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Interplay between [Formula: see text]-core and community structure in complex networks.

ABSTRACT: The organisation of a network in a maximal set of nodes having at least k neighbours within the set, known as [Formula: see text]-core decomposition, has been used for studying various phenomena. It has been shown that nodes in the innermost [Formula: see text]-shells play a crucial role in contagion processes, emergence of consensus, and resilience of the system. It is known that the [Formula: see text]-core decomposition of many empirical networks cannot be explained by the degree of each node alone, or equivalently, random graph models that preserve the degree of each node (i.e., configuration model). Here we study the [Formula: see text]-core decomposition of some empirical networks as well as that of some randomised counterparts, and examine the extent to which the [Formula: see text]-shell structure of the networks can be accounted for by the community structure. We find that preserving the community structure in the randomisation process is crucial for generating networks whose [Formula: see text]-core decomposition is close to the empirical one. We also highlight the existence, in some networks, of a concentration of the nodes in the innermost [Formula: see text]-shells into a small number of communities.

SUBMITTER: Malvestio I

PROVIDER: S-EPMC7477593 | biostudies-literature | 2020 Sep

REPOSITORIES: biostudies-literature

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Interplay between [Formula: see text]-core and community structure in complex networks.

Malvestio Irene I Cardillo Alessio A Masuda Naoki N

Scientific reports 20200907 1

The organisation of a network in a maximal set of nodes having at least k neighbours within the set, known as [Formula: see text]-core decomposition, has been used for studying various phenomena. It has been shown that nodes in the innermost [Formula: see text]-shells play a crucial role in contagion processes, emergence of consensus, and resilience of the system. It is known that the [Formula: see text]-core decomposition of many empirical networks cannot be explained by the degree of each node ...[more]

PMID: 32895432

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Project description:The experimental value for the isospin amplitude [Formula: see text] in [Formula: see text] decays has been successfully explained within the standard model (SM), both within the large [Formula: see text] approach to QCD and by QCD lattice calculations. On the other hand within the large [Formula: see text] approach the value of [Formula: see text] is by at least [Formula: see text] below the data. While this deficit could be the result of theoretical uncertainties in this approach and could be removed by future precise QCD lattice calculations, it cannot be excluded that the missing piece in [Formula: see text] comes from new physics (NP). We demonstrate that this deficit can be significantly softened by tree-level FCNC transitions mediated by a heavy colourless [Formula: see text] gauge boson with a flavour-violating left-handed coupling [Formula: see text] and an approximately universal flavour diagonal right-handed coupling [Formula: see text] to the quarks. The approximate flavour universality of the latter coupling assures negligible NP contributions to [Formula: see text]. This property, together with the breakdown of the GIM mechanisms at tree level, allows one to enhance significantly the contribution of the leading QCD-penguin operator [Formula: see text] to [Formula: see text]. A large fraction of the missing piece in the [Formula: see text] rule can be explained in this manner for [Formula: see text] in the reach of the LHC, while satisfying the constraints from [Formula: see text], [Formula: see text], [Formula: see text], LEP-II and the LHC. The presence of a small right-handed flavour-violating coupling [Formula: see text] and of enhanced matrix elements of [Formula: see text] left-right operators allows one to satisfy simultaneously the constraints from [Formula: see text] and [Formula: see text], although this requires some fine-tuning. We identify the quartic correlation between [Formula: see text] contributions to [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. The tests of this proposal will require much improved evaluations of [Formula: see text] and [Formula: see text] within the SM, of [Formula: see text] as well as precise tree-level determinations of [Formula: see text] and [Formula: see text]. We present correlations between [Formula: see text], [Formula: see text] and [Formula: see text] with and without the [Formula: see text] rule constraint and generalise the whole analysis to [Formula: see text] with colour ([Formula: see text]) and [Formula: see text] with FCNC couplings. In the latter case no improvement on [Formula: see text] can be achieved without destroying the agreement of the SM with the data on [Formula: see text]. Moreover, this scenario is very tightly constrained by [Formula: see text]. On the other hand, in the context of the [Formula: see text] rule [Formula: see text] is even more effective than [Formula: see text]: it provides the missing piece in [Formula: see text] for [Formula: see text]-[Formula: see text].

Project description:The Josephson effect in point contacts between an "ordinary" superconductor [Formula: see text]In[Formula: see text] ([Formula: see text]) and single crystals of the Fe-based superconductor Ba[Formula: see text]K[Formula: see text](FeAs)[Formula: see text] ([Formula: see text]), was investigated. In order to shed light on the order parameter symmetry of Ba[Formula: see text]K[Formula: see text](FeAs)[Formula: see text], the dependence of the Josephson supercurrent [Formula: see text] on the temperature and on [Formula: see text] with [Formula: see text] was studied. The dependencies of the critical current on temperature [Formula: see text] and of the amplitudes of the first current steps of the current-voltage characteristic [Formula: see text] [Formula: see text] on the power of microwave radiation with frequency [Formula: see text] were measured. It is shown that the dependencies [Formula: see text] are close to the well-known Ambegaokar-Baratoff (AB) dependence for tunnel contacts between "ordinary" superconductors and to the dependence calculated by Burmistrova et al. (Phys Rev B 91, 214501 (2015)) for microshorts between an "ordinary" superconductor and a two-band superconductor with [Formula: see text] order parameter symmetry at certain values of the transparency of boundaries and thickness of the transition layer. It is found that the dependencies [Formula: see text] cannot be approximated within the resistively shunted model using the normalized microwave frequencies [Formula: see text] with characteristic voltages [Formula: see text], [Formula: see text]-normal resistance of the contact) found from the low-voltage parts of the current-voltage characteristics. The reasons for this failure are discussed and a method is proposed for accurately determining the value of [Formula: see text], which takes into account all the features of the point contact affecting the period of the dependence [Formula: see text]. An analysis of the [Formula: see text] and [Formula: see text] dependencies shows that the superconducting current of the Josephson contacts under investigation is proportional to the [Formula: see text] of the phase difference [Formula: see text], [Formula: see text]. The implications of these results on the symmetry of the order parameter are also discussed.

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Interplay between [Formula: see text]-core and community structure in complex networks.

Publications

Interplay between [Formula: see text]-core and community structure in complex networks.

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