Related papers: Hebbian plasticity rules abrupt desynchronization …
The gradual evolution of the restricted hierarchical three body problem is analyzed analytically, focusing on conditions of Kozai-Lidov Cycles that may lead to orbital flips from prograde to retrograde motion due to the octupole (third…
The Hubbard model provides a simple framework in which one can study how certain aspects of the electronic structure of strongly interacting systems can be tuned to optimize the superconducting pairing correlations and how these changes…
Adaptation plays a fundamental role in shaping the structure of a complex network and improving its functional fitting. Even when increasing the level of synchronization in a biological system is considered as the main driving force for…
We investigate the emergence of synchronization in the second-order Kuramoto model with adaptive simplicial interactions on a globally connected network. This inertial Kuramoto framework describes systems, where oscillator frequencies…
Lateral inhibition models coupled with Hebbian plasticity have been shown to learn factorised causal representations of input stimuli, for instance, oriented edges are learned from natural images. Currently, these models require the…
A fundamental aspect of learning in biological neural networks is the plasticity property which allows them to modify their configurations during their lifetime. Hebbian learning is a biologically plausible mechanism for modeling the…
The hidden geometry of simplicial complexes can influence the collective dynamics of nodes in different ways depending on the simplex-based interactions of various orders and competition between local and global structural features. We…
In terms of Dirac matrices the self-dual and anti-self-dual decomposition of a conformal supergravity is given and a self-dual conformal supergravity theory is developed as a connection dynamic theory in which the basic dynamic variabes…
We study the superconducting instabilities of singlet and triplet pairing in a two-dimensional Hubbard model on the basis of the third-order perturbation theory (TOPT). We investigate the effect of the vertex correction that is given by…
A class of adaptation functions is found for which a synchronous oscillation mode exists in the network of phase oscillators with triadic couplings. It is shown that the destruction of the synchronous mode occurs differently for networks…
From biology to social science, the functioning of a wide range of systems is the result of elementary interactions which involve more than two constituents, so that their description has unavoidably to go beyond simple…
We investigate a generalized Kuramoto phase-oscillator model with Hebb-like couplings that evolve according to a stochastic differential equation on various topologies. Numerical simulations show that even with identical oscillators, there…
In this paper, we study recurrent neural networks in the presence of pairwise learning rules. We are specifically interested in how the attractor landscapes of such networks become altered as a function of the strength and nature (Hebbian…
The aim of the present paper is to study the effects of Hebbian learning in random recurrent neural networks with biological connectivity, i.e. sparse connections and separate populations of excitatory and inhibitory neurons. We furthermore…
Adaptive network is a powerful presentation to describe different real-world phenomena. However, current models often neglect higher-order interactions (beyond pairwise interactions) and diverse adaptation types (cooperative and…
The phase diagram of the Hubbard model is studied at weak coupling in two and three spatial dimensions. It is shown that the Neel temperature and the order parameter in d=3 are smaller than the Hartree-Fock predictions by a factor of…
Recent studies of dynamic properties in complex systems point out the profound impact of hidden geometry features known as simplicial complexes, which enable geometrically conditioned many-body interactions. Studies of collective behaviours…
Sought-after ordered structures of mixtures of hard anisotropic nanoparticles can often be thermodynamically unfavorable due to the components' geometric incompatibility to densely pack into regular lattices. A simple compatibilization rule…
Adaptive dynamical networks appear in various real-word systems. One of the simplest phenomenological models for investigating basic properties of adaptive networks is the system of coupled phase oscillators with adaptive couplings. In this…
We demonstrate how some problems arising in simplicial quantum gravity can be successfully addressed within the framework of combinatorial group theory. In particular, we argue that the number of simplicial 3-manifolds having a fixed…