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Jet substructure observables are crucial for exploring the effects of the hot, dense medium and differentiating between quark and gluon jets. In this paper, we investigate the modification of jet shape by calculating the differential girth at LHC energies, ranging from pp to Pb--Pb collisions. The differential girth distribution exhibits a wave-like pattern, which offers a better explanation for the radial spreading of jet energy and large-angle radiation effects. We fit the differential girth distribution with a sine wave function to obtain the amplitude, angular frequency, initial phase, and offset distance parameters as a function of jet radius. The results clearly differentiate between pp and heavy-ion collisions, with varying dependencies on centrality and collision energy. Our findings shed new light on the understanding of radial jet energy loss in the QGP (quark-gluon plasma) medium, and provide additional potential observables for measuring jet shape at the LHC in the future., Comment: 7 pages, 6 figures

The observed architecture of ecological and socio-economic networks differs significantly from that of random networks. From a network science standpoint, non-random structural patterns observed in real networks call for an explanation of their emergence and an understanding of their potential systemic consequences. This article focuses on one of these patterns: nestedness. Given a network of interacting nodes, nestedness can be described as the tendency for nodes to interact with subsets of the interaction partners of better-connected nodes. Known since more than $80$ years in biogeography, nestedness has been found in systems as diverse as ecological mutualistic organizations, world trade, inter-organizational relations, among many others. This review article focuses on three main pillars: the existing methodologies to observe nestedness in networks; the main theoretical mechanisms conceived to explain the emergence of nestedness in ecological and socio-economic networks; the implications of a nested topology of interactions for the stability and feasibility of a given interacting system. We survey results from variegated disciplines, including statistical physics, graph theory, ecology, and theoretical economics. Nestedness was found to emerge both in bipartite networks and, more recently, in unipartite ones; this review is the first comprehensive attempt to unify both streams of studies, usually disconnected from each other. We believe that the truly interdisciplinary endeavour -- while rooted in a complex systems perspective -- may inspire new models and algorithms whose realm of application will undoubtedly transcend disciplinary boundaries., Comment: In press. 140 pages, 34 figures

Complex networks are often used to represent systems that are not static but grow with time: people make new friendships, new papers are published and refer to the existing ones, and so forth. To assess the statistical significance of measurements made on such networks, we propose a randomization methodology---a time-respecting null model---that preserves both the network's degree sequence and the time evolution of individual nodes' degree values. By preserving the temporal linking patterns of the analyzed system, the proposed model is able to factor out the effect of the system's temporal patterns on its structure. We apply the model to the citation network of Physical Review scholarly papers and the citation network of US movies. The model reveals that the two datasets are strikingly different with respect to their degree-degree correlations, and we discuss the important implications of this finding on the information provided by paradigmatic node centrality metrics such as indegree and Google's PageRank. The randomization methodology proposed here can be used to assess the significance of any structural property in growing networks, which could bring new insights into the problems where null models play a critical role, such as the detection of communities and network motifs., Comment: 13 pages, 10 figures

Identifying the node spreading influence in networks is an important task to optimally use the network structure and ensure the more efficient spreading in information. In this paper, by taking into account the shortest distance between a target node and the node set with the highest $k$-core value, we present an improved method to generate the ranking list to evaluate the node spreading influence. Comparing with the epidemic process results for four real networks and the Barab\'{a}si-Albert network, the parameterless method could identify the node spreading influence more accurately than the ones generated by the degree $k$, closeness centrality, $k$-shell and mixed degree decomposition methods. This work would be helpful for deeply understanding the node importance of a network., Comment: 6 pages, 3 figures