Related papers: Self-Organized Criticality from Protected Mean-Fie…
In an N-level quantum mechanical system, the problem of unitary feedback stabilization of mixed density operators to periodic orbits admits a natural Lyapunov-based time-varying feedback design. A global description of the domain of…
Organisms are equipped with regulatory systems that display a variety of dynamical behaviours ranging from simple stable steady states, to switching and multistability, to oscillations. Earlier work has shown that oscillations in protein…
Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power law form for power spectra of temporal fluctuations on all space-time…
Stimuli-responsive macromolecules display large conformational changes during their dynamics, sometimes switching states, and are an integral property for the development of soft functional materials. Here, we introduce a mean-field…
Self-organized network dynamics prevails for systems across physics, biology and engineering. How external signals generate distributed responses in networked systems fundamentally underlies their function, yet is far from fully understood.…
Restoring critical loads after extreme events demands adaptive control to maintain distribution-grid resilience, yet uncertainty in renewable generation, limited dispatchable resources, and nonlinear dynamics make effective restoration…
We develop a systematic extension of mode-coupling theory (MCT) that incorporates critical dynamical fluctuations. Starting from a microscopic diagrammatic theory, we identify dominant classes of divergent diagrams near the mode-coupling…
We present a compact dynamical mean-field theory (DMFT) for large networks of coupled phase oscillators whose phases live on the circle $S^1$ and interact with both coherent mean-field coupling and quenched randomness. Starting from wrapped…
The mean field (MF) theory of multilayer neural networks centers around a particular infinite-width scaling, where the learning dynamics is closely tracked by the MF limit. A random fluctuation around this infinite-width limit is expected…
We construct a stochastic dynamical systems theory in which sustainability is a structural boundary property of a fully coupled Earth--Human--Production system. Each subsystem is modelled as a vector-valued process governed by stochastic…
The brain criticality hypothesis has largely only characterized brain dynamics in terms of their self-similarity, although experimental evidence suggests that the brain exhibits significant multifractality. To understand how multifractality…
Atmospheric flows exhibit selfsimilar fluctuations on all scales(space-time) ranging from climate(kilometers/years) to turbulence(millimeters/seconds) manifested as fractal geometry to the global cloud cover pattern concomitant with inverse…
Self-organized criticality elucidates the conditions under which physical and biological systems tune themselves to the edge of a second-order phase transition, with scale invariance. Motivated by the empirical observation of bimodal…
The basic laws of physics are simple, so why is the world complex? The theory of self-organized criticality posits that complex behavior in nature emerges from the dynamics of extended, dissipative systems that evolve through a sequence of…
Most classical (non-spiking) neural network models disregard internal neuron dynamics and treat neurons as simple input integrators. However, biological neurons have an internal state governed by complex dynamics that plays a crucial role…
We study the Reflect-Reflect-Relax (RRR) algorithm in its small-step (flow-limit) regime. In the smooth transversal setting, we show that the transverse dynamics form a hyperbolic sink, yielding exponential decay of a natural gap measure.…
The process of renormalisation in nonperturbative Hamiltonian Effective Field Theory (HEFT) is examined in the $\Delta$-resonance scattering channel. As an extension of effective field theory incorporating the L\"uscher formalism, HEFT…
Recovering continuous-time dynamics from discrete observations is difficult because local supervision (e.g., pointwise regression targets, derivative approximations, or equation residuals) loses fidelity as the observation interval grows.…
We examine the dynamics of a compressible active nematic liquid crystal on a frictional substrate. When frictional damping dominates over viscous dissipation, we eliminate flow in favor of active stresses to obtain a minimal dynamical model…
Neural implicit functions have recently shown promising results on surface reconstructions from multiple views. However, current methods still suffer from excessive time complexity and poor robustness when reconstructing unbounded or…