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Frustrated systems are ubiquitous and interesting because their behavior is difficult to predict. Magnetism offers extreme examples in the form of spin lattices where all interactions between spins cannot be simultaneously satisfied. Such…
We study the non-equilibrium dynamics of a disordered quantum system consisting of harmonic oscillators in a $d$-dimensional lattice. If the system is sufficiently localized, we show that, starting from a broad class of initial product…
The intricate interplay between charge motion and magnetic order in geometrically frustrated lattices is central for the properties of many two-dimensional quantum materials. The triangular lattice antiferromagnet is a canonical example of…
Understanding thermal fluctuations yields insights into a wide range of behaviors in many-body systems. In this work, we analyze the dynamical adaptation of two-dimensional crystalline lattice system under harmonic interaction in response…
Specific activator and repressor transcription factors which bind to specific regulator DNA sequences, play an important role in gene activity control. Interactions between genes coding such transcription factors should explain the…
The problem of finding the minimum-energy configuration of particles on a lattice, subject to a generic short-ranged repulsive interaction, is studied analytically. The study is relevant to charge ordered states of interacting fermions, as…
A lattice walk model is said to be reluctant if the defining step set has a strong drift towards the boundaries. We describe efficient random generation strategies for these walks.
Many biological systems can sense periodical variations in a stimulus input and produce well-timed, anticipatory responses after the input is removed. Such systems show memory effects for retaining timing information in the stimulus and…
Conversational AI systems require guardrails to prevent harmful outputs, yet existing approaches use static rules that cannot adapt to new threats or deployment contexts. We introduce Lattice, a framework for self-constructing and…
Frustration is a ubiquitous phenomenon in many-body physics that influences the nature of the system in a profound way with exotic emergent behavior. Despite its long research history, the analytical or numerical investigations on…
It is known that the stability of a feedback interconnection of two linear time-invariant systems implies that the graphs of the open-loop systems are quadratically separated. This separation is defined by an object known as the multiplier.…
In a recent paper, we presented an intelligent evolutionary search technique through genetic programming (GP) for finding new analytical expressions of nonlinear dynamical systems, similar to the classical Lorenz attractor's which also…
Lattice models of coupled dynamical systems lead to a variety of complex behaviors. Between the individual motion of independent units and the collective behavior of members of a population evolving synchronously, there exist more…
Regulation of gene expression is the consequence of interactions between the promoter of the gene and the transcription factors (TFs). In this paper, we explore the features of a genetic network where the TFs (activators and repressors)…
Quenched disorder effects on frustrated systems are explored by considering random fluctuations on the antiferromagnetic (AF) interactions between spins on the checkerboard lattice. The replica framework is adopted within a cluster…
We propose a general strategy for feedback control design of complex dynamical systems exploiting the nonlinear mechanisms in a systematic unsupervised manner. These dynamical systems can have a state space of arbitrary dimension with…
A spin-1/2 chain model that includes three spin interactions can effectively describe the dynamics of two species of bosons trapped in an optical lattice with a triangular-ladder configuration. A perturbative theoretical approach and…
Geometric frustration arises when lattice structure prevents simultaneous minimization of local interactions. It leads to highly degenerate ground states and, subsequently, complex phases of matter such as water ice, spin ice and frustrated…
Inhibitory circuits of relaxation oscillators are often-used models for the dynamics of biological networks. We present a qualitative and quantitative stability analysis of such a circuit constituted by three reciprocally coupled…
The antiferromagnetic Ising model on a triangular lattice (AFIT) exemplifies the most classical frustration system, arising from its triangular geometry that prevents all interactions from being simultaneously satisfied. Understanding…