Related papers: Renormalization of Complex Networks with Partition…
Deterministic reaction networks (RNs) are tools to model diverse biological phenomena characterized by particle systems, when there are abundant number of particles. Examples include but are not limited to biochemistry, molecular biology,…
Information spreads across social and technological networks, but often the network structures are hidden from us and we only observe the traces left by the diffusion processes, called cascades. Can we recover the hidden network structures…
Functional complex networks have meant a pivotal change in the way we understand complex systems, being the most outstanding one the human brain. These networks have classically been reconstructed using a frequentist approach that, while…
We introduce a new technique for gradient normalization during neural network training. The gradients are rescaled during the backward pass using normalization layers introduced at certain points within the network architecture. These…
We propose a modularization method that decomposes a deep neural network (DNN) into small modules from a functionality perspective and recomposes them into a new model for some other task. Decomposed modules are expected to have the…
The common real-world feature of individuals migrating through a network -- either in real space or online -- significantly complicates understanding of network processes. Here we show that even though a network may appear static on…
Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the…
Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…
In this paper we define a new class of weighted complex networks sharing several properties with fractal sets, and whose topology can be completely analytically characterized in terms of the involved parameters and of the fractal dimension.…
We report on parallel observations in two seemingly unrelated areas of dynamical network research. The one is the so-called small world phenomenon and/or the observation of scale freeness in certain types of large (empirical) networks and…
The possible usefulness of the renormalization group method in Nuclear Physics is pointed out in this talk in the context of the nuclear multifragmentation. The presentation is rather superficial and sketchy, to indicate the main lines…
Satisfiability is a classic problem in computational complexity theory, in which one wishes to determine whether an assignment of values to a collection of Boolean variables exists in which all of a collection of clauses composed of logical…
Some recent results showed that renormalization group can be considered as a promising framework to address open issues in data analysis. In this work, we focus on one of these aspects, closely related to principal component analysis for…
Normalizing flows have emerged as an important family of deep neural networks for modelling complex probability distributions. In this note, we revisit their coupling and autoregressive transformation layers as probabilistic graphical…
We analyze a semi-infinite one-dimensional random walk process with a biased motion that is incremental in one direction and long-range in the other. On a network with a fixed hierarchy of long-range jumps, we find with exact…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
It has been recognized that many complex dynamical systems in the real world require a description in terms of multiplex networks, where a set of common, mutually connected nodes belong to distinct network layers and play a different role…
In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant…
There is a pressing need for a description of complex systems that includes considerations of the underlying network of interactions, for a diverse range of biological, technological and other networks. In this work relationships between…
We introduce models of generic rigidity percolation in two dimensions on hierarchical networks, and solve them exactly by means of a renormalization transformation. We then study how the possibility for the network to self organize in order…