相关论文: Period-two cycles in a feed-forward layered neural…

Distinguished from the system with one order parameter, systems described by two or more order parameters will manifest more complex and much richer phase diagram and critical phenomena. In systems of two order parameters, the phase…

Focusing on a two-field Swift-Hohenberg model with linear nonreciprocal interactions, this study investigates how emerging higher-codimension points act as organizing centers for the nonequilibrium phase diagram that features various steady…

The nonlinear response of an adsorbed layer on a periodic substrate to an external force is studied via a two dimensional uniaxial Frenkel-Kontorova model. The nonequlibrium properties of the model are simulated by Brownian molecular…

Priming is the ability of the brain to more quickly activate a target concept in response to a related stimulus (prime). Experiments point to the existence of an overlap between the populations of the neurons coding for different stimuli.…

Persistent currents flowing through disordered mesoscopic rings threaded by a magnetic flux are investigated. Models of fermions with on-site interactions (Hubbard model) or models of spinless fermions with nearest neighbor interactions are…

We study the dissipative dynamics of a one-dimensional bosonic system described in terms of the bipartite Bose-Hubbard model with alternating gain and loss. This model exhibits the $\mathcal{PT}$ symmetry under some specific conditions and…

Feed-forward layers constitute two-thirds of a transformer model's parameters, yet their role in the network remains under-explored. We show that feed-forward layers in transformer-based language models operate as key-value memories, where…

We consider heteroclinic attractor networks motivated by models of competition between neural populations during binocular rivalry. We show that Gamma distributions of dominance times observed experimentally in binocular rivalry and other…

Quantum interactions exchanging different types of particles play a pivotal r\^{o}le in quantum many-body theory, but they are not sufficiently investigated from a mathematical perspective. Here, we consider a system made of two fermions…

We study the one- and two- dimensional extended Hubbard model by means of the Composite Operator Method within the 2-pole approximation. The fermionic propagator is computed fully self-consistently as a function of temperature, filling and…

Studies have been made on the phase transition phenomena of an oscillator network model based on a standard Hebb learning rule like the Hopfield model. The relative phase informations---the in-phase and anti-phase, can be embedded in the…

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…

Phase-transition phenomena in deep learning (grokking, emergent capabilities, and ontological reorganization under context shift) have been studied through several lenses, including representational compression, singular learning theory,…

Cold atom experiments can now realize mixtures where different components move in different spatial dimensions. We investigate a fermion mixture where one species is constrained to move along a one-dimensional lattice embedded in a…

We study the phase behavior of a symmetric binary polymer blend which is confined into a thin film. The film surfaces interact with the monomers via short range potentials. We calculate the phase behavior within the self-consistent field…

Phase separation in complex systems is a ubiquitous phenomenon. While simple theories predict coarsening until only macroscopically large phases remain, concrete models often exhibit patterns with finite length scales. To unify such models,…

We study the microscopic dynamics of competing ordered phases in a two-dimensional correlated electron model, which is driven with a pulsed electric field of finite duration. In order to go beyond a mean-field treatment of the electronic…

Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…

This paper is concerned with the modeling and analysis of two of the most commonly used recurrent neural network models (i.e., Hopfield neural network and firing-rate neural network) with dynamic recurrent connections undergoing Hebbian…

We investigate the quantum phases of bosons in a two-chain-coupled ladder. This bosonic ladder is generally in a biased configuration, meaning that the two chains of the ladder can have dramatically different on-site interactions and…