Related papers: Renormalization Group Approach to Oscillator Synch…
A formalism based on the fermionic functional-renormalization-group approach to interacting electron models defined on a lattice is presented. One-loop flow equations for the coupling constants and susceptibilities in the particle-particle…
Networks of coupled nonlinear oscillators have been used to model circadian rhythms, flashing fireflies, Josephson junction arrays, high-voltage electric grids, and many other kinds of self-organizing systems. Recently, several authors have…
The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections…
An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…
The similarity renormalization group procedure formulated in terms of effective particles is briefly reviewed in a series of selected examples that range from the model matrix estimates of its numerical accuracy to issues of the Poincare…
Synchronization in networks of coupled oscillators is a widely studied topic with extensive scientific and engineering applications. In this paper, we study the frequency synchronization problem for networks of Kuramoto oscillators with…
We describe a new method to compute renormalized coupling constants in a Monte Carlo renormalization group calculation. The method can be used for a general class of models, e.g., lattice spin or gauge models. The basic idea is to simulate…
Synchronization in a lattice of a finite population of phase oscillators with algebraically decaying, non-normalized coupling is studied by numerical simulations. A critical level of decay is found, below which full locking takes place if…
Starting from the study of one-dimensional potentials in quantum mechanics having a small distance behavior described by a harmonic oscillator, we extend this way of analysis to models where such a behavior is not generally expected. In…
Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or…
It is argued that cluster methods provide a viable alternative to Wilson's momentum shell integration technique at the early stage of renormalization in the field-theoretic models with strongly coupled fields because these methods allow for…
We revisit optimization of functional renormalization group flows by analyzing regularized loop integrals. This leads us to a principle, the Principle of Strongest Singularity, and a corresponding order relation which allows to order…
A novel regime of synchronization, called remote synchronization, where the peripheral nodes form a phase synchronized cluster not including the hub, was recently observed in star motifs. We show the existence of a more general dynamical…
Local repulsive coupling tend to a desynchronize ensembles of globally coupled oscillators, but when the repulsive coupling is nonlocal, multi-cluster chimeras can result. In this case, several groups of synchronized oscillators (the…
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although…
The data preprocessing stage is crucial in clustering. Features may describe entities using different scales. To rectify this, one usually applies feature normalisation aiming at rescaling features so that none of them overpowers the others…
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…
Renormalization group calculations are used to give exact solutions for rigidity percolation on hierarchical lattices. Algebraic scaling transformations for a simple example in two dimensions produce a transition of second order, with an…
In the past decade, synchronization on complex networks has attracted increasing attentions from various research disciplines. Most previous works, however, focus only on the dynamic behaviors of synchronization process in the stable…
We use renormalization group to calculate the reunion and survival exponents of a set of random walkers interacting with a long range $1/r^2$ and a short range interaction. These exponents are used to study the binding-unbinding transition…