Canonical horizontal visibility graphs are uniquely determined by their degree sequence

Horizontal visibility graphs (HVGs) are graphs constructed in correspondence with number sequences that have been introduced and explored recently in the context of graph-theoretical time series analysis. In most of the cases simple measures based on the degree sequence (or functionals of these such as entropies over degree and joint degree distributions) appear to be highly informative features for automatic classification and provide nontrivial information on the associated dynam- ical process, working even better than more sophisticated topological metrics. It is thus an open question why these seemingly simple measures capture so much information. Here we prove that, under suitable conditions, there exist a bijection between the adjacency matrix of an HVG and its degree sequence, and we give an explicit construction of such bijection. As a consequence, under these conditions HVGs are unigraphs and the degree sequence fully encapsulates all the information of these graphs, thereby giving a plausible reason for its apparently unreasonable effectiveness

A combinatorial framework to quantify peak/pit asymmetries in complex dynamics

LL’s acknowledges funding from an EPSRC Early Career Fellowship EP/P01660X/1

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Genetic Variation of European Beech Populations and Their Progeny from Northeast Germany to Southwest Switzerland

Climate change can adversely affect the growth of European beech (Fagus sylvatica L.) across its entire distribution range. Therefore, knowledge of the adaptive potential of this species to changing climatic conditions is of foremost importance. Genetic diversity is the basis for adaptation to environmental stress, and the regeneration phase of forests is a key stage affecting genetic diversity. Nevertheless, little is known about the effect of climate change on the genetic diversity of adult trees compared to their progeny. Here, we present genetic diversity data for 24 beech populations ranging from northeast Germany to southwest Switzerland. Potentially adaptive genetic variation was studied using single nucleotide polymorphism (SNP) markers in candidate genes that are possibly involved in adaptive trait variation. In addition, more than 2000 adult trees and 3000 of their seedlings were genotyped with simple sequence repeat (SSR) markers to determine selectively neutral genetic diversity and differentiation among populations. All populations showed high SSR and SNP variation, and no differences in genetic diversity were found between adult trees and their offspring. The genetic differentiation between adults and seedlings within the same stands was also insignificant or very low. Therefore, we can conclude tentatively that the transfer of genetic variation among tree generations, currently, is not much affected by climate change, at least in the studied beech populations

Genetic Variation of European Beech Populations and Their Progeny from Northeast Germany to Southwest Switzerland

Текст статьи не публикуется в открытом доступе в соответствии с политикой журнала.Climate change can adversely affect the growth of European beech (Fagus sylvatica L.) across its entire distribution range. Therefore, knowledge of the adaptive potential of this species to changing climatic conditions is of foremost importance. Genetic diversity is the basis for adaptation to environmental stress, and the regeneration phase of forests is a key stage affecting genetic diversity. Nevertheless, little is known about the effect of climate change on the genetic diversity of adult trees compared to their progeny. Here, we present genetic diversity data for 24 beech populations ranging from northeast Germany to southwest Switzerland. Potentially adaptive genetic variation was studied using single nucleotide polymorphism (SNP) markers in candidate genes that are possibly involved in adaptive trait variation. In addition, more than 2000 adult trees and 3000 of their seedlings were genotyped with simple sequence repeat (SSR) markers to determine selectively neutral genetic diversity and differentiation among populations. All populations showed high SSR and SNP variation, and no differences in genetic diversity were found between adult trees and their offspring. The genetic differentiation between adults and seedlings within the same stands was also insignificant or very low. Therefore, we can conclude tentatively that the transfer of genetic variation among tree generations, currently, is not much affected by climate change, at least in the studied beech populations