years, such as the minimal spanning tree (MST) by Mantegna and the planar maximally filtered graph (PMFG) by Tumminello et al., should be celebrated. Here, we show how one can systematically improve upon this paradigm along two separate directions. First, we used topological data analysis (TDA) to extend the notions of nodes and links in networks to faces, tetrahedrons, or k-simplices in simplicial complexes. Second, we used the Ollivier-Ricci curvature (ORC) to acquire geometric information that cannot be provided by simple information filtering. In this sense, MSTs and PMFGs are but first steps to revealing the topological backbones of financial networks. This is something that TDA can elucidate more fully, following which the ORC can help us flesh out the geometry of financial networks. We applied these two approaches to a recent stock market crash in Taiwan and found that, beyond fusions and fissions, other non-fusion/fission processes such as cavitation, annihilation, rupture, healing, and puncture might also be important. We also successfully identified neck regions that emerged during the crash, based on their negative ORCs, and performed a case study on one such neck region.


Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1043 ◽  
Author(s):  
Stanisław Drożdż ◽  
Jarosław Kwapień ◽  
Paweł Oświęcimka ◽  
Tomasz Stanisz ◽  
Marcin Wątorek

Social systems are characterized by an enormous network of connections and factors that can influence the structure and dynamics of these systems. Among them the whole economical sphere of human activity seems to be the most interrelated and complex. All financial markets, including the youngest one, the cryptocurrency market, belong to this sphere. The complexity of the cryptocurrency market can be studied from different perspectives. First, the dynamics of the cryptocurrency exchange rates to other cryptocurrencies and fiat currencies can be studied and quantified by means of multifractal formalism. Second, coupling and decoupling of the cryptocurrencies and the conventional assets can be investigated with the advanced cross-correlation analyses based on fractal analysis. Third, an internal structure of the cryptocurrency market can also be a subject of analysis that exploits, for example, a network representation of the market. In this work, we approach the subject from all three perspectives based on data from a recent time interval between January 2019 and June 2020. This period includes the peculiar time of the Covid-19 pandemic; therefore, we pay particular attention to this event and investigate how strong its impact on the structure and dynamics of the market was. Besides, the studied data covers a few other significant events like double bull and bear phases in 2019. We show that, throughout the considered interval, the exchange rate returns were multifractal with intermittent signatures of bifractality that can be associated with the most volatile periods of the market dynamics like a bull market onset in April 2019 and the Covid-19 outburst in March 2020. The topology of a minimal spanning tree representation of the market also used to alter during these events from a distributed type without any dominant node to a highly centralized type with a dominating hub of USDT. However, the MST topology during the pandemic differs in some details from other volatile periods.


Bacteriology ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 8-13
Author(s):  
V.M. Sorokin ◽  
◽  
A.S. Vodop’janov ◽  
R.V. Pisanov ◽  
◽  
...  

For the first time INDEL-typing method of Helicobacter pylori strains is offered. Analysis of the nucleotide sequences of 69 strains from the local database was carried out. Ten INDEL-markers were identified, five of which, with the highest variability, served as the basis for the differentiation scheme. INDEL-typing of twenty one strains of H. pylori of different geographical origin was carried out. Аnd fifteen individual genotypes with a high diversity index were identified (DI = 0.95). For cluster analysis, the MST (minimal spanning tree) method was used, which demonstrated a clear distribution of clusters according to the geographical origin of the strains studied. In addition to the proposed method of typing, if necessary, the MLVAtyping method can be used. Keywords: Helicobacter pylori, PCR, INDEL, MST dendrogram, MLVA, geographical origin


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