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Many experimental results, both in-vivo and in-vitro, support the idea that the brain cortex operates near a critical point, and at the same time works as a reservoir of precise spatio-temporal patterns. However the mechanism at the basis…

We consider a one-dimensional vehicular network where the time headway (time difference between successive vehicles as they pass a point on the roadway) follows the shifted-exponential distribution. We show that neglecting the impact of…

In a range of scientific coauthorship networks, transitions emerge in degree distributions, correlations between degrees and local clustering coefficients, etc. The existence of those transitions could be regarded as a result of the…

Using molecular dynamics simulations, we investigate the crystallization pathways of two exemplary systems that form the same complex crystal structure but differ fundamentally in the nature of their particle interactions. One system is…

Despite the remarkable empirical performance of Transformers, their theoretical understanding remains elusive. Here, we consider a deep multi-head self-attention network, that is closely related to Transformers yet analytically tractable.…

Hysteresis in organic electrochemical transistors (OECT) is a basic effect in which the measured current depends on the voltage sweep direction and velocity. This phenomenon has an important impact on different aspects of the application of…

Subdiffusion on graphs is often modeled by time-fractional diffusion equations, yet its structural and dynamical consequences remain unclear. We show that subdiffusive transport on graphs is a memory-driven process generated by a random…

Phase diagrams and hysteresis loops were obtained by Monte Carlo simulations and a mean-field method for a simplified model of a spin-crossover material with a two-step transition between the high-spin and low-spin states. This model is a…

Reversible to irreversible (R-IR) transitions arise in numerous periodically driven collectively interacting systems that, after a certain number of driving cycles, organize into a reversible state where the particle trajectories repeat, or…

The study of diffusion in Hamiltonian systems has been a problem of interest for a number of years. In this paper we explore the influence of self-consistency on the diffusion properties of systems described by coupled symplectic maps.…

The explosion of data throughout the biomedical sciences provides unprecedented opportunities to learn about the dynamics of evolution and disease progression, but harnessing these large and diverse datasets remains challenging. Here, we…

First Order Reversal Curves (FORCs) have been used for a number of years for the extraction of information from magnetization measurements. The results are most unambiguous for irreversible processes -- for a collection of Preisach…

Many real-world interactions (e.g., researcher collaborations and email communication) occur among multiple entities. These group interactions are naturally modeled as hypergraphs. In graphs, transitivity is helpful to understand the…

Onset and loss of synchronization in coupled oscillators are of fundamental importance in understanding emergent behavior in natural and man-made systems, which range from neural networks to power grids. We report on experiments with…

Transformers face quadratic complexity and memory issues with long sequences, prompting the adoption of linear attention mechanisms using fixed-size hidden states. However, linear models often suffer from limited recall performance, leading…

The methods of the probability theory have been used in order to build up a new model of hysteresis. It turns out that the reversal points of the control parameter (e. g., the magnetic field) are Markov points which determine the stochastic…

We extend the notion of memristive systems to capacitive and inductive elements, namely capacitors and inductors whose properties depend on the state and history of the system. All these elements show pinched hysteretic loops in the two…

Like ants, some microorganisms are known to leave trails on surfaces to communicate. We explore how trail-mediated self-interaction could affect the behavior of individual microorganisms when diffusive spreading of the trail is negligible…

Memory is inherently entangled with prediction and planning. Flexible behavior in biological and artificial agents depends on the interplay of learning from the past and predicting the future in ever-changing environments. This chapter…

Spin-glass models of associative memories are a cornerstone between statistical physics and theoretical neuroscience. In these networks, stochastic spin-like units interact through a synaptic matrix shaped by local Hebbian learning. In…