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In this paper, we pose a hypothesis that the structure of communities in complex networks may result from their latent fractal properties. This hypothesis is based not only on the general observation that many real networks have multilevel…
We study the convergence of certain subseries of the harmonic series corresponding to increasing sequences of integers whose digits in a certain base are not uniformly distributed. We also discuss the case of irregular sequences, where the…
The problem of reconstructing a sequence of independent and identically distributed symbols from a set of equal size, consecutive, fragments, as well as a dependent reference sequence, is considered. First, in the regime in which the…
The presence of large-scale real-world networks with various architectures has motivated an active research towards a unified understanding of diverse topologies of networks. Such studies have revealed that many networks with the scale-free…
Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in…
This paper contains the proofs of Theorems 2 and 3 of the article entitled Random Electrical Networks on Complete Graphs, written by the same authors and published in the Journal of the London Mathematical Society, vol. 30 (1984), pp.…
In this paper we continue our investigation of the analogical neural network, paying interest to its replica symmetric behavior in the absence of external fields of any type. Bridging the neural network to a bipartite spin-glass, we…
In this work, we study the fractal and multifractal properties of a family of fractal networks introduced by Gallos {\it et al.} ({\it Proc. Natl. Acad. Sci. U.S.A.}, 2007, {\bf 104}: 7746). In this fractal network model, there is a…
We perfect the recursion-transform method to be a complete theory, which can derive the general exact resistance between any two nodes in a resistor network with several arbitrary boundaries. As application of the method, we give a profound…
Recurrently coupled oscillators that are sufficiently heterogeneous and/or randomly coupled can show an asynchronous activity in which there are no significant correlations among the units of the network. The asynchronous state can…
Despite numerous studies, the relationship between network structure and fracture remains unclear. In this study, the fracture properties of end-linking networks were compared with those of loop-free analogs made from star prepolymers by…
The fractal necklaces in R^d (d>1) introduced in this paper are a class of connected fractal sets generated by the so-called necklace IFSs, for which a lot of basic topology questions are interesting. We give two subclasses of fractal…
It is well known that Pascal's triangle exhibits fractal behavior when reduced modulo a prime. We show that the triangle of Fibonomial coefficients has a similar nature modulo two. Specifically, for any $m \ge 0$, the subtriangle consisting…
This paper expands on the previously described reflectionless filters - that is, filters having, in principle, identically-zero reflection coefficient at all frequencies - by introducing a wide variety of new reflectionless structures that…
Real world networks have, for a long time, been modelled by scale-free networks, which have many sparsely connected nodes and a few highly connected ones (the hubs). However, both in society and in biology, a new structure must be…
Complex networks from such different fields as biology, technology or sociology share similar organization principles. The possibility of a unique growth mechanism promises to uncover universal origins of collective behaviour. In…
Fibonacci cubes are induced subgraphs of hypercube graphs obtained by restricting the vertex set to those binary strings which do not contain consecutive 1s. This class of graphs has been studied extensively and generalized in many…
We study the reliability of large networks of coupled neural oscillators in response to fluctuating stimuli. Reliability means that a stimulus elicits essentially identical responses upon repeated presentations. We view the problem on two…
Power grid networks, as well as neuronal networks with synaptic plasticity, describe real-world systems of tremendous importance for our daily life. The investigation of these seemingly unrelated types of dynamical networks has attracted…
In this article, we take a closer look at the reliability of large minimal networks constructed by repeated compositions of the simplest possible networks. For a given number of devices $n=2^m$ we define the set of all the possible…